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Hidden symmetries, spin and charge of artificial magnetic monopoles
Authors:
Alexander I Nesterov,
Gennady P Berman
Abstract:
We discuss the non-Abelian artificial magnetic monopoles associated with $n$-level energy crossing in quantum systems. We found that hidden symmetries reveal themselves as observables such as spin, charge, and other physical degrees of freedom. We illustrated our results on concrete examples of two and three energy-level crossing. Our results can be useful for modeling of various phenomena in phys…
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We discuss the non-Abelian artificial magnetic monopoles associated with $n$-level energy crossing in quantum systems. We found that hidden symmetries reveal themselves as observables such as spin, charge, and other physical degrees of freedom. We illustrated our results on concrete examples of two and three energy-level crossing. Our results can be useful for modeling of various phenomena in physical and biological systems.
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Submitted 14 April, 2021;
originally announced April 2021.
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In Response to COVID-19: Configuration Model of the Epidemic Spreading
Authors:
Alexander I Nesterov,
Pablo Héctor Mata Villafuerte,
Gennady P Berman
Abstract:
A configuration model for epidemic spread, based on a scale-free network, is introduced. We obtain the analytical solutions describing both unstable and stable dynamics of the epidemic spreading, and demonstrate how these regimes can interchange during the epidemic. We apply the model to the COVID-19 case and demonstrate the predictive features of our model.
A configuration model for epidemic spread, based on a scale-free network, is introduced. We obtain the analytical solutions describing both unstable and stable dynamics of the epidemic spreading, and demonstrate how these regimes can interchange during the epidemic. We apply the model to the COVID-19 case and demonstrate the predictive features of our model.
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Submitted 8 July, 2020;
originally announced July 2020.
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Noise-Assisted Quantum Exciton and Electron Transfer in Bio-Complexes with Finite Donor and Acceptor Bandwidths
Authors:
Alexander I. Nesterov,
Gennady P. Berman,
Marco Merkli,
Avadh Saxena
Abstract:
We present an analytic and numerical study of noise-assisted quantum exciton (electron) transfer (ET) in a bio-complex, consisting of an electron donor and acceptor (a dimer), modeled by interacting continuous electron bands of finite widths. The interaction with the protein-solvent environment is modeled by a stationary stochastic process (noise) acting on all the donor and acceptor energy levels…
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We present an analytic and numerical study of noise-assisted quantum exciton (electron) transfer (ET) in a bio-complex, consisting of an electron donor and acceptor (a dimer), modeled by interacting continuous electron bands of finite widths. The interaction with the protein-solvent environment is modeled by a stationary stochastic process (noise) acting on all the donor and acceptor energy levels. We start with discrete energy levels for both bands. Then, by using a continuous {limit} for the electron spectra, we derive integro-differential equations for ET dynamics between two bands. Finally, we derive from these equations rate-type differential equations for ET dynamics. We formulate the conditions of validity of the rate-type equations. We consider different regions of parameters characterizing the widths of the donor and acceptor bands and the strength of the dimer-noise interaction. For a simplified model with a single energy level donor and a continuous acceptor band, we derive a generalized analytic expression and provide numerical simulations for the ET rate. They are consistent with Wigner-Weisskopf, Förster-type, and Marcus-type expressions, in their corresponding regime of parameters.Our analytic results are confirmed by numerical simulations. We demonstrate how our theoretical results are modified {when both the donor and the acceptor are described by finite bands}. We also show that, for a relatively wide acceptor band, the efficiency of the ET from donor to acceptor can be close to 100% for a broad range of noise amplitudes, for both "downhill" and "uphill" ET, for sharp and flat redox potentials, and for reasonably short times. We discuss possible experimental implementations of our approach with application to bio-complexes.
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Submitted 20 December, 2018; v1 submitted 19 December, 2018;
originally announced December 2018.
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Multiscale cyclic dynamics in light harvesting complex in presence of vibrations and noise
Authors:
Shmuel Gurvitz,
Gennady P. Berman,
Richard T. Sayre
Abstract:
Starting from the many-body Schrödinger equation, we derive a new type of Lindblad Master equations describing a cyclic exciton/electron dynamics in the light harvesting complex and the reaction center. These equations resemble the Master equations for the electric current in mesoscopic systems, and they go beyond the single-exciton description by accounting for the multi-exciton states accumulate…
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Starting from the many-body Schrödinger equation, we derive a new type of Lindblad Master equations describing a cyclic exciton/electron dynamics in the light harvesting complex and the reaction center. These equations resemble the Master equations for the electric current in mesoscopic systems, and they go beyond the single-exciton description by accounting for the multi-exciton states accumulated in the antenna, as well as the charge-separation, fluorescence and photo-absorption. Although these effects take place on very different timescales, their inclusion is necessary for a consistent description of the exciton dynamics. Our approach reproduces both coherent and incoherent dynamics of exciton motion along the antenna in the presence of vibrational modes and noise. We applied our results to evaluate energy (exciton) and fluorescent currents as a function of sunlight intensity.
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Submitted 17 June, 2020; v1 submitted 16 April, 2018;
originally announced April 2018.
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Multiscale Multiexciton Cyclic Dynamics in Light Harvesting Complex
Authors:
Shmuel Gurvitz,
Gennady P. Berman,
Richard T. Sayre
Abstract:
Usually the study of energy-transfer in the light harvesting complex is limited by a single-exciton motion along the antenna. Starting from the many-body Schrödinger equation, we derived Lindblad-type Master equations describing the cyclic exciton-electron dynamics of the light harvesting complex, originated from charge reduction of a donor. These equations, resembling the Master equations for the…
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Usually the study of energy-transfer in the light harvesting complex is limited by a single-exciton motion along the antenna. Starting from the many-body Schrödinger equation, we derived Lindblad-type Master equations describing the cyclic exciton-electron dynamics of the light harvesting complex, originated from charge reduction of a donor. These equations, resembling the Master equations for the electric current in mesoscopic systems, go beyond the single-exciton description by accounting for the multi-exciton states accumulated in the antenna, as well as the charge-separation, fluorescence and initial photo-absorption. Although these effects take place on very different time-scales, we demonstrate that their inclusion is necessary for a consistent description of the exciton dynamics. We applied our results to evaluate the energy (exciton) current and for the fluorescent current depending on the light-intensity.
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Submitted 4 June, 2017;
originally announced June 2017.
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Sub-$μ$eV Decoherence-Induced Population Pulsation Resonances in an InGaN system
Authors:
Cameron Nelson,
Yong-Ho Ra,
Zetian Mi,
Paul Berman,
Duncan G. Steel
Abstract:
We report on high frequency resolution coherent nonlinear optical spectroscopy on an ensemble of InGaN disks in GaN nanowires at 300 K. Sub-$μ$eV resonances in the inhomogeneously broadened third order ($χ^{(3)}$) absorption spectrum show asymmetric line shapes, where the degree of asymmetry depends on the wavelength of the excitation beams. Theory based on the Optical Bloch Equations (OBE) indica…
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We report on high frequency resolution coherent nonlinear optical spectroscopy on an ensemble of InGaN disks in GaN nanowires at 300 K. Sub-$μ$eV resonances in the inhomogeneously broadened third order ($χ^{(3)}$) absorption spectrum show asymmetric line shapes, where the degree of asymmetry depends on the wavelength of the excitation beams. Theory based on the Optical Bloch Equations (OBE) indicates that the lineshape asymmetry is a result of fast decoherence in the system and the narrow resonances originate from coherent population pulsations that are induced by decoherence in the system. Using the OBE, we estimate that the decoherence time of the optically induced dipole (formed between the unexcited ground state the excited electron-hole pair) at room temperature is 125 fs, corresponding to a linewidth of ~10 meV. The decay time of the excitation is ~5-10 ns, depending on the excitation energy. The lineshapes are well fit with the OBE indicating that the resonances are characterized by discrete levels with no evidence of many body physics.
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Submitted 17 June, 2017; v1 submitted 29 May, 2017;
originally announced May 2017.
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Production of Entanglement Entropy by Decoherence
Authors:
M. Merkli,
G. P. Berman,
R. T. Sayre,
X. Wang,
A. I. Nesterov
Abstract:
We examine the dynamics of entanglement entropy of all parts in an open system consisting of a two-level dimer interacting with an environment of oscillators. The dimer-environment interaction is almost energy conserving. We find the precise link between decoherence and production of entanglement entropy. We show that not all environment oscillators carry significant entanglement entropy and we id…
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We examine the dynamics of entanglement entropy of all parts in an open system consisting of a two-level dimer interacting with an environment of oscillators. The dimer-environment interaction is almost energy conserving. We find the precise link between decoherence and production of entanglement entropy. We show that not all environment oscillators carry significant entanglement entropy and we identify the oscillator frequency regions which contribute to the production of entanglement entropy. Our results hold for arbitrary strengths of the dimer-environment interaction, and they are mathematically rigorous.
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Submitted 26 June, 2017; v1 submitted 14 February, 2017;
originally announced February 2017.
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Dynamical model of the kinesin protein motor
Authors:
Alexander I Nesterov,
Gennady P Berman,
Mónica F Ramírez
Abstract:
We model and simulate the stepping dynamics of the kinesin motor including electric and mechanical forces, environmental noise, and the complicated potentials produced by tracking and neighboring protofilaments. Our dynamical model supports the hand-over-hand mechanism of the kinesin stepping. Our theoretical predictions and numerical simulations include the off-axis displacements of the kinesin h…
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We model and simulate the stepping dynamics of the kinesin motor including electric and mechanical forces, environmental noise, and the complicated potentials produced by tracking and neighboring protofilaments. Our dynamical model supports the hand-over-hand mechanism of the kinesin stepping. Our theoretical predictions and numerical simulations include the off-axis displacements of the kinesin heads while the steps are performed. The results obtained are in a good agreement with recent experiments on the kinesin dynamics.
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Submitted 28 April, 2016;
originally announced April 2016.
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Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model
Authors:
Alexander I Nesterov,
Mónica F Ramírez,
Gennady P Berman,
Nick E Mavromatos
Abstract:
We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of th…
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We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.
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Submitted 20 April, 2016;
originally announced April 2016.
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Atom interferometry in the presence of an external test mass
Authors:
B. Dubetsky,
S. B. Libby,
P. R. Berman
Abstract:
The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resul…
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The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses, and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. By increasing the effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where the quantum corrections can be measured. The expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.
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Submitted 11 March, 2016; v1 submitted 3 January, 2016;
originally announced January 2016.
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Dynamics of a Chlorophyll Dimer in Collective and Local Thermal Environments
Authors:
M. Merkli,
G. P. Berman,
R. T. Sayre,
S. Gnanakaran,
M. Könenberg,
A. I. Nesterov,
H. Song
Abstract:
We present a theoretical analysis of exciton transfer and decoherence effects in a photosynthetic dimer interacting with collective (correlated) and local (uncorrelated) protein-solvent environments. Our approach is based on the framework of the spin-boson model. We derive explicitly the thermal relaxation and decoherence rates of the exciton transfer process, valid for arbitrary temperatures and…
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We present a theoretical analysis of exciton transfer and decoherence effects in a photosynthetic dimer interacting with collective (correlated) and local (uncorrelated) protein-solvent environments. Our approach is based on the framework of the spin-boson model. We derive explicitly the thermal relaxation and decoherence rates of the exciton transfer process, valid for arbitrary temperatures and for arbitrary (in particular, large) interaction constants between the dimer and the environments. We establish a generalization of the Marcus formula, giving reaction rates for dimer levels possibly individually and asymmetrically coupled to environments. We identify rigorously parameter regimes for the validity of the generalized Marcus formula.
The existence of long living quantum coherences at ambient temperatures emerges naturally from our approach.
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Submitted 14 December, 2015;
originally announced December 2015.
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Non-Hermitian Quantum Annealing and Superradiance
Authors:
Alexander I. Nesterov,
Gennady P. Berman,
Fermín Aceves de la Cruz,
Juan Carlos Beas Zepeda
Abstract:
We consider the non-Hermitian quantum annealing for the one-dimentional Ising spin chain, and for a large number of qubits. We show that the annealing time is significanly reduced for the non-Hermitian algorithm in comparison with the Hermitian one. We also demonstrtate the relation of the non-Hermitian quantum annealing with the superadiance transition in this system.
We consider the non-Hermitian quantum annealing for the one-dimentional Ising spin chain, and for a large number of qubits. We show that the annealing time is significanly reduced for the non-Hermitian algorithm in comparison with the Hermitian one. We also demonstrtate the relation of the non-Hermitian quantum annealing with the superadiance transition in this system.
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Submitted 4 December, 2015;
originally announced December 2015.
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On Improving the Performance of Nonphotochemical Quenching in CP29 Light-Harvesting Antenna Complex
Authors:
Gennady P. Berman,
Alexander I. Nesterov,
Richard T. Sayre,
Susanne Still
Abstract:
We model and simulate the performance of charge-transfer in nonphotochemical quenching (NPQ) in the CP29 light-harvesting antenna-complex associated with photosystem II (PSII). The model consists of five discrete excitonic energy states and two sinks, responsible for the potentially damaging processes and charge-transfer channels, respectively. We demonstrate that by varying (i) the parameters of…
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We model and simulate the performance of charge-transfer in nonphotochemical quenching (NPQ) in the CP29 light-harvesting antenna-complex associated with photosystem II (PSII). The model consists of five discrete excitonic energy states and two sinks, responsible for the potentially damaging processes and charge-transfer channels, respectively. We demonstrate that by varying (i) the parameters of the chlorophyll-based dimer, (ii) the resonant properties of the protein-solvent environment interaction, and (iii) the energy transfer rates to the sinks, one can significantly improve the performance of the NPQ. Our analysis suggests strategies for improving the performance of the NPQ in response to environmental changes, and may stimulate experimental verification.
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Submitted 3 December, 2015;
originally announced December 2015.
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Superradiance Transition and Nonphotochemical Quenching in Photosynthetic Complexes
Authors:
Gennady P. Berman,
Alexander I. Nesterov,
Gustavo V. López,
Richard T. Sayre
Abstract:
We demonstrate numerically that superradiance could play a significant role in nonphotochemical quenching (NPQ) in light-harvesting complexes. Our model consists of a network of five interconnected sites (discrete excitonic states) that are responsible for the NPQ mechanism. Damaging and charge transfer states are linked to their sinks (independent continuum electron spectra), in which the chemica…
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We demonstrate numerically that superradiance could play a significant role in nonphotochemical quenching (NPQ) in light-harvesting complexes. Our model consists of a network of five interconnected sites (discrete excitonic states) that are responsible for the NPQ mechanism. Damaging and charge transfer states are linked to their sinks (independent continuum electron spectra), in which the chemical reactions occur. The superradiance transition in the charge transfer (or in the damaging) channel, occurs at particular electron transfer rates from the discrete to the continuum electron spectra, and can be characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. All five excitonic sites interact with their protein environment that is modeled by a random stochastic process. We find the region of parameters in which the superradiance transition into the charge transfer channel takes place. We demonstrate that this superradiance transition has the capability of producing optimal NPQ performance.
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Submitted 24 April, 2015;
originally announced April 2015.
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The Radical Pair Mechanism and the Avian Chemical Compass: Quantum Coherence and Entanglement
Authors:
Yiteng Zhang,
Gennady P. Berman,
Sabre Kais
Abstract:
We review the spin radical pair mechanism which is a promising explanation of avian navigation. This mechanism is based on the dependence of product yields on (1) the hyperfine interaction involving electron spins and neighboring nuclear spins and (2) the intensity and orientation of the geomagnetic field. One surprising result is that even at ambient conditions quantum entanglement of electron sp…
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We review the spin radical pair mechanism which is a promising explanation of avian navigation. This mechanism is based on the dependence of product yields on (1) the hyperfine interaction involving electron spins and neighboring nuclear spins and (2) the intensity and orientation of the geomagnetic field. One surprising result is that even at ambient conditions quantum entanglement of electron spins can play an important role in avian magnetoreception. This review describes the general scheme of chemical reactions involving radical pairs generated from singlet and triplet precursors; the spin dynamics of the radical pairs; and the magnetic field dependence of product yields caused by the radical pair mechanism. The main part of the review includes a description of the chemical compass in birds. We review: the general properties of the avian compass; the basic scheme of the radical pair mechanism; the reaction kinetics in cryptochrome; quantum coherence and entanglement in the avian compass; and the effects of noise. We believe that the "quantum avian compass" can play an important role in avian navigation and can also provide the foundation for a new generation of sensitive and selective magnetic-sensing nano-devices.
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Submitted 23 March, 2015; v1 submitted 2 February, 2015;
originally announced February 2015.
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Decoherence and Spin Echo in Biological Systems
Authors:
Alexander I. Nesterov,
Gennady P. Berman
Abstract:
The spin echo approach is extended to include bio-complexes for which the interaction with dynamical noise is strong. Significant restoration of the free induction decay signal due to homogeneous (decoherence) and inhomogeneous (dephasing) broadening is demonstrated analytically and numerically, for both an individual dimer of interacting chlorophylls and for an ensemble of dimers. This approach i…
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The spin echo approach is extended to include bio-complexes for which the interaction with dynamical noise is strong. Significant restoration of the free induction decay signal due to homogeneous (decoherence) and inhomogeneous (dephasing) broadening is demonstrated analytically and numerically, for both an individual dimer of interacting chlorophylls and for an ensemble of dimers. This approach is based on an exact and closed system of ordinary differential equations that can be easily solved for a wide range of parameters that are relevant for bio-applications.
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Submitted 8 January, 2015;
originally announced January 2015.
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Possible Role of Interference and Sink Effects in Nonphotochemical Quenching in Photosynthetic Complexes
Authors:
Gennady P. Berman,
Alexander I. Nesterov,
Shmuel Gurvitz,
Richard T. Sayre
Abstract:
We describe a simple and consistent quantum mathematical model that simulates the possible role of quantum interference and sink effects in the nonphotochemical quenching (NPQ) in light-harvesting complexes (LHCs). Our model consists of a network of five interconnected sites (excitonic states) responsible for the NPQ mechanism: (i) Two excited states of chlorophyll molecules, $ChlA^*$ and…
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We describe a simple and consistent quantum mathematical model that simulates the possible role of quantum interference and sink effects in the nonphotochemical quenching (NPQ) in light-harvesting complexes (LHCs). Our model consists of a network of five interconnected sites (excitonic states) responsible for the NPQ mechanism: (i) Two excited states of chlorophyll molecules, $ChlA^*$ and $ChlB^*$, forming an LHC dimer, which is initially populated; (ii) A "damaging" site which is responsible for production of singlet oxygen and other destructive outcomes; (iii) The $(ChlA-Zea)^*$ heterodimer excited state (Zea indicates zeaxanthin); and (iv) The charge transfer state of this heterodimer, $(ChlA^{-}-Zea^{+})^*$. In our model, both damaging and charge transfer states are described by discrete electron energy levels attached to their sinks, that mimic the continuum part of electron energy spectrum, as at these sites the electron participates in quasi-irreversible chemical reactions. All five excitonic sites interact with the protein environment that is modeled using a stochastic approach. As an example, we apply our model to demonstrate possible contributions of quantum interference and sink effects in the NPQ mechanism in the CP29 minor LHC. Our numerical results on the quantum dynamics of the reduced density matrix, demonstrate a possible way to significantly suppress, under some conditions, the damaging channel using quantum interference effects and sinks. The results demonstrate the possible role of interference and sink effects for modeling, engineering, and optimizing the performance of the NPQ processes in both natural and artificial light-harvesting complexes.
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Submitted 10 December, 2014;
originally announced December 2014.
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Vertical dipole above a dielectric or metallic half-space - energy flow considerations
Authors:
P. R. Berman,
S. Zandbergen,
G. Khitrova
Abstract:
The emission pattern from a classical dipole located above and oriented perpendicular to a metallic or dielectric half space is calculated for a dipole driven at constant amplitude. This is a problem considered originally by Sommerfeld and analyzed subsequently by numerous authors. In contrast to most previous treatments, however, we focus on the energy flow in the metal or dielectric. It is shown…
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The emission pattern from a classical dipole located above and oriented perpendicular to a metallic or dielectric half space is calculated for a dipole driven at constant amplitude. This is a problem considered originally by Sommerfeld and analyzed subsequently by numerous authors. In contrast to most previous treatments, however, we focus on the energy flow in the metal or dielectric. It is shown that the radial Poynting vector in the metal points inwards when the frequency of the dipole is below the surface plasmon resonance frequency. In this case, energy actually flows of the interface at small radii. The Joule heating in the metal is also calculated and it is shown explicitly that Poynting's theorem holds for a cylindrical surface in the metal. When the metal is replaced by a dielectric having permittivity less than that of the medium in which the dipole is immersed, it is found that energy flows out of the interface for sufficiently large radii. In all cases it is assumed that the imaginary part of the permittivity of the metal or dielectric is much less than unity.
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Submitted 14 May, 2015; v1 submitted 8 December, 2014;
originally announced December 2014.
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The Role of Protein Fluctuation Correlations in Electron Transfer in Photosynthetic Complexes
Authors:
Alexander I. Nesterov,
Gennady P. Berman
Abstract:
We consider the dependence of the electron transfer in photosynthetic complexes on correlation properties of random fluctuations of the protein environment. The electron subsystem is modeled by a finite network of connected electron (exciton) sites. The fluctuations of the protein environment are modeled by random telegraph processes, which act either collectively (correlated) or independently (un…
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We consider the dependence of the electron transfer in photosynthetic complexes on correlation properties of random fluctuations of the protein environment. The electron subsystem is modeled by a finite network of connected electron (exciton) sites. The fluctuations of the protein environment are modeled by random telegraph processes, which act either collectively (correlated) or independently (uncorrelated) on the electron sites. We derived an exact closed system of first-order linear differential equations with constant coefficients, for the average density matrix elements and for their first moments. Under some conditions, we obtain analytic expressions for the electron transfer rates. We compare the correlated and uncorrelated regimes, and demonstrated numerically that the uncorrelated fluctuations of the protein environment can, under some conditions, either increase or decrease the electron transfer rates.
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Submitted 28 November, 2014;
originally announced December 2014.
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Multi-Scale Exciton and Electron Transfer in Multi-Level Donor-Acceptor System
Authors:
Shmuel Gurvitz,
Alexander I. Nesterov,
Gennady P. Berman
Abstract:
We study theoretically the noise-assisted quantum exciton (electron) transfer (ET) in bio-complexes consisting of a single-level electron donor and an acceptor which has a complicated internal structure, and is modeled by many electron energy levels. Interactions are included between the donor and the acceptor energy levels and with the protein-solvent noisy environment. Different regions of param…
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We study theoretically the noise-assisted quantum exciton (electron) transfer (ET) in bio-complexes consisting of a single-level electron donor and an acceptor which has a complicated internal structure, and is modeled by many electron energy levels. Interactions are included between the donor and the acceptor energy levels and with the protein-solvent noisy environment. Different regions of parameters are considered, which characterize (i) the number of the acceptor levels, (ii) the acceptor \band-width", and (iii) the amplitude of noise and its correlation time. Under some conditions, we derive analytical expressions for the ET rate and efficiency. We obtain equal occupation of all levels at large times, independently of the structure of the acceptor band and the noise parameters, but under the condition of non-degeneracy of the acceptor energy levels. We discuss the multi-scale dynamics of the acceptor population, and the accompanying effect of quantum coherent oscillations. We also demonstrate that for large number of levels in the acceptor band, the efficiency of ET can be close to 100%, for both downhill and uphill transitions and for sharp and at redox potentials.
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Submitted 8 September, 2017; v1 submitted 22 April, 2014;
originally announced April 2014.
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Sensitivity and Entanglement in the Avian Chemical Compass
Authors:
Yiteng Zhang,
Gennady P. Berman,
Sabre Kais
Abstract:
The Radical Pair Mechanism can help to explain avian orientation and navigation. Some evidence indicates that the intensity of external magnetic fields plays an important role in avian navigation. In this paper, based on a two-stage strategy, we demonstrate that birds could reasonably detect the directions of geomagnetic fields and gradients of these fields using a yield-based chemical compass tha…
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The Radical Pair Mechanism can help to explain avian orientation and navigation. Some evidence indicates that the intensity of external magnetic fields plays an important role in avian navigation. In this paper, based on a two-stage strategy, we demonstrate that birds could reasonably detect the directions of geomagnetic fields and gradients of these fields using a yield-based chemical compass that is sensitive enough for navigation. Also, we find that the lifetime of entanglement in this proposed compass is angle-dependent and long enough to allow adequate electron transfer between molecules.
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Submitted 31 January, 2014;
originally announced February 2014.
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A Quantum Biological Switch Based on Superradiance Transitions
Authors:
D. Ferrari,
G. L. Celardo,
G. P. Berman,
R. T. Sayre,
F. Borgonovi
Abstract:
A linear chain of connected electron sites with two asymmetric sinks, one attached to each end, is used as a simple model of quantum electron transfer in photosynthetic bio-complexes. For a symmetric initial population in the middle of the chain, it is expected that electron transfer is mainly directed towards the strongest coupled sink. However, we show that quantum effects radically change this…
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A linear chain of connected electron sites with two asymmetric sinks, one attached to each end, is used as a simple model of quantum electron transfer in photosynthetic bio-complexes. For a symmetric initial population in the middle of the chain, it is expected that electron transfer is mainly directed towards the strongest coupled sink. However, we show that quantum effects radically change this intuitive "classical" mechanism, so that electron transfer can occur through the weaker coupled sink with maximal efficiency. Using this capability, we show how to design a quantum switch that can transfer an electron to the left or right branch of the chain, by changing the coupling to the sinks. The operational principles of this quantum device can be understood in terms of superradiance transitions and subradiant states. This switching, being a pure quantum effect, can be used as a witness of wave--like behaviour of excitations in molecular chains. When realistic data are used for the photosystem II reaction center, this quantum biological switch is shown to retain its reliability, even at room temperature.
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Submitted 5 July, 2013;
originally announced July 2013.
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Noise-assisted quantum electron transfer in photosynthetic complexes
Authors:
Alexander I. Nesterov,
Gennady P. Berman,
José Manuel Sánchez Martínez,
Richard T. Sayre
Abstract:
Electron transfer (ET) between primary electron donors and acceptors is modeled in the photosystem II reaction center (RC). Our model includes (i) two discrete energy levels associated with donor and acceptor, interacting through a dipole-type matrix element and (ii) two continuum manifolds of electron energy levels ("sinks"), which interact directly with the donor and acceptor. Namely, two discre…
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Electron transfer (ET) between primary electron donors and acceptors is modeled in the photosystem II reaction center (RC). Our model includes (i) two discrete energy levels associated with donor and acceptor, interacting through a dipole-type matrix element and (ii) two continuum manifolds of electron energy levels ("sinks"), which interact directly with the donor and acceptor. Namely, two discrete energy levels of the donor and acceptor are embedded in their independent sinks through the corresponding interaction matrix elements. We also introduce classical (external) noise which acts simultaneously on the donor and acceptor (collective interaction). We derive a closed system of integro-differential equations which describes the non-Markovian quantum dynamics of the ET. A region of parameters is found in which the ET dynamics can be simplified, and described by coupled ordinary differential equations. Using these simplified equations, both sharp and flat redox potentials are analyzed. We analytically and numerically obtain the characteristic parameters that optimize the ET rates and efficiency in this system.
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Submitted 29 April, 2013;
originally announced April 2013.
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Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain
Authors:
Alexander I. Nesterov,
Gennady P. Berman,
Juan C. Beas Zepeda,
Alan R. Bishop
Abstract:
A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to N=1024 spins) that our approach leads to a significant reduction of the annealing time that is proportional to $\ln N$, which is much less than the time (proportional to $N^2$) required for the quantum annealing base…
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A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to N=1024 spins) that our approach leads to a significant reduction of the annealing time that is proportional to $\ln N$, which is much less than the time (proportional to $N^2$) required for the quantum annealing based on the corresponding Hermitian algorithm. We propose to use this approach to achieve similar speed-up for NP-complete problems by using classical computers in combination with quantum algorithms.
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Submitted 26 February, 2013;
originally announced February 2013.
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Non-Hermitian Quantum Annealing in the Ferromagnetic Ising Model
Authors:
Alexander I. Nesterov,
Juan Carlos Beas Zepeda,
Gennady P. Berman
Abstract:
We developed a non-Hermitian quantum optimization algorithm to find the ground state of the ferromagnetic Ising model with up to 1024 spins (qubits). Our approach leads to significant reduction of the annealing time. Analytical and numerical results demonstrate that the total annealing time is proportional to ln N, where N is the number of spins. This encouraging result is important in using class…
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We developed a non-Hermitian quantum optimization algorithm to find the ground state of the ferromagnetic Ising model with up to 1024 spins (qubits). Our approach leads to significant reduction of the annealing time. Analytical and numerical results demonstrate that the total annealing time is proportional to ln N, where N is the number of spins. This encouraging result is important in using classical computers in combination with quantum algorithms for the fast solutions of NP-complete problems. Additional research is proposed for extending our dissipative algorithm to more complicated problems.
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Submitted 26 February, 2013; v1 submitted 13 November, 2012;
originally announced November 2012.
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Multiphoton electron detachment by a superposition of static and ac filds
Authors:
A. G. Kofman,
G. P. Berman
Abstract:
A theory of electron detachment from atoms or negative ions by a superposition of a static and a laser (or, more generally, ac) fields, parallel to each other, is developed in the case when the photon energy and the field amplitude are much less than the detachment energy and intra-ion field, respectively. Simple analytical results together with their validity conditions are obtained. Several qual…
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A theory of electron detachment from atoms or negative ions by a superposition of a static and a laser (or, more generally, ac) fields, parallel to each other, is developed in the case when the photon energy and the field amplitude are much less than the detachment energy and intra-ion field, respectively. Simple analytical results together with their validity conditions are obtained. Several qualitatively different regimes of detachment have been identified. Applications of the present theory to electron emission from metal and semiconductor surfaces and from photosynthetic bio-complexes are discussed.
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Submitted 29 October, 2012;
originally announced October 2012.
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Quantum search using non-Hermitian adiabatic evolution
Authors:
Alexander I. Nesterov,
Gennady P. Berman
Abstract:
We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the s…
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We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment.
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Submitted 22 August, 2012;
originally announced August 2012.
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Non-Hermitian approach for modeling of noise-assisted quantum electron transfer in photosynthetic complexes
Authors:
Alexander I. Nesterov,
Gennady P. Berman,
Alan R. Bishop
Abstract:
We model the quantum electron transfer (ET) in the photosynthetic reaction center (RC), using a non-Hermitian Hamiltonian approach. Our model includes (i) two protein cofactors, donor and acceptor, with discrete energy levels and (ii) a third protein pigment (sink) which has a continuous energy spectrum. Interactions are introduced between the donor and acceptor, and between the acceptor and the s…
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We model the quantum electron transfer (ET) in the photosynthetic reaction center (RC), using a non-Hermitian Hamiltonian approach. Our model includes (i) two protein cofactors, donor and acceptor, with discrete energy levels and (ii) a third protein pigment (sink) which has a continuous energy spectrum. Interactions are introduced between the donor and acceptor, and between the acceptor and the sink, with noise acting between the donor and acceptor. The noise is considered classically (as an external random force), and it is described by an ensemble of two-level systems (random fluctuators). Each fluctuator has two independent parameters, an amplitude and a switching rate. We represent the noise by a set of fluctuators with fitting parameters (boundaries of switching rates), which allows us to build a desired spectral density of noise in a wide range of frequencies. We analyze the quantum dynamics and the efficiency of the ET as a function of (i) the energy gap between the donor and acceptor, (ii) the strength of the interaction with the continuum, and (iii) noise parameters. As an example, numerical results are presented for the ET through the active pathway in a quinone-type photosystem II RC.
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Submitted 3 April, 2012;
originally announced April 2012.
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Modeling of Low and High Frequency Noise by Slow and Fast Fluctuators
Authors:
Alexander I. Nesterov,
Gennady P. Berman
Abstract:
We study the dynamics of dephasing in a quantum two-level system by modeling both 1/f and high-frequency noise by random telegraph processes. Our approach is based on a so-called spin-fluctuator model in which a noisy environment is modeled by a large number of fluctuators. In the continuous limit we obtain an effective random process (ERP) that is described by a distribution function of the fluct…
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We study the dynamics of dephasing in a quantum two-level system by modeling both 1/f and high-frequency noise by random telegraph processes. Our approach is based on a so-called spin-fluctuator model in which a noisy environment is modeled by a large number of fluctuators. In the continuous limit we obtain an effective random process (ERP) that is described by a distribution function of the fluctuators. In a simplified model, we reduce the ERP to the two (slow and fast) ensembles of fluctuators. Using this model, we study decoherence in a superconducting flux qubit and we compare our theoretical results with the available experimental data. We demonstrate good agreement of our theoretical predictions with the experiments. Our approach can be applied to many quantum systems, such as biological complexes, semiconductors, superconducting and spin qubits, where the effects of interaction with the environment are essential.
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Submitted 20 April, 2012; v1 submitted 11 January, 2012;
originally announced January 2012.
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Non-Demolition Dispersive Measurement of a Superconducting Qubit with a Microstrip SQUID Amplifier
Authors:
G. P. Berman,
D. I. Kamenev,
D. Kinion,
V. I. Tsifrinovich
Abstract:
We have studied the possibility of a single-shot non-demolition measurement of a superconducting qubit using a microstrip SQUID amplifier (MSA). The Johnson noise generated by all resistors in the MSA is taken into consideration. We show that a single-shot non-demolition measurement is possible with six photons in the measurement resonator. For a phase qubit inductively coupled to a measurement re…
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We have studied the possibility of a single-shot non-demolition measurement of a superconducting qubit using a microstrip SQUID amplifier (MSA). The Johnson noise generated by all resistors in the MSA is taken into consideration. We show that a single-shot non-demolition measurement is possible with six photons in the measurement resonator. For a phase qubit inductively coupled to a measurement resonator we have obtained the expression for the mutual inductance required for measurement of the qubit state.
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Submitted 1 December, 2011;
originally announced December 2011.
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arXiv:1111.7060
[pdf]
physics.ins-det
cond-mat.other
nucl-ex
physics.comp-ph
physics.med-ph
quant-ph
Radiation Damping for Speeding-up NMR Applications
Authors:
Gennady P. Berman,
Michelle A. Espy,
Vyacheslav N. Gorshkov,
Vladimir I. Tsifrinovich,
Petr L. Volegov
Abstract:
We demonstrate theoretically and numerically how to control the NMR relaxation rate after application of the standard spin echo technique. Using radiation damping, we return the nuclear magnetization to its equilibrium state during a time interval that is negligible compared to the relaxation time. We obtain an estimate for optimal radiation damping which is consistent with our numerical simulatio…
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We demonstrate theoretically and numerically how to control the NMR relaxation rate after application of the standard spin echo technique. Using radiation damping, we return the nuclear magnetization to its equilibrium state during a time interval that is negligible compared to the relaxation time. We obtain an estimate for optimal radiation damping which is consistent with our numerical simulations.
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Submitted 25 November, 2011;
originally announced November 2011.
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Scintillation reduction for combined Gaussian-vortex beam propagating through turbulent atmosphere
Authors:
G. P. Berman,
V. N. Gorshkov,
S. V. Torous
Abstract:
We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams (PCBs), including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index (SI) of the signal at the detector is analyzed. A method for significantly red…
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We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams (PCBs), including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index (SI) of the signal at the detector is analyzed. A method for significantly reducing the SI, by averaging the signal at the detector over a set of PCBs, is described. This novel method is to generate the PCBs by combining two laser beams - Gaussian and vortex beams, with different frequencies (the difference between these two frequencies being significantly smaller than the frequencies themselves). In this case, the SI is effectively suppressed without any high-frequency modulators.
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Submitted 15 January, 2011;
originally announced January 2011.
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arXiv:1006.3945
[pdf]
physics.optics
cond-mat.stat-mech
physics.ao-ph
physics.comp-ph
physics.ins-det
Scintillation Reduction for Laser Beams Propagating Through Turbulent Atmosphere
Authors:
G. P. Berman,
V. N. Gorshkov,
S. V. Torous
Abstract:
We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams, including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index (SI) of the signal at the detector is analyzed. These studies were performed for diff…
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We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams, including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index (SI) of the signal at the detector is analyzed. These studies were performed for different dimensions of the detector, distances of propagation, and strengths of the atmospheric turbulence. Methods for significantly reducing the scintillation index are described. These methods utilize averaging of the signal at the detector over a set of partially coherent beams (PCBs). It is demonstrated that the most effective approach is using a set of PCBs with definite initial directions of propagation relative to the z-axis. This approach results in a significant compensation of the beam wandering which in many cases is the main contributor to the SI. A novel method is to generate the PCBs by combining two laser beams - Gaussian and vortex beams, with different frequencies (the difference between these two frequencies being significantly smaller than the frequencies themselves). In this case, the effective suppression of the SI does not require high-frequency modulators. This result is important for achieving gigabit data-rates in long-distance laser communication through turbulent atmospheres.
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Submitted 16 November, 2010; v1 submitted 20 June, 2010;
originally announced June 2010.
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Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam
Authors:
G. P. Berman,
A. R. Bishop,
B. M. Chernobrod,
V. N. Gorshkov,
D. C. Lizon,
D. I. Moody,
D. C. Nguyen,
S. V. Torous
Abstract:
We demonstrate experimentally and numerically that the application of a partially coherent beam (PCB) in combination with time averaging leads to a significant reduction in the scintillation index. We use a simplified experimental approach in which the atmospheric turbulence is simulated by a phase diffuser. The role of the speckle size, the amplitude of the phase modulation, and the strength of…
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We demonstrate experimentally and numerically that the application of a partially coherent beam (PCB) in combination with time averaging leads to a significant reduction in the scintillation index. We use a simplified experimental approach in which the atmospheric turbulence is simulated by a phase diffuser. The role of the speckle size, the amplitude of the phase modulation, and the strength of the atmospheric turbulence are examined. We obtain good agreement between our numerical simulations and our experimental results. This study provides a useful foundation for future applications of PCB-based methods of scintillation reduction in physical atmospheres.
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Submitted 24 June, 2009;
originally announced June 2009.
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Influence of Phase Diffuser Dynamics on Scintillations of Laser Radiation in Earth Atmosphere: Long-Distance Propagation
Authors:
G. P. Berman,
A. A. Chumak
Abstract:
The effect of a random phase diffuser on fluctuations of laser light (scintillations) is studied. Not only spatial but also temporal phase variations introduced by the phase diffuser are analyzed. The explicit dependence of the scintillation index on finite-time phase variations is obtained for long propagation paths. It is shown that for large amplitudes of phase fluctuations, a finite-time eff…
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The effect of a random phase diffuser on fluctuations of laser light (scintillations) is studied. Not only spatial but also temporal phase variations introduced by the phase diffuser are analyzed. The explicit dependence of the scintillation index on finite-time phase variations is obtained for long propagation paths. It is shown that for large amplitudes of phase fluctuations, a finite-time effect decreases the ability of phase diffuser to suppress the scintillations.
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Submitted 31 March, 2009;
originally announced March 2009.
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Intrinsic dissipation in cantilevers
Authors:
G. P. Berman,
A. A. Chumak
Abstract:
We consider the effects of a velocity-independent friction force on cantilever damping. It is shown that this dissipation mechanism causes nonlinear effects in the cantilever vibrations. The size of the nonlinearity increases with decreasing cantilever velocity. Our analysis makes it possible to understand experiments [Stipe et al, PRL 87, 096801 (2001)] where an amplitude dependence of the cant…
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We consider the effects of a velocity-independent friction force on cantilever damping. It is shown that this dissipation mechanism causes nonlinear effects in the cantilever vibrations. The size of the nonlinearity increases with decreasing cantilever velocity. Our analysis makes it possible to understand experiments [Stipe et al, PRL 87, 096801 (2001)] where an amplitude dependence of the cantilever eigenfrequency and anomalous dissipation was observed only at small amplitudes.
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Submitted 17 September, 2007;
originally announced September 2007.
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Terahertz and Infrared Uncooled Detector Based on a Microcantilever as a Radiation Pressure Sensor
Authors:
Gennady P. Berman,
Boris M. Chernobrod,
Alan R. Bishop,
Vyacheslav N. Gorshkov
Abstract:
We consider a far infrared (terahertz), room-temperature detector based on a microcantilever sensor of the radiation pressure. This system has a significantly higher sensitivity than existing uncooled detectors in the far infrared (terahertz) spectral region. The significant enhancement of sensitivity is due the combination non-absorption detection method and high quality optical microcavity. Ou…
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We consider a far infrared (terahertz), room-temperature detector based on a microcantilever sensor of the radiation pressure. This system has a significantly higher sensitivity than existing uncooled detectors in the far infrared (terahertz) spectral region. The significant enhancement of sensitivity is due the combination non-absorption detection method and high quality optical microcavity. Our theoretical analysis of the detector sensitivity and numerical simulations demonstrate that the narrowband heterodyne detector with the band width 30 MHz has a minimal measurable intensity by three orders of magnitude less than conventional uncooled detectors. In the case of the broadband detector, the noise equivalent temperature difference (NETD) is 7.6 mK, which is significantly smaller than for conventional uncooled thermal detectors.
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Submitted 5 March, 2007;
originally announced March 2007.
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Suppression of Intensity Fluctuations in Free Space High-Speed Optical Communication Based on Spectral Encoding of a Partially Coherent Beam
Authors:
Gennady P. Berman,
Alan R. Bishop,
Boris M. Chernobrod,
Dinh C. Nguyen,
Vyacheslav N. Gorshkov
Abstract:
A new concept of a free-space, high-speed (Gbps) optical communication system based on spectral encoding of radiation from a broadband pulsed laser is developed. It is shown that, in combination with the use of partially coherent laser beams and a relatively slow photosensor, scintillations can be suppressed by orders of magnitude for distances of more than 10 km. We also consider the spectral e…
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A new concept of a free-space, high-speed (Gbps) optical communication system based on spectral encoding of radiation from a broadband pulsed laser is developed. It is shown that, in combination with the use of partially coherent laser beams and a relatively slow photosensor, scintillations can be suppressed by orders of magnitude for distances of more than 10 km. We also consider the spectral encoding of radiation from a LED as a gigabit rate solution of the "last mile" problem and rapid-deployment systems for disaster recovery.
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Submitted 5 February, 2007; v1 submitted 5 February, 2007;
originally announced February 2007.
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Numerical simulations on cleaning the neutron trap for measuring the neutron lifetime
Authors:
Vyacheslav N. Gorshkov,
Gennady P. Berman
Abstract:
We present the results of numerical simulations of the dynamical behavior of trajectories of ultra cold neutrons (UCN) in a magnetic trap. The main goal of our simulations was to optimize the trap parameters in order to minimize the characteristic times for removing from the trap those untrapped neutrons with relatively long escape times (cleaning the trap). Our results demonstrate that, by a pr…
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We present the results of numerical simulations of the dynamical behavior of trajectories of ultra cold neutrons (UCN) in a magnetic trap. The main goal of our simulations was to optimize the trap parameters in order to minimize the characteristic times for removing from the trap those untrapped neutrons with relatively long escape times (cleaning the trap). Our results demonstrate that, by a proper choice of the trap parameters cleaning times can be reduced to 15 sec, or even less. Many other dynamical characteristics of the neutrons in the trap, including the conservation of the adiabatic invariant which characterizes the orientation of the magnetic moment along the local magnetic field, are also discussed.
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Submitted 6 November, 2006;
originally announced November 2006.
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Quantum computing with magnetic atoms in optical lattices of reduced periodicity
Authors:
Boris Ravaine,
Andrei Derevianko,
P. R. Berman
Abstract:
We investigate the feasibility of combining Raman optical lattices with a quantum computing architecture based on lattice-confined magnetically interacting neutral atoms. A particular advantage of the standing Raman field lattices comes from reduced interatomic separations leading to increased interatomic interactions and improved multi-qubit gate performance. Specifically, we analyze a $J=3/2$…
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We investigate the feasibility of combining Raman optical lattices with a quantum computing architecture based on lattice-confined magnetically interacting neutral atoms. A particular advantage of the standing Raman field lattices comes from reduced interatomic separations leading to increased interatomic interactions and improved multi-qubit gate performance. Specifically, we analyze a $J=3/2$ Zeeman system placed in $% σ_{+}-σ_{-}$ Raman fields which exhibit $λ/4$ periodicity. We find that the resulting CNOT gate operations times are in the order of millisecond. We also investigate motional and magnetic-field induced decoherences specific to the proposed architecture.
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Submitted 24 June, 2006; v1 submitted 20 June, 2006;
originally announced June 2006.
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Cooling in reduced period optical lattices: non-zero Raman detuning
Authors:
V. S. Malinovsky,
P. R. Berman
Abstract:
In a previous paper [Phys. Rev. A 72, 033415 (2005)], it was shown that sub-Doppler cooling occurs in a standing-wave Raman scheme (SWRS) that can lead to reduced period optical lattices. These calculations are extended to allow for non-zero detuning of the Raman transitions. New physical phenomena are encountered, including cooling to non-zero velocities, combinations of Sisyphus and "corkscrew…
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In a previous paper [Phys. Rev. A 72, 033415 (2005)], it was shown that sub-Doppler cooling occurs in a standing-wave Raman scheme (SWRS) that can lead to reduced period optical lattices. These calculations are extended to allow for non-zero detuning of the Raman transitions. New physical phenomena are encountered, including cooling to non-zero velocities, combinations of Sisyphus and "corkscrew" polarization cooling, and somewhat unusual origins of the friction force. The calculations are carried out in a semi-classical approximation and a dressed state picture is introduced to aid in the interpretation of the results.
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Submitted 6 May, 2006;
originally announced May 2006.
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The Fermi-Pasta-Ulam problem: 50 years of progress
Authors:
G. P. Berman,
F. M. Izrailev
Abstract:
A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection w…
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A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Bose-particles are also considered.
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Submitted 8 March, 2005; v1 submitted 29 November, 2004;
originally announced November 2004.
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On the role of coupling in mode selective excitation using ultrafast pulse shaping in stimulated Raman spectroscopy
Authors:
S. A. Malinovskaya,
P. H. Bucksbaum,
P. R. Berman
Abstract:
The coherence of two, coupled two-level systems, representing vibrational modes in a semiclassical model, is calculated in weak and strong fields for various coupling schemes and for different relative phases between initial state amplitudes. A relative phase equal to $π$ projects the system into a dark state. The selective excitation of one of the two, two-level systems is studied as a function…
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The coherence of two, coupled two-level systems, representing vibrational modes in a semiclassical model, is calculated in weak and strong fields for various coupling schemes and for different relative phases between initial state amplitudes. A relative phase equal to $π$ projects the system into a dark state. The selective excitation of one of the two, two-level systems is studied as a function of coupling strength and initial phases.
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Submitted 3 May, 2004;
originally announced May 2004.
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Theory of selective excitation in Stimulated Raman Scattering
Authors:
S. A. Malinovskaya,
P. H. Bucksbaum,
P. R. Berman
Abstract:
A semiclassical model is used to investigate the possibility of selectively exciting one of two closely spaced, uncoupled Raman transitions. The duration of the intense pump pulse that creates the Raman coherence is shorter than the vibrational period of a molecule (impulsive regime of interaction). Pulse shapes are found that provide either enhancement or suppression of particular vibrational e…
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A semiclassical model is used to investigate the possibility of selectively exciting one of two closely spaced, uncoupled Raman transitions. The duration of the intense pump pulse that creates the Raman coherence is shorter than the vibrational period of a molecule (impulsive regime of interaction). Pulse shapes are found that provide either enhancement or suppression of particular vibrational excitations.
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Submitted 25 June, 2003; v1 submitted 24 June, 2003;
originally announced June 2003.
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Spin Relaxation Caused by Thermal Excitations of High Frequency Modes of Cantilever Vibrations
Authors:
G. P. Berman,
V. N. Gorshkov,
D. Rugar,
V. I. Tsifrinovich
Abstract:
We consider the process of spin relaxation in the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. We simulated the spin relaxation caused by thermal excitations of the high frequency cantilever modes in the region of the Rabi frequency of the spin sub-system. The minimum relaxation time obtained in our simulations is greater but of the same ord…
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We consider the process of spin relaxation in the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. We simulated the spin relaxation caused by thermal excitations of the high frequency cantilever modes in the region of the Rabi frequency of the spin sub-system. The minimum relaxation time obtained in our simulations is greater but of the same order of magnitude as one measured in recent experiments. We demonstrated that using a cantilever with nonuniform cross-sectional area may significantly increase spin relaxation time.
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Submitted 28 March, 2003;
originally announced March 2003.
-
$\fracλ{8}$-period optical potentials
Authors:
B. Dubetsky,
P. R. Berman
Abstract:
A Raman configuration of counterpropagating traveling wave fields, one of which is $lin\bot lin$ polarized and the other $lin\Vert lin$ polarized, is shown to lead to optical potentials having $\fracλ{8}$ periodicity. Such optical potentials may be used to construct optical lattices having $% \fracλ{8}$ periodicity. Using numerical diagonalization, we obtain the optical potentials for…
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A Raman configuration of counterpropagating traveling wave fields, one of which is $lin\bot lin$ polarized and the other $lin\Vert lin$ polarized, is shown to lead to optical potentials having $\fracλ{8}$ periodicity. Such optical potentials may be used to construct optical lattices having $% \fracλ{8}$ periodicity. Using numerical diagonalization, we obtain the optical potentials for $^{\text{85}}$Rb atoms.
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Submitted 3 July, 2002;
originally announced July 2002.
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$λ/4$, $λ/8$, and higher order atom gratings via Raman transitions
Authors:
B. Dubetsky,
P. R. Berman
Abstract:
A method is proposed for producing atom gratings having period $λ/4$ and $λ/8$ using optical fields having wavelength $λ$. Counterpropagating optical fields drive Raman transitions between ground state sublevels. The Raman fields can be described by an effective two photon field having wave vector 2 k, where k is the propagation vector of one of the fields. By combining this Raman field with {\e…
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A method is proposed for producing atom gratings having period $λ/4$ and $λ/8$ using optical fields having wavelength $λ$. Counterpropagating optical fields drive Raman transitions between ground state sublevels. The Raman fields can be described by an effective two photon field having wave vector 2 k, where k is the propagation vector of one of the fields. By combining this Raman field with {\em another} Raman field having propagation vector -2 k, one, in effect, creates a standing wave Raman field \label{91}%which whose ``intensity'' varies as $\cos (4 k\cdot r).$ When atoms move through this standing wave field, atom gratings having period $λ/4$ are produced, with the added possibility that the total ground state population in a given ground state manifold can have $λ/8$ periodicity. The conditions required to produce such gratings are derived. Moreover, it is shown that even higher order gratings having periodicity smaller than $λ/8$ can be produced using a multicolor field geometry involving three (two-photon) Raman fields. Although most calculations are carried out in the Raman-Nath approximation, the use of Raman fields to create reduced period optical lattices is also discussed.
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Submitted 4 February, 2002; v1 submitted 9 January, 2002;
originally announced January 2002.
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Atom gratings produced by large angle atom beam splitters
Authors:
B. Dubetsky,
P. R. Berman
Abstract:
An asymptotic theory of atom scattering by large amplitude periodic potentials is developed in the Raman-Nath approximation. The atom grating profile arising after scattering is evaluated in the Fresnel zone for triangular, sinusoidal, magneto-optical, and bichromatic field potentials. It is shown that, owing to the scattering in these potentials, two \QTR{em}{groups} of momentum states are prod…
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An asymptotic theory of atom scattering by large amplitude periodic potentials is developed in the Raman-Nath approximation. The atom grating profile arising after scattering is evaluated in the Fresnel zone for triangular, sinusoidal, magneto-optical, and bichromatic field potentials. It is shown that, owing to the scattering in these potentials, two \QTR{em}{groups} of momentum states are produced rather than two distinct momentum components. The corresponding spatial density profile is calculated and found to differ significantly from a pure sinusoid.
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Submitted 24 May, 2001; v1 submitted 16 May, 2001;
originally announced May 2001.
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Spectrum of light scattering from an extended atomic wave packet
Authors:
B. Dubetsky,
P. R. Berman
Abstract:
The spectrum of the light scattered from an extended atomic wave packet is calculated. For a wave packet consisting of two spatially separated peaks moving on parallel trajectories, the spectrum contains Ramsey-like fringes that are sensitive to the phase difference between the two components of the wave packet. Using this technique, one can establish the mutual coherence of the two components o…
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The spectrum of the light scattered from an extended atomic wave packet is calculated. For a wave packet consisting of two spatially separated peaks moving on parallel trajectories, the spectrum contains Ramsey-like fringes that are sensitive to the phase difference between the two components of the wave packet. Using this technique, one can establish the mutual coherence of the two components of the wave packet without recombining them.
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Submitted 30 March, 2001;
originally announced March 2001.
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Recoil-Induced-Resonances in Nonlinear, Ground-State, Pump-Probe Spectroscopy
Authors:
C. P. Search,
P. R. Berman
Abstract:
A theory of pump-probe spectroscopy is developed in which optical fields drive two-photon Raman transitions between ground states of an ensemble of three-level $Λ$ atoms. Effects related to the recoil the atoms undergo as a result of their interactions with the fields are fully accounted for in this theory. The linear absorption coefficient of a weak probe field in the presence of two pump field…
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A theory of pump-probe spectroscopy is developed in which optical fields drive two-photon Raman transitions between ground states of an ensemble of three-level $Λ$ atoms. Effects related to the recoil the atoms undergo as a result of their interactions with the fields are fully accounted for in this theory. The linear absorption coefficient of a weak probe field in the presence of two pump fields of arbitrary strength is calculated. For subrecoil cooled atoms, the spectrum consists of eight absorption lines and eight emission lines. In the limit that $χ_{1}\ll χ_{2}$, where $χ_{1}$ and $χ_{2}$ are the Rabi frequencies of the two pump fields, one recovers the absorption spectrum for a probe field interacting with an effective two-level atom in the presence of a single pump field. However when $χ_{1}\gtrsim χ_{2}$, new interference effects arise that allow one to selectively turn on and off some of these recoil induced resonances.
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Submitted 2 February, 2001; v1 submitted 1 December, 2000;
originally announced December 2000.