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The fractal geometry and the mapping of Efimov states to Bloch states
Authors:
Ehoud Pazy
Abstract:
Efimov states are known to have a discrete real space scale invariance, working in momentum space we identify the relevant discrete scale invariance for the scattering amplitude defining its Weierstrass function as well. Through the use of the mathematical formalism for discrete scale invariance for the scattering amplitude we identify the scaling parameters from the pole structure of the correspo…
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Efimov states are known to have a discrete real space scale invariance, working in momentum space we identify the relevant discrete scale invariance for the scattering amplitude defining its Weierstrass function as well. Through the use of the mathematical formalism for discrete scale invariance for the scattering amplitude we identify the scaling parameters from the pole structure of the corresponding zeta function, it's zeroth order pole is fixed by the Efimov physics. The corresponding geometrical fractal structure for Efimov physics in momentum space is identified as a ray across a logarithmic spiral. This geometrical structure also appears in the physics of atomic collapse in the relativistic regime connecting it to Efimov physics. Transforming to logarithmic variables in momentum space we map the three-body scattering amplitude into Bloch states and the ladder of energies of the Efimov states are simply obtained interms of the Bohr-Sommerfeld quantization rule. Thus through the mapping the complex problem of three-body short range interaction is transformed to that of a non-interacting single particle in a discrete lattice.
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Submitted 25 May, 2020;
originally announced May 2020.
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Matter-wave squeezing and the generation of SU(1,1) and SU(2) coherent-states via Feshbach resonances
Authors:
I. Tikhonenkov,
E. Pazy,
Y. B. Band,
A. Vardi
Abstract:
Pair operators for boson and fermion atoms generate SU(1,1) and SU(2) Lie algebras, respectively. Consequently, the pairing of boson and fermion atoms into diatomic molecules via Feshbach resonances, produces SU(1,1) and SU(2) coherent states, making bosonic pairing the matter-wave equivalent of parametric coupling and fermion pairing equivalent to the Dicke model of quantum optics. We discuss t…
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Pair operators for boson and fermion atoms generate SU(1,1) and SU(2) Lie algebras, respectively. Consequently, the pairing of boson and fermion atoms into diatomic molecules via Feshbach resonances, produces SU(1,1) and SU(2) coherent states, making bosonic pairing the matter-wave equivalent of parametric coupling and fermion pairing equivalent to the Dicke model of quantum optics. We discuss the properties of atomic states generated in the dissociation of molecular Bose-Einstein condensates into boson or fermion constituent atoms. The SU(2) coherent states produced in dissociation into fermions give Poissonian atom-number distributions, whereas the SU(1,1) states generated in dissociation into bosons result in super-poissonian distributions, in analogy to two-photon squeezed states. In contrast, starting from an atomic gas produces coherent number distributions for bosons and super-poissonian distributions for fermions.
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Submitted 6 November, 2007;
originally announced November 2007.
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Many-body effects on adiabatic passage through Feshbach resonances
Authors:
I. Tikhonenkov,
E. Pazy,
Y. B. Band,
M. Fleischhauer,
A. Vardi
Abstract:
We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting s…
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We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate alpha, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $Gamma\propto alpha$ is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.
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Submitted 21 May, 2006;
originally announced May 2006.
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Nonlinear adiabatic passage from fermion atoms to boson molecules
Authors:
E. Pazy,
I Tikhonenkov,
Y. B. Band,
M. Fleischhauer,
A. Vardi
Abstract:
We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction $Γ$ on the sweep rate $α$ varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for la…
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We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction $Γ$ on the sweep rate $α$ varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number $N$. The power-law is linear, $Γ\propto α$, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and $Γ\propto α^{1/3}$ when it is larger. Experimental data agree better with a linear dependence than with an exponential Landau-Zener fit, indicating that many-body effects are significant in the atom-molecule conversion process.
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Submitted 9 March, 2005;
originally announced March 2005.
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Holstein model and Peierls instability in 1D boson-fermion lattice gases
Authors:
E. Pazy,
A. Vardi
Abstract:
We study an ultracold bose-fermi mixture in a one dimensional optical lattice. When boson atoms are heavier then fermion atoms the system is described by an adiabatic Holstein model, exhibiting a Peierls instability for commensurate fermion filling factors. A Bosonic density wave with a wavenumber of twice the Fermi wavenumber will appear in the quasi one-dimensional system.
We study an ultracold bose-fermi mixture in a one dimensional optical lattice. When boson atoms are heavier then fermion atoms the system is described by an adiabatic Holstein model, exhibiting a Peierls instability for commensurate fermion filling factors. A Bosonic density wave with a wavenumber of twice the Fermi wavenumber will appear in the quasi one-dimensional system.
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Submitted 12 August, 2004;
originally announced August 2004.
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Spin state readout by quantum jump technique: for the purpose of quantum computing
Authors:
E. Pazy,
T. Calarco,
P. Zoller
Abstract:
Utilizing the Pauli-blocking mechanism we show that shining circular polarized light on a singly-charged quantum dot induces spin dependent fluorescence. Employing the quantum-jump technique we demonstrate that this resonance luminescence, due to a spin dependent optical excitation, serves as an excellent readout mechanism for measuring the spin state of a single electron confined to a quantum d…
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Utilizing the Pauli-blocking mechanism we show that shining circular polarized light on a singly-charged quantum dot induces spin dependent fluorescence. Employing the quantum-jump technique we demonstrate that this resonance luminescence, due to a spin dependent optical excitation, serves as an excellent readout mechanism for measuring the spin state of a single electron confined to a quantum dot.
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Submitted 21 April, 2004;
originally announced April 2004.
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On the conversion efficiency of ultracold fermionic atoms to bosonic molecules via Feshbach resonances
Authors:
E. Pazy,
A. Vardi,
Y. B. Band
Abstract:
We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of $^{40}$K and $^{6}$Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau Zener transition but faster than ``the collision rate'' in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficien…
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We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of $^{40}$K and $^{6}$Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau Zener transition but faster than ``the collision rate'' in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin-states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair-states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter thereby increasing the conversion efficiency; ``the collision rate'' is the pair decorrelation rate.
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Submitted 12 August, 2004; v1 submitted 15 March, 2004;
originally announced March 2004.
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Long time relaxation of interacting electrons in the regime of hopping conduction
Authors:
D. N. Tsigankov,
E. Pazy,
B. D. Laikhtman,
A. L. Efros
Abstract:
Using numerical simulations we studied the long time relaxation of the hopping conductivity. Even though no modern computation is able to simulate the behavior of a large size system over minutes or hours so as to observe the relaxation, still we have been able to show that the long time relaxation and aging effect observed in experiments can be explained in terms of slow transitions between dif…
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Using numerical simulations we studied the long time relaxation of the hopping conductivity. Even though no modern computation is able to simulate the behavior of a large size system over minutes or hours so as to observe the relaxation, still we have been able to show that the long time relaxation and aging effect observed in experiments can be explained in terms of slow transitions between different pseudoground states. This was achieved by showing that different pseudoground states may have different conductivities and that the dispersion of conductivities is in agreement with the experimental data. We considered two different two-dimensional models with electron-electron interaction: the lattice model and the random site model, corresponding to ``strong'' and ``weak'' effective disorder. For the lattice model, effectively strong disorder, we have shown that the universality of the Coulomb gap, which is responsible for the universal Efros-Shklovskii law for the conductivity, suppresses the long time relaxation of conductivity since the universality strongly decreases the dispersion of conductivities of the pseudoground states.
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Submitted 22 July, 2003;
originally announced July 2003.
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Photocurrent in conjugated polymers
Authors:
Baruch Horovitz,
Ehoud Pazy
Abstract:
Nonlinear photocurrent carriers in conjugated polymers, such as polarons, bipolarons and solitons, are considered at low photon energies where a tunnelling process is necessary. We show that polarons usually dominate the photocurrent I due to a novel electric field assisted tunnelling for which ln(I) ~ -E^{-2/3}. For near degenerate polymers an electric field E which exceeds the confinement pote…
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Nonlinear photocurrent carriers in conjugated polymers, such as polarons, bipolarons and solitons, are considered at low photon energies where a tunnelling process is necessary. We show that polarons usually dominate the photocurrent I due to a novel electric field assisted tunnelling for which ln(I) ~ -E^{-2/3}. For near degenerate polymers an electric field E which exceeds the confinement potential and frequencies above twice the soliton energy, soliton tunnelling is favored. Photocurrent data can then be used to identify the remarkable phenomenon of soliton conduction.
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Submitted 23 April, 2003;
originally announced April 2003.
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Calculation of pure dephasing for excitons in quantum dots
Authors:
E. Pazy
Abstract:
Pure dephasing of an exciton in a small quantum dot by optical and acoustic phonons is calculated using the ``independent boson model''. Considering the case of zero temperature the dephasing is shown to be only partial which manifests itself in the polarization decaying to a finite value. Typical dephasing times can be assigned even though the spectra exhibits strongly non-Lorentzian line shape…
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Pure dephasing of an exciton in a small quantum dot by optical and acoustic phonons is calculated using the ``independent boson model''. Considering the case of zero temperature the dephasing is shown to be only partial which manifests itself in the polarization decaying to a finite value. Typical dephasing times can be assigned even though the spectra exhibits strongly non-Lorentzian line shapes. We show that the dephasing from LO phonon scattering, occurs on a much larger time scale than that of dephasing due to acoustic phonons which for low temperatures are also a more efficient dephasing mechanism. The typical dephasing time is shown to strongly depend on the quantum dot size whereas the electron phonon ``coupling strength'' and external electric fields tend mostly to effect the residual coherence. The relevance of the dephasing times for current quantum information processing implementation schemes in quantum dots is discussed.
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Submitted 20 December, 2002;
originally announced December 2002.
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Spin-based optical quantum gates via Pauli blocking in semiconductor quantum dots
Authors:
E. Pazy,
E. Biolatti,
T. Calarco,
I. D'Amico,
P. Zanardi,
F. Rossi,
P. Zoller
Abstract:
We present a solid-state implementation of ultrafast conditional quantum gates. Our proposal for a quantum-computing device is based on the spin degrees of freedom of electrons confined in semiconductor quantum dots, thus benefiting from relatively long decoherence times. More specifically, combining Pauli blocking effects with properly tailored ultrafast laser pulses, we are able to obtain sub-…
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We present a solid-state implementation of ultrafast conditional quantum gates. Our proposal for a quantum-computing device is based on the spin degrees of freedom of electrons confined in semiconductor quantum dots, thus benefiting from relatively long decoherence times. More specifically, combining Pauli blocking effects with properly tailored ultrafast laser pulses, we are able to obtain sub-picosecond spin-dependent switching of the Coulomb interaction, which is the essence of our conditional phase-gate proposal. This allows us to realize {\it a fast two qubit gate which does not translate into fast decoherence times} and paves the road for an all-optical spin-based quantum computer.
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Submitted 28 February, 2002; v1 submitted 19 September, 2001;
originally announced September 2001.
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Storage Qubits and Their Potential Implementation Through a Semiconductor Double Quantum Dot
Authors:
E. Pazy,
I. D'Amico,
P. Zanardi,
F. Rossi
Abstract:
In the context of a semiconductor based implementation of a quantum computer the idea of a quantum storage bit is presented and a possible implementation using a double quantum dot structure is considered. A measurement scheme using a stimulated Raman adiabatic passage is discussed.
In the context of a semiconductor based implementation of a quantum computer the idea of a quantum storage bit is presented and a possible implementation using a double quantum dot structure is considered. A measurement scheme using a stimulated Raman adiabatic passage is discussed.
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Submitted 9 August, 2001; v1 submitted 14 March, 2001;
originally announced March 2001.
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Phonon-Coupled Electron Tunneling in Two and Three-Dimensional Tunneling Configurations
Authors:
E. Pazy,
B. Laikhtman
Abstract:
We treat a tunneling electron coupled to acoustical phonons through a realistic electron phonon interaction: deformation potential and piezoelectric, in two or three-dimensional tunneling configurations. Making use of slowness of the phonon system compared to electron tunneling, and using a Green function method for imaginary time, we are able to calculate the change in the transition probabilit…
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We treat a tunneling electron coupled to acoustical phonons through a realistic electron phonon interaction: deformation potential and piezoelectric, in two or three-dimensional tunneling configurations. Making use of slowness of the phonon system compared to electron tunneling, and using a Green function method for imaginary time, we are able to calculate the change in the transition probability due to the coupling to phonons. It is shown using standard renormalization procedure that, contrary to the one-dimensional case, second order perturbation theory is sufficient in order to treat the deformation potential coupling, which leads to a small correction to the transmission coefficient prefactor. In the case of piezoelectric coupling, which is found to be closely related to the piezoelectric polaron problem, vertex corrections need to be considered. Summing leading logarithmic terms, we show that the piezoelectric coupling leads to a significant change of the transmission coefficient.
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Submitted 23 December, 1999;
originally announced December 1999.
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One Dimensional Phonon Coupled Electron Tunneling: A Realistic Model
Authors:
E. Pazy,
B. Laikhtman
Abstract:
The transition probability for a one dimensional tunneling electron coupled to acoustical phonons is calculated, with the Feynman path-integral method for zero temperature. We considered a realistic electron phonon interaction (deformation potential, piezoelectric), making use of slowness of the phonon system compared to electron tunneling. We show that the problem of the complex non-linear coup…
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The transition probability for a one dimensional tunneling electron coupled to acoustical phonons is calculated, with the Feynman path-integral method for zero temperature. We considered a realistic electron phonon interaction (deformation potential, piezoelectric), making use of slowness of the phonon system compared to electron tunneling. We show that the problem of the complex non-linear coupling of a tunneling electron to the zero point fluctuations of a phonon field is equivalent to that of an electron tunneling through a slow fluctuating spatially uniform barrier, thus resulting in an increase of the tunneling probability due to electron coupling with zero-point phonon oscillations. We calculated also the the energy change of the tunneling electron due to phonon emission.
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Submitted 1 August, 1999; v1 submitted 25 November, 1998;
originally announced November 1998.