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Microscopic motility of isolated E. coli flagella
Authors:
Franky Djutanta,
Peter T. Brown,
Bonfilio Nainggolan,
Alexis Coullomb,
Sritharini Radhakrishnan,
Jason Sentosa,
Bernard Yurke,
Rizal F. Hariadi,
Douglas P. Shepherd
Abstract:
The fluctuation-dissipation theorem describes the intimate connection between the Brownian diffusion of thermal particles and their drag coefficients. In the simple case of spherical particles, it takes the form of the Stokes-Einstein relationship that links the particle geometry, fluid viscosity, and diffusive behavior. However, studying the fundamental properties of microscopic asymmetric partic…
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The fluctuation-dissipation theorem describes the intimate connection between the Brownian diffusion of thermal particles and their drag coefficients. In the simple case of spherical particles, it takes the form of the Stokes-Einstein relationship that links the particle geometry, fluid viscosity, and diffusive behavior. However, studying the fundamental properties of microscopic asymmetric particles, such as the helical-shaped propeller used by $\textit{E. coli}$, has remained out of reach for experimental approaches due to the need to quantify correlated translation and rotation simultaneously with sufficient spatial and temporal resolution. To solve this outstanding problem, we generated volumetric movies of fluorophore-labeled, freely diffusing, isolated $\textit{E. Coli}$ flagella using oblique plane microscopy. From these movies, we extracted trajectories and determined the hydrodynamic propulsion matrix directly from the diffusion of flagella via a generalized Einstein relation. Our results validate prior proposals, based on macroscopic wire helices and low Reynolds number scaling laws, that the average flagellum is a highly inefficient propeller. Specifically, we found the maximum propulsion efficiency of flagella is less than 5%. Beyond extending Brownian motion analysis to asymmetric 3D particles, our approach opens new avenues to study the propulsion matrix of particles in complex environments where direct hydrodynamic approaches are not feasible.
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Submitted 31 August, 2022; v1 submitted 29 August, 2022;
originally announced August 2022.
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High fidelity transfer of an arbitrary quantum state between harmonic oscillators
Authors:
K. Jahne,
B. Yurke,
U. Gavish
Abstract:
It is shown that by switching a specific time-dependent interaction between a harmonic oscillator and a transmission line (a waveguide, an optical fiber, etc.) the quantum state of the oscillator can be transferred into that of another oscillator coupled to the distant other end of the line, with a fidelity that is independent of the initial state of both oscillators. For a transfer time $T$, th…
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It is shown that by switching a specific time-dependent interaction between a harmonic oscillator and a transmission line (a waveguide, an optical fiber, etc.) the quantum state of the oscillator can be transferred into that of another oscillator coupled to the distant other end of the line, with a fidelity that is independent of the initial state of both oscillators. For a transfer time $T$, the fidelity approaches 1 exponentially in $γT$ where $γ$ is a characteristic damping rate. Hence, a good fidelity is achieved even for a transfer time of a few damping times. Some implementations are discussed.
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Submitted 24 November, 2006;
originally announced November 2006.
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Mass Detection with Nonlinear Nanomechanical Resonator
Authors:
Eyal Buks,
Bernard Yurke
Abstract:
Nanomechanical resonators having small mass, high resonance frequency and low damping rate are widely employed as mass detectors. We study the performances of such a detector when the resonator is driven into a region of nonlinear oscillations. We predict theoretically that in this region the system acts as a phase-sensitive mechanical amplifier. This behavior can be exploited to achieve noise s…
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Nanomechanical resonators having small mass, high resonance frequency and low damping rate are widely employed as mass detectors. We study the performances of such a detector when the resonator is driven into a region of nonlinear oscillations. We predict theoretically that in this region the system acts as a phase-sensitive mechanical amplifier. This behavior can be exploited to achieve noise squeezing in the output signal when homodyne detection is employed for readout. We show that mass sensitivity of the device in this region may exceed the upper bound imposed by thermomechanical noise upon the sensitivity when operating in the linear region. On the other hand, we show that the high mass sensitivity is accompanied by a slowing down of the response of the system to a change in the mass.
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Submitted 5 July, 2006; v1 submitted 9 June, 2006;
originally announced June 2006.
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Dephasing due to Intermode Coupling in Superconducting Stripline Resonators
Authors:
Eyal Buks,
Bernard Yurke
Abstract:
The nonlinearity exhibited by the kinetic inductance of a superconducting stripline couples stripline resonator modes together in a manner suitable for quantum non-demolition measurement of the number of photons in a given resonator mode. Quantum non-demolition measurement is accomplished by coherently driving another resonator mode, referred to as the detector mode, and measuring its response.…
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The nonlinearity exhibited by the kinetic inductance of a superconducting stripline couples stripline resonator modes together in a manner suitable for quantum non-demolition measurement of the number of photons in a given resonator mode. Quantum non-demolition measurement is accomplished by coherently driving another resonator mode, referred to as the detector mode, and measuring its response. We show that the sensitivity of such a detection scheme is directly related to the dephasing rate induced by such an intermode coupling. We show that high sensitivity is expected when the detector mode is driven into the nonlinear regime and operated close to a point where critical slowing down occurs.
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Submitted 4 November, 2005; v1 submitted 3 November, 2005;
originally announced November 2005.
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Performance of cavity-parametric amplifiers, employing Kerr nonlinearites, in the presence of two-photon loss
Authors:
Bernard Yurke,
Eyal Buks
Abstract:
Two-photon loss mechanisms often accompany a Kerr nonlinearity. The kinetic inductance exhibited by superconducting transmission lines provides an example of a Kerr-like nonlinearity that is accompanied by a nonlinear resistance of the two-photon absorptive type. Such nonlinear dissipation can degrade the performance of amplifiers and mixers employing a Kerr-like nonlinearity as the gain or mixi…
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Two-photon loss mechanisms often accompany a Kerr nonlinearity. The kinetic inductance exhibited by superconducting transmission lines provides an example of a Kerr-like nonlinearity that is accompanied by a nonlinear resistance of the two-photon absorptive type. Such nonlinear dissipation can degrade the performance of amplifiers and mixers employing a Kerr-like nonlinearity as the gain or mixing medium. As an aid for parametric amplifier design, we provide a quantum analysis of a cavity parametric amplifier employing a Kerr nonlinearity that is accompanied by a two-photon absorptive loss. Because of their usefulness in diagnostics, we obtain expressions for the pump amplitude within the cavity, the reflection coefficient for the pump amplitude reflected off of the cavity, the parametric gain, and the intermodulation gain. Expressions by which of the degree of squeezing can be computed are also presented.
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Submitted 10 November, 2005; v1 submitted 3 May, 2005;
originally announced May 2005.
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Quantum noise minimization in transistor amplifiers
Authors:
U. Gavish,
B. Yurke,
Y. Imry
Abstract:
General quantum restrictions on the noise performance of linear transistor amplifiers are used to identify the region in parameter space where the quantum-limited performance is achievable and to construct a practical procedure for approaching it experimentally using only the knowledge of directly measurable quantities: the gain, (differential) conductance and the output noise. A specific exampl…
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General quantum restrictions on the noise performance of linear transistor amplifiers are used to identify the region in parameter space where the quantum-limited performance is achievable and to construct a practical procedure for approaching it experimentally using only the knowledge of directly measurable quantities: the gain, (differential) conductance and the output noise. A specific example of resonant barrier transistors is discussed.
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Submitted 10 April, 2006; v1 submitted 27 May, 2005;
originally announced May 2005.
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Heisenberg constraints on mesoscopic and molecular amplifiers
Authors:
U. Gavish,
B. Yurke,
Y. Imry
Abstract:
Heisenberg uncertainty relations for current components impose constraints on the performance of linear amplifiers. Here we derive such constraints for amplifiers in which the input signal modulates a bias current in order to produce an amplified output. These amplifiers include transistors, macroscopic, mesoscopic, or molecular, operated as linear amplifiers.
Heisenberg uncertainty relations for current components impose constraints on the performance of linear amplifiers. Here we derive such constraints for amplifiers in which the input signal modulates a bias current in order to produce an amplified output. These amplifiers include transistors, macroscopic, mesoscopic, or molecular, operated as linear amplifiers.
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Submitted 20 July, 2004;
originally announced July 2004.
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Generalized constraints on quantum amplification
Authors:
U. Gavish,
B. Yurke,
Y. Imry
Abstract:
We derive quantum constraints on the minimal amount of noise added in linear amplification involving input or output signals whose component operators do not necessarily have c-number commutators, as is the case for fermion currents. This is a generalization of constraints derived for the amplification of bosonic fields whose components posses c-number commutators.
We derive quantum constraints on the minimal amount of noise added in linear amplification involving input or output signals whose component operators do not necessarily have c-number commutators, as is the case for fermion currents. This is a generalization of constraints derived for the amplification of bosonic fields whose components posses c-number commutators.
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Submitted 15 July, 2004;
originally announced July 2004.
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Applications of nonequilibrium Kubo formula to the detection of quantum noise
Authors:
U. Gavish,
Y. Imry,
B. Yurke
Abstract:
The Kubo fluctuation-dissipation theorem relates the current fluctuations of a system in an equilibrium state with the linear AC-conductance. This theorem holds also out of equilibrium provided that the system is in a stationary state and that the linear conductance is replaced by the (dynamic) conductance with respect to the non equilibrium state. We provide a simple proof for that statement an…
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The Kubo fluctuation-dissipation theorem relates the current fluctuations of a system in an equilibrium state with the linear AC-conductance. This theorem holds also out of equilibrium provided that the system is in a stationary state and that the linear conductance is replaced by the (dynamic) conductance with respect to the non equilibrium state. We provide a simple proof for that statement and then apply it in two cases. We first show that in an excess noise measurement at zero temperature, in which the impedance matching is maintained while driving a mesoscopic sample out of equilibrium, it is the nonsymmetrized noise power spectrum which is measured, even if the bare measurement, i.e. without extracting the excess part of the noise, obtains the symmetrized noise. As a second application we derive a commutation relation for the two components of fermionic or bosonic currents which holds in every stationary state and which is a generalization of the one valid only for bosonic currents. As is usually the case, such a commutation relation can be used e.g. to derive Heisenberg uncertainty relationships among these current components.
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Submitted 26 May, 2004; v1 submitted 12 April, 2004;
originally announced April 2004.
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What quantity is measured in an excess noise experiment?
Authors:
U. Gavish,
Y. Imry,
Y. Levinson,
B. Yurke
Abstract:
Consider a measurement in which the current coming out of a mesoscopic sample is filtered around a given frequency, amplified, measured and squared. Then this process is repeated many times and the results are averaged. Often, two such measurements are performed on the same system in and out of equilibrium (the nonequilibrium state can be obtained by a variety of methods, e.g., by applying a DC…
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Consider a measurement in which the current coming out of a mesoscopic sample is filtered around a given frequency, amplified, measured and squared. Then this process is repeated many times and the results are averaged. Often, two such measurements are performed on the same system in and out of equilibrium (the nonequilibrium state can be obtained by a variety of methods, e.g., by applying a DC voltage or electromagnetic radiation to the sample). The excess noise is defined as the difference in the noise between these two measurements. We find that this excess noise is given by the excess of the non-symmetrized power-spectrum of the current-noise. This result holds for a rather general class of experimental setups.
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Submitted 28 November, 2002;
originally announced November 2002.
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Experimental Measurement of the Persistence Exponent of the Planar Ising Model
Authors:
B. Yurke,
A. N. Pargellis,
S. N. Majumdar,
C. Sire
Abstract:
Using a twisted nematic liquid crystal system exhibiting planar Ising model dynamics, we have measured the scaling exponent $θ$ which characterizes the time evolution, $p(t) \sim t^{-θ}$, of the probability p(t) that the local order parameter has not switched its state by the time t. For 0.4 seconds to 200 seconds following the phase quench, the system exhibits scaling behavior and, measured ove…
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Using a twisted nematic liquid crystal system exhibiting planar Ising model dynamics, we have measured the scaling exponent $θ$ which characterizes the time evolution, $p(t) \sim t^{-θ}$, of the probability p(t) that the local order parameter has not switched its state by the time t. For 0.4 seconds to 200 seconds following the phase quench, the system exhibits scaling behavior and, measured over this interval, $θ= 0.19 \pm 0.031$, in good agreement with theoretical analysis and numerical simulations.
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Submitted 19 November, 1996; v1 submitted 14 November, 1996;
originally announced November 1996.