arXiv subjects

E. Lutz

Publications and source records attributed to E. Lutz.

18 recordsLinked to original sources

arXiv2019

Heat and work along individual trajectories of a quantum bit

We use a near quantum limited detector to experimentally track individual quantum state trajectories of a driven qubit formed by the hybridization of a waveguide cavity and a transmon circuit. For each measured quantum coherent trajectory, we separately identify energy changes of the qubit as heat and work, and verify the first law of thermodynamics for an open quantum system. We further establish the consistency of these results by comparison with the master equation approach and the two-projective-measurement scheme, both for open and closed dynamics, with the help of a quantum feedback loop that compensates for the exchanged heat and effectively isolates the qubit.

quant-ph↗

arXiv2018

Non-equilibrium thermodynamics of continuously measured quantum systems: a circuit-QED implementation

We propose a fully operational framework to study the non-equilibrium thermodynamics of a quantum system $S$ that is coupled to a detector $D$ whose state is continuously monitored, allowing to single out individual quantum trajectories of $S$. We focus on detailed fluctuation theorems and characterize the entropy production of the system. We establish fundamental differences with respect to the thermodynamic of unmonitored, unitarily evolved systems. We consider the paradigmatic example of circuit-QED, where superconducting qubits can be coupled to a continuously monitored resonator and show numerical simulations using state of the art experimental parameters.

quant-ph↗

arXiv2018

Information gain and loss for a quantum Maxwell's demon

We use continuous weak measurements of a driven superconducting qubit to experimentally study the information dynamics of a quantum Maxwell's demon. We show how information gained by a demon who can track single quantum trajectories of the qubit can be converted into work using quantum coherent feedback. We verify the validity of a quantum fluctuation theorem with feedback by utilizing information obtained along single trajectories. We demonstrate, in particular, that quantum backaction can lead to a loss of information in imperfect measurements. We furthermore probe the transition between information gain and loss by varying the initial purity of the qubit.

quant-ph↗

arXiv2016

Aging Wiener-Khinchin Theorem and Critical Exponents of $1/f$ Noise

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum $\left\langle S_{t_m}(ω)\right\rangle$ where $t_m$ is the measurement time. For processes with an aging correlation function of the form $\left\langle I(t)I(t+τ)\right\rangle=t^Υϕ_{\rm EA}(τ/t)$, where $ϕ_{\rm EA}(x)$ is a nonanalytic function when $x$ is small, we find aging $1/f$ noise. Aging $1/f$ noise is characterized by five critical exponents. We derive the relations between the scaled correlation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of $1/f$ noise. We illustrate our results for blinking quantum dot models, single-file diffusion and Brownian motion in logarithmic potential.

cond-mat.stat-mech↗

arXiv2015

Irreversibility and the arrow of time in a quenched quantum system

Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergence, between a microscopic process and its time-reverse. Our result addresses the concept of irreversibility from a microscopic quantum standpoint.

quant-ph↗

arXiv2013

Scaling Green-Kubo relation and application to three aging systems

The Green-Kubo formula relates the spatial diffusion coefficient to the stationary velocity autocorrelation function. We derive a generalization of the Green-Kubo formula valid for systems with long-range or nonstationary correlations for which the standard approach is no longer valid. For the systems under consideration, the velocity autocorrelation function $\langle v(t+τ) v(t) \rangle$ asymptotically exhibits a certain scaling behavior and the diffusion is anomalous $\langle x^2(t) \rangle \simeq 2 D_νt^ν$. We show how both the anomalous diffusion coefficient $D_ν$ and exponent $ν$ can be extracted from this scaling form. Our scaling Green-Kubo relation thus extends an important relation between transport properties and correlation functions to generic systems with scale invariant dynamics. This includes stationary systems with slowly decaying power law correlations as well as aging systems, whose properties depend on the the age of the system. Even for systems that are stationary in the long time limit, we find that the long time diffusive behavior can strongly depend on the initial preparation of the system. In these cases, the diffusivity $D_ν$ is not unique and we determine its values for a stationary respectively nonstationary initial state. We discuss three applications of the scaling Green-Kubo relation: Free diffusion with nonlinear friction corresponding to cold atoms diffusing in optical lattices, the fractional Langevin equation with external noise recently suggested to model active transport in cells and the Lévy walk with numerous applications, in particular blinking quantum dots. These examples underline the wide applicability of our approach, which is able to treat very different mechanisms of anomalous diffusion.

cond-mat.stat-mech↗

arXiv2012

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the super-aging behavior.

cond-mat.stat-mech↗

arXiv2012

Anomalous spatial diffusion and multifractality in optical lattices

Transport of cold atoms in shallow optical lattices is characterized by slow, nonstationary momentum relaxation. We here develop a projector operator method able to derive in this case a generalized Smoluchowski equation for the position variable. We show that this explicitly non-Markovian equation can be written as a systematic expansion involving higher-order derivatives. We use the latter to compute arbitrary moments of the spatial distribution and analyze their multifractal properties.

cond-mat.stat-mech↗

arXiv2011

Fluctuations of time averages for Langevin dynamics in a binding force field

We derive a simple formula for the fluctuations of the time average around the thermal mean for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, et al. in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large non-ergodic fluctuations and show how they are related to a super-aging correlation function.

cond-mat.stat-mech↗

arXiv2011

Solution of the Fokker-Planck equation with a logarithmic potential

We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large $|x|$ using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does not fully describe the long time limit of this problem. Instead this limit is characterized by an infinite covariant density. This non-normalizable density yields the mean square displacement of the particles, which for a certain range of parameters exhibits anomalous diffusion. In a symmetric potential with an asymmetric initial condition, the average position decays anomalously slowly. This problem also has applications outside the thermal context, as in the diffusion of the momenta of atoms in optical molasses.

cond-mat.stat-mech↗

arXiv2011

Quantum Walk with Jumps

We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest neighbor but to another multi-port at a fixed distance - we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping an universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size.

quant-ph↗

arXiv2002

Anomalous diffusion and Tsallis statistics in an optical lattice

We point out a connection between anomalous quantum transport in an optical lattice and Tsallis' generalized thermostatistics. Specifically, we show that the momentum equation for the semiclassical Wigner function that describes atomic motion in the optical potential, belongs to a class of transport equations recently studied by Borland [PLA 245, 67 (1998)]. The important property of these ordinary linear Fokker--Planck equations is that their stationary solutions are exactly given by Tsallis distributions. Dissipative optical lattices are therefore new systems in which Tsallis statistics can be experimentally studied.

cond-mat.stat-mech↗

arXiv2002

Effect of initial correlations on short-time decoherence

We study the effect of initial correlations on the short-time decoherence of a particle linearly coupled to a bath of harmonic oscillators. We analytically evaluate the attenuation coefficient of a Schroedinger cat state both for a free and a harmonically bound particle, with and without initial thermal correlations between the particle and the bath. While short-time decoherence appears to be independent of the system in the absence of initial correlations, we find on the contrary that, for initial thermal correlations, decoherence becomes system dependent even for times much shorter than the characteristic time of the system. The temperature behavior of this system dependence is discussed.

cond-mat.mes-hall↗

arXiv2002

Noise-assisted classical adiabatic pumping in a symmetric periodic potential

We consider a classical overdamped Brownian particle moving in a symmetric periodic potential. We show that a net particle flow can be produced by adiabatically changing two external periodic potentials with a spatial and a temporal phase difference. The classical pumped current is found to be independent of the friction and to vanish both in the limit of low and high temperature. Below a critical temperature, adiabatic pumping appears to be more efficient than transport due to a constant external force.

cond-mat.stat-mech↗

arXiv2001

Anomalous Levy decoherence

We investigate the decoherence of a small quantum system weakly coupled to a complex, chaotic environment when the dynamics is not Gaussian but Levy anomalous. By studying the time dependence of the linear entropy and the damping of the interference of two Gaussian wave packets in the Wigner representation, we show that the decoherence time for a quantum Levy stable process is always smaller than for Gaussian diffusion.

cond-mat.stat-mech↗

arXiv2001

Fractional Langevin equation

We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffusion exhibit the same power-law behavior. Here we show that their lowest moments are actually all identical, except the second moment of the velocity. This provides a simple criterion which enables to distinguish these two non-Markovian processes.

cond-mat.stat-mech↗

arXiv2000

Fractional transport equations for Levy stable processes

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a Brownian system subjected to a Levy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limit of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the Smoluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equations recently proposed are clarified.

cond-mat.stat-mech↗

arXiv2000

Anomalous diffusion through coupling to a fractal environment: Microscopic derivation of the "whip-back" effect

Two models for quantum Brownian motion - the Oscillator Bath (OB) model and the Random-Band-Matrix (RBM) model - are compared and a relation between the spectral density function I(w) and the variance (Vab)^2 is established. The extension to a fractal environment is then considered and the microscopic origin of anomalous diffusion is discussed. In particular, it is shown that the asymptotic behavior of the normalized velocity auto-correlation function (VACF) is entirely determined by the band form factor. This allows for a microscopic derivation of the "whip-back" effect.

cond-mat.stat-mech↗