Eric Lutz

Experimental verification of Landauer/'s principle linking information and thermodynamics

In 1961, Rolf Landauer argued that the erasure of information is a dissipative process. A minimal quantity of heat, proportional to the thermal energy and called the Landauer bound, is necessarily produced when a classical bit of information is deleted. A direct consequence of this logically irreversible transformation is that the entropy of the environment increases by a finite amount. Despite its fundamental importance for information theory and computer science, the erasure principle has not been verified experimentally so far, the main obstacle being the difficulty of doing single-particle experiments in the low-dissipation regime. Here we experimentally show the existence of the Landauer bound in a generic model of a one-bit memory. Using a system of a single colloidal particle trapped in a modulated double-well potential, we establish that the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles. This result demonstrates the intimate link between information theory and thermodynamics. It further highlights the ultimate physical limit of irreversible computation.

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 subdiffusion 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 that enable us to distinguish these two non-Markovian processes.

Fluctuation theorems : Work is not an observable

The characteristic function of the work performed by an external time-dependent force on a Hamiltonian quantum system is identified with the time-ordered correlation function of the exponentiated systems Hamiltonian. A similar expression is obtained for the averaged exponential work which is related to the free energy difference of equilibrium systems by the Jarzynski work theorem.

Quantum speed limit for non-Markovian dynamics.

We derive a Margolus-Levitin-type bound on the minimal evolution time of an arbitrarily driven open quantum system. We express this quantum speed limit time in terms of the operator norm of the nonunitary generator of the dynamics. We apply these results to the damped Jaynes-Cummings model and demonstrate that the corresponding bound is tight. We further show that non-Markovian effects can speed up quantum evolution and therefore lead to a smaller quantum speed limit time.

A single atom heat engine

Making a teeny tiny engine Steam locomotives, cars, and the drinking bird toy all convert heat into useful work as it cycles between two reservoirs at different temperatures. Usually, the working substance where the heat-work conversion occurs is a liquid or a gas, consisting of many molecules. Roβnagel et al. have made a working substance of a single calcium ion in a tapered ion trap. A laser-cooling beam plays the part of a cold reservoir for the calcium ion, and in turn, electric field noise acts as a hot reservoir. Science, this issue p. 325 A calcium ion held in a tapered trap is used as the working substance of a tiny thermodynamic engine. Heat engines convert thermal energy into mechanical work and generally involve a large number of particles. We report the experimental realization of a single-atom heat engine. An ion is confined in a linear Paul trap with tapered geometry and driven thermally by coupling it alternately to hot and cold reservoirs. The output power of the engine is used to drive a harmonic oscillation. From direct measurements of the ion dynamics, we were able to determine the thermodynamic cycles for various temperature differences of the reservoirs. We then used these cycles to evaluate the power P and efficiency η of the engine, obtaining values up to P = 3.4 × 10–22 joules per second and η = 0.28%, consistent with analytical estimations. Our results demonstrate that thermal machines can be reduced to the limit of single atoms.

Single-Ion Heat Engine at Maximum Power

O. Abah, J. Roßnagel, G. Jacob, S. Deffner, 3 F. Schmidt-Kaler, K. Singer, and E. Lutz 4 Department of Physics, University of Augsburg, D-86159 Augsburg, Germany Institut für Quantenphysik, Universität Mainz, 55128 Mainz, Germany Department of Chemistry and Biochemistry and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742, USA Dahlem Center for Complex Quantum Systems, FU Berlin, D-14195 Berlin, Germany

Energetics of quantum correlations

We consider a photo-Carnot engine that consists of a single-mode radiation field in an optical cavity. One the heat reservoirs is made of a beam of thermally entangled pairs of two-level atoms that interact resonantly with the cavity. We express the thermodynamic efficiency of the engine in terms of the quantum discord of the atomic pair and find that it can exceed its classical value. Our results show that useful work can be extracted from quantum correlations, indicating that the latter are a valuable resource in quantum thermodynamics.

Generalized clausius inequality for nonequilibrium quantum processes.

We show that the nonequilibrium entropy production for a driven quantum system is larger than the Bures length, the geometric distance between its actual state and the corresponding equilibrium state. This universal lower bound generalizes the Clausius inequality to arbitrary nonequilibrium processes beyond linear response. We further derive a fundamental upper bound for the quantum entropy production rate and discuss its connection to the Bremermann-Bekenstein bound.

Employing trapped cold ions to verify the quantum Jarzynski equality.

We propose a scheme to investigate the nonequilibrium work distribution of a quantum particle under well controlled transformations of the external potential, exploiting the versatility of a single ion in a segmented linear Paul trap. We describe in detail how the motional quantum state of a single ion can be prepared, manipulated, and finally readout to fully determine the free energy difference in both harmonic and anharmonic potentials. Uniquely to our system, we show how an ion may be immersed in an engineered laser-field reservoir. Trapped ions therefore represent an ideal tool for investigating the Jarzynski equality in open and closed quantum systems.

Energy–time uncertainty relation for driven quantum systems

We derive generalizations of the energy–time uncertainty relation for driven quantum systems. Using a geometric approach based on the Bures length between mixed quantum states, we obtain explicit expressions for the quantum speed limit time, valid for arbitrary initial and final quantum states and arbitrary unitary driving protocols. Our results establish the fundamental limit on the rate of evolution of closed quantum systems.