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arXiv:1803.10423 · Physical Review Letters

Experimental Verification of a Jarzynski-Related Information-Theoretic Equality by a Single Trapped Ion

Tian‐Jian Xiong, L.-L. Yan, Fei Zhou, K. Rehan, Danfu Liang, Liang Chen, W. L. Yang, Zhihao Ma, Mang Feng, Vlatko Vedral

Published Jan 5, 2018• 54 citations
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Abstract

Most nonequilibrium processes in thermodynamics are quantified only by inequalities; however, the Jarzynski relation presents a remarkably simple and general equality relating nonequilibrium quantities with the equilibrium free energy, and this equality holds in both the classical and quantum regimes. We report a single-spin test and confirmation of the Jarzynski relation in the quantum regime using a single ultracold ^{40}Ca^{+} ion trapped in a harmonic potential, based on a general information-theoretic equality for a temporal evolution of the system sandwiched between two projective measurements. By considering both initially pure and mixed states, respectively, we verify, in an exact and fundamental fashion, the nonequilibrium quantum thermodynamics relevant to the mutual information and Jarzynski equality.

DOI
10.1103/physrevlett.120.010601

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Reply to comment in arXiv:1802.01382

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Here we respond to a comment [arXiv:1802.01382] submitted recently on 'Experimental Verification of a Jarzynski-Related Information-Theoretic Equality by a Single Trapped Ion' PRL 120 010601 (2018). We consider that the argument is the thermalization in a quantum system, which is different from the counterpart in conventional thermodynamics.

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Comment on “Experimental Verification of a Jarzynski-Related Information-Theoretic Equality by a Single Trapped Ion”

Michele Campisi, Peter Hänggi A

The target paper presents an experimental verification of a "Jarzynski-related" equality. We show that the latter equality is in fact not related to the Jarzynski equality.

arXiv:1802.01382•Physical Review Letters•Aug 24, 2018•3 citations
Most nonequilibrium processes in thermodynamics are quantified only by inequalities; however, the Jarzynski relation presents a remarkably simple and general equality relating nonequilibrium quantities with the equilibrium free energy, and this equality holds in both the classical and quantum regimes. We report a single-spin test and confirmation of the Jarzynski relation in the quantum regime using a single ultracold ^{40}Ca^{+} ion trapped in a harmonic potential, based on a general information-theoretic equality for a temporal evolution of the system sandwiched between two projective measurements. By considering both initially pure and mixed states, respectively, we verify, in an exact and fundamental fashion, the nonequilibrium quantum thermodynamics relevant to the mutual information and Jarzynski equality.
We derive a general information–theoretic equality for a system undergoing two projective measurements separated by a general temporal evolution. The equality implies the non-negativity of the mutual information between the measurement outcomes of the earlier and later projective measurements. We show that it also contains the Jarzynski relation between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. Our result elucidates the information–theoretic underpinning of thermodynamics and explains why the Jarzynski relation holds identically both quantumly as well as classically.
The Jarzynski equality (JE), which connects the equilibrium free energy with nonequilibrium work statistics, plays a crucial role in quantum thermodynamics. Although practical quantum systems are usually multilevel systems, most tests of the JE were executed in two-level systems. A rigorous test of the JE by directly measuring the work distribution of a physical process in a high-dimensional quantum system remains elusive. Here, we report an experimental test of the JE in a single spin-1 system. We realized nondemolition projective measurement of this three-level system via cascading high-fidelity single-shot readouts and directly measured the work distribution utilizing the two-point measurement protocol. The validity of the JE was verified from the nonadiabatic to adiabatic zone and under different effective temperatures. Our work puts the JE on a solid experimental foundation and makes the nitrogen-vacancy (NV) center system a mature toolbox to perform advanced experiments of stochastic quantum thermodynamics.
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.
The quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics.Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production.Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum relaxation processes, strongly depends on the drive-to-decay ratio and the initial state.Furthermore, we carry out experimental verification of this informationtheoretical bound by means of a single spin embedded in an ultracold trapped 40 Ca + ion.Our finding, based on a two-level model, is fundamental to any quantum thermodynamical process and indicates much difference and complexity in quantum thermodynamics with respect to the conventionally classical counterpart.