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arXiv:1806.11256 · Quantum

Coherent fluctuation relations: from the abstract to the concrete

Zoë Holmes, Sebastian Weidt, David Jennings, Janet Anders, Florian Mintert

Published Feb 25, 2019• 32 citations
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Abstract

Recent studies using the quantum information theoretic approach to thermodynamics show that the presence of coherence in quantum systems generates corrections to classical fluctuation theorems. To explicate the physical origins and implications of such corrections, we here convert an abstract framework of an autonomous quantum Crooks relation into quantum Crooks equalities for well-known coherent, squeezed and cat states. We further provide a proposal for a concrete experimental scenario to test these equalities. Our scheme consists of the autonomous evolution of a trapped ion and uses a position dependent AC Stark shift.

DOI
10.22331/q-2019-02-25-124

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Recent studies using the quantum information theoretic approach to thermodynamics show that the presence of coherence in quantum systems generates corrections to classical fluctuation theorems. To explicate the physical origins and implications of such corrections, we here convert an abstract framework of an autonomous quantum Crooks relation into quantum Crooks equalities for well-known coherent, squeezed and cat states. We further provide a proposal for a concrete experimental scenario to test these equalities. Our scheme consists of the autonomous evolution of a trapped ion and uses a position dependent AC Stark shift.
Quantum thermodynamics seeks to extend the laws of thermodynamics to equilibrium and non-equilibrium systems on the nano-scale. Over the last decade a large body of theoretical research into quantum thermodynamics has been produced; however, experimental research is yet to catch up with the impressive lead set by theory. This is especially true of quantum information theoretic approaches which have proven an effective means of incorporating quantum effects into thermodynamics but seem resistant to experimental implementation. This thesis aims to counter this shortcoming by proposing concrete physical realisations} of quantum thermodynamics to help bridge the gap between theory and experiment. This task is approached directly in chapter 2 by constructing an experimental implementation of a fluctuation relation developed from a quantum information theoretic perspective. Our proposal involves the autonomous evolution of a trapped ion and uses a tapered laser beam to implement a position dependent AC Stark shift. In order to test the fluctuation relation we convert the abstract framework of an autonomous quantum Crooks equality into quantum Crooks equalities for coherent, squeezed and cat states. These new relations highlight the physical origins and implications of coherence induced corrections to classical fluctuation relations and prompt a discussion on the interplay between coherence and irreversibility. In chapter 3 we turn our attention to Gibbs' iconic thought experiments on the work that can be extracted from the mixing of gases. Here we argue that optomechanical setups, involving a cavity in which a membrane is inserted, provide a suitable platform both to generalise such thought experiments to the quantum regime and to explore quantum thermodynamic signatures of distinguishability. We find, in contrast to classical thermodynamics, that the work that can be extracted from the mixing of the two photon gases varies continuously with their distinguishability. Finally, we demonstrate that the bunching of photons, arising from their Bosonic character, generates an energetic footprint that does not exist in classical thermodynamics.
Abstract We investigate manipulations of pure quantum states under incoherent or strictly incoherent operations assisted by a coherence battery, that is, a storage device whose degree of coherence is allowed to fluctuate in the process. This leads to the derivation of fluctuation relations for quantum coherence, analogous to Jarzynski’s and Crooks’ relations for work in thermodynamics. Coherence is thus revealed as another instance of a physical resource, in addition to athermality and entanglement, for which a connection is established between the majorisation framework (regulating pure state transformations under suitable free operations) and the emergence of fluctuation theorems. Our study is hoped to provide further insight into the general structure of battery assisted quantum resource theories, and more specifically into the interplay between quantum coherence and quantum thermodynamics.
In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum entanglement. Here we introduce the notion of a `coherent work process', and show that it is the direct extension of a work process in classical mechanics into quantum theory. This leads to the notion of `decomposable' and `non-decomposable' quantum coherence and gives a new perspective on recent results in the theory of asymmetry as well as early analysis in the theory of classical random variables. Within the context of recent fluctuation relations, originally framed in terms of quantum channels, we show that coherent work processes play the same role as their classical counterparts, and so provide a simple physical primitive for quantum coherence in such systems. We also introduce a pure state effective potential as a tool with which to analyze the coherent component of these fluctuation relations, and which leads to a notion of temperature-dependent mean coherence, provides connections with multi-partite entanglement, and gives a hierarchy of quantum corrections to the classical Crooks relation in powers of inverse temperature.
In recent years, a quantum information theoretic framework has emerged for incorporating non-classical phenomena into fluctuation relations. Here, we elucidate this framework by exploring deviations from classical fluctuation relations resulting from the athermality of the initial thermal system and quantum coherence of the system's energy supply. In particular, we develop Crooks-like equalities for an oscillator system which is prepared either in photon added or photon subtracted thermal states and derive a Jarzynski-like equality for average work extraction. We use these equalities to discuss the extent to which adding or subtracting a photon increases the informational content of a state, thereby amplifying the suppression of free energy increasing process. We go on to derive a Crooks-like equality for an energy supply that is prepared in a pure binomial state, leading to a non-trivial contribution from energy and coherence on the resultant irreversibility. We show how the binomial state equality fits in relation to a previously derived coherent state equality and offers a richer feature-set.
Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to quantum multipartite information dynamics, where both the system and the environment are multipartite without assuming any thermodynamic constraints. Based on the two-point measurement scheme and the classical probability, we establish the fluctuation theorem for the dynamics of classical multipartite mutual information. By extending to quasiprobability, we derive quantum fluctuation theorems for multipartite coherence and quantum correlations, presenting them in both integral and detailed forms. Our theoretical results are illustrated and verified using three-qubit examples, and feasible experimental verification protocols are proposed. These findings uncover the statistical structure underlying the nonequilibrium quantum information dynamics, providing fundamental insights and alternative tools for advancing quantum technologies.