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arXiv:2207.14325

Probing coherent quantum thermodynamics using a trapped ion

O. Onishchenko, G. Guarnieri, Pablo Rosillo-Rodes, D. R. M. Pijn, Janine Hilder, Ulrich Poschinger, Martí Perarnau-Llobet, Jens Eisert, Ferdinand Schmidt‐Kaler

Published Jul 28, 2022• 1 citation
arXivHTMLPDF

Abstract

Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, a regime in which coherences and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work, we report an experimental measurement of the genuine quantum correction to the classical work fluctuation-dissipation relation (FDR). We employ a single trapped ion qubit, realizing thermalization and coherent drive via laser pulses, to implement a quantum coherent work protocol. The results from a sequence of two-time work measurements display agreement with the recently proven quantum work FDR, violating the classical FDR by more than $10.9$ standard deviations. We furthermore determine that our results are incompatible with any SPAM error-induced correction to the FDR by more than 10 standard deviations. Finally, we show that the quantum correction vanishes in the high-temperature limit, again in agreement with theoretical predictions.

DOI
10.48550/arxiv.2207.14325

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Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, a regime in which coherences and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work, we report an experimental measurement of the genuine quantum correction to the classical work fluctuation-dissipation relation (FDR). We employ a single trapped ion qubit, realizing thermalization and coherent drive via laser pulses, to implement a quantum coherent work protocol. The results from a sequence of two-time work measurements display agreement with the recently proven quantum work FDR, violating the classical FDR by more than 10.910.910.9 standard deviations. We furthermore determine that our results are incompatible with any SPAM error-induced correction to the FDR by more than 10 standard deviations. Finally, we show that the quantum correction vanishes in the high-temperature limit, again in agreement with theoretical predictions.
Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, where coherence and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work, we demonstrate the possibility to experimentally measure and benchmark a genuine quantum correction, induced by quantum friction, to the classical work fluctuation-dissipation relation. This is achieved by combining laser-induced coherent Hamiltonian rotations and energy measurements on a trapped ion. Our results demonstrate that recent developments in stochastic quantum thermodynamics can be used to benchmark and unambiguously distinguish genuine quantum coherent signatures generated along driving protocols, even in presence of experimental SPAM errors and, most importantly, beyond the regimes for which theoretical predictions are available (e.g., in slow driving).
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Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.
Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.
An important result in classical stochastic thermodynamics is the work fluctuation-dissipation relation (FDR), which states that the dissipated work done along a slow process is proportional to the resulting work fluctuations. We show that slowly driven quantum systems violate this FDR whenever quantum coherence is generated along the protocol, and we derive a quantum generalization of the work FDR. The additional quantum terms in the FDR are found to lead to a non-Gaussian work distribution. Fundamentally, our result shows that quantum fluctuations prohibit finding slow protocols that minimize both dissipation and fluctuations simultaneously, in contrast to classical slow processes. Instead, we develop a quantum geometric framework to find processes with an optimal trade-off between the two quantities.
The thermodynamic uncertainty relation (TUR) imposes a fundamental constraint between current fluctuations and entropy production, providing a refined formulation of the second law for micro- and nanoscale systems. Quantum violations of the classical TUR reveal genuinely quantum thermodynamic effects, which are essential for improving performance and enabling optimization in quantum technologies. In this work, we analyze the TUR in a class of paradigmatic quantum thermal-machine models whose operation is enabled by coherent coupling between two energy levels forming a virtual qubit. Steady-state coherences are confined to this virtual-qubit subspace, while in the absence of coherent coupling the system satisfies detailed balance with the thermal reservoirs and supports no steady-state heat currents. We show that the steady-state currents and entropy production can be fully reproduced by an effective classical Markov process, whereas current fluctuations acquire an additional purely quantum correction originating from coherence. As a result, the thermodynamic uncertainty naturally decomposes into a classical (diagonal) contribution and a coherent contribution. The latter becomes negative under resonant conditions and reaches its minimum at the coupling strength that maximizes steady-state coherence. We further identify the conditions for minimizing the thermodynamic uncertainty, and the criteria for surpassing the classical TUR bound in the vicinity of the reversible limit.