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arXiv:2104.13427 · Quantum Science and Technology

Nonequilibrium fluctuations of a quantum heat engine

Tobias Denzler, Jonas F. G. Santos, Eric Lutz, Roberto M. Serra

Published Aug 1, 2024• 17 citations
arXivHTMLPDF

Abstract

Abstract The thermodynamic properties of quantum heat engines are stochastic owing to the presence of thermal and quantum fluctuations. We here experimentally investigate the efficiency and nonequilibrium entropy production statistics of a spin-1/2 quantum Otto cycle in a nuclear magnetic resonance setup. We first study the correlations between work and heat within a cycle by extracting their joint distribution for different driving times. We show that near perfect correlation, corresponding to the tight-coupling condition between work and heat, can be achieved. In this limit, the reconstructed efficiency distribution is peaked at the deterministic thermodynamic efficiency, and fluctuations are strongly suppressed. We further successfully test the second law in the form of a joint fluctuation relation for work and heat in the quantum cycle. Our results characterize the statistical features of a small-scale thermal machine in the quantum domain, and provide means to control them.

DOI
10.1088/2058-9565/ad6287

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Abstract The thermodynamic properties of quantum heat engines are stochastic owing to the presence of thermal and quantum fluctuations. We here experimentally investigate the efficiency and nonequilibrium entropy production statistics of a spin-1/2 quantum Otto cycle in a nuclear magnetic resonance setup. We first study the correlations between work and heat within a cycle by extracting their joint distribution for different driving times. We show that near perfect correlation, corresponding to the tight-coupling condition between work and heat, can be achieved. In this limit, the reconstructed efficiency distribution is peaked at the deterministic thermodynamic efficiency, and fluctuations are strongly suppressed. We further successfully test the second law in the form of a joint fluctuation relation for work and heat in the quantum cycle. Our results characterize the statistical features of a small-scale thermal machine in the quantum domain, and provide means to control them.
Developments in the thermodynamics of small quantum systems envisage nonclassical thermal machines. In this scenario, energy fluctuations play a relevant role in the description of irreversibility. We experimentally implement a quantum heat engine based on a spin-1/2 system and nuclear magnetic resonance techniques. Irreversibility at a microscope scale is fully characterized by the assessment of energy fluctuations associated with the work and heat flows. We also investigate the efficiency lag related to the entropy production at finite time. The implemented heat engine operates in a regime where both thermal and quantum fluctuations (associated with transitions among the instantaneous energy eigenstates) are relevant to its description. Performing a quantum Otto cycle at maximum power, the proof-of-concept quantum heat engine is able to reach an efficiency for work extraction (η≈42%) very close to its thermodynamic limit (η=44%).
In this work we study the effect of quantum and thermal fluctuations on the statistics of quantum heat engine performance parameters, like efficiency and power. We begin by deriving an explicit solution for the characteristic function of the heat distribution of a thermal quantum harmonic oscillator. We then derive a general framework based on the standard two-point-measurement scheme to compute the efficiency distribution of a quantum Otto cycle. We analyze the generic properties of this distribution for scale-invariant driving Hamiltonians which describe a large class of single-particle, many-body, and nonlinear systems. We find that the efficiency is deterministic and that its mean is equal to the macroscopic efficiency for adiabatic driving. We continue our research by studying the efficiency large deviation function of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto cycles. While the efficiency statistics follow the ’universal’ theory of Verley et al. [Nature Commun. 5, 4721 (2014)] for nonadiabatic driving, we find that the latter framework does not apply in the adiabatic regime. We can relate this unusual property to the perfect anticorrelation between work output and heat input that suppresses thermal as well as quantum fluctuations. We then probe our findings in an experimental NMR setup using spin-1/2 systems and find them to agree rather well with our theoretical predictions. Afterward, we move on to the finite-time quantum Carnot cycle and investigate its power fluctuations. In particular, we consider how level degeneracy and level number, two commonly found properties in quantum systems, influence the relative work fluctuations. We find that their optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results highlight that these parameters can be employed to realize high-performance, high-stability cyclic quantum heat engines.
Abstract The efficiency of small thermal machines is typically a fluctuating quantity. We here study the efficiency large deviation properties of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto motors. To this end, we analytically compute their joint characteristic functions for heat and work based on the two-projective-measurement approach. We investigate work–heat correlations within the respective engine cycles and find, for generic scale-invariant quantum heat engines, that work and heat are perfectly anticorrelated for adiabatic driving. In this limit, the effects of thermal as well as quantum fluctuations are suppressed, the large deviation functions are singular and the stochastic efficiency is equal to the macroscopic efficiency.
The efficiency of quantum heat engines is a stochastic quantity owing to the presence of thermal and quantum fluctuations.We here extend the standard two-projective-measurement scheme to derive the efficiency distribution of a quantum Otto engine.We analyze the generic properties of this distribution for scale-invariant driving Hamiltonians which describe a large class of single-particle, many-body, and nonlinear systems.We find that the mean efficiency is equal to the macroscopic efficiency for adiabatic driving.It generally diverges for nonadiabatic driving when no heat is absorbed while work is produced.We further compute the quantum efficiency statistics for an analytically solvable two-level engine and investigate its classical-to-quantum transition.
The efficiency of small thermal machines is typically a fluctuating quantity. We here study the efficiency large deviation properties of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto motors. To this end, we analytically compute their joint characteristic functions for heat and work based on the two-projective-measurement approach. We investigate work–heat correlations within the respective engine cycles and find, for generic scale-invariant quantum heat engines, that work and heat are perfectly anticorrelated for adiabatic driving. In this limit, the effects of thermal as well as quantum fluctuations are suppressed, the large deviation functions are singular and the stochastic efficiency is equal to the macroscopic efficiency.
The fast-developing quantum technology is propelling thermal machine, which lies at the heart of thermodynamics, into a new golden era. Being stochastic because of the non-negligible thermal and quantum fluctuations, the efficiency and power of a finite-time quantum heat engine exhibit a trade-off, preventing the simultaneous achievement of high power and high efficiency. Conventional studies treat the statistics of a heat engine by assuming canonical thermalization, which is valid only under weak-coupling conditions. We here investigate the noncanonical effect on the statistics of the efficiency and power for a finite-time quantum Otto cycle. It is revealed that their average values and variances are highly controllable by engineering the energy spectrum structure of the composite system consisting of the working substance and the bath. Near the quantum critical point induced by the formation of a bound state in the energy spectrum, the average efficiency and power can be boosted simultaneously, meanwhile, both of their variances are decreased. Deepening our understanding of the usefulness of quantum reservoir engineering in thermodynamics, our result lays the foundation for the realization of efficient and stable quantum energy devices.