Abstract
Elucidating the energy transfer between a quantum system and a reservoir is a central issue in quantum non-equilibrium thermodynamics, which could provide novel tools to engineer quantum-enhanced heat engines. The lack of information on the reservoir inherently limits the practical insight that can be gained on the exchange process of open quantum systems. Here, we investigate the energy transfer for an open quantum system in the framework of quantum fluctuation relations. As a novel toolbox, we employ a nitrogen-vacancy center spin qubit in diamond, subject to repeated quantum projective measurements and a tunable dissipation channel. In the presence of energy fluctuations originated by dissipation and quantum projective measurements, the experimental results, supplemented by numerical simulations, show the validity of the energy exchange fluctuation relation, where the energy scale factor encodes missing reservoir information in the system out-of-equilibrium steady state properties. This result is complemented by a theoretical argument showing that, also for an open three-level quantum system, the existence of an out-of-equilibrium steady state dictates a unique time-independent value of the energy scale factor for which the fluctuation relation is verified. Our findings pave the way to the investigation of energy exchange mechanisms in arbitrary open quantum systems.
Highlights
The connection among statistical properties of out-ofequilibrium dynamical systems, thermodynamics quantities, and information theory has been deeply investigated in classical and quantum systems and codified in terms of fluctuation relations [1,2,3,4,5,6,7]
We explored the quantum exchange fluctuation relation for an open quantum system coupled to a tunable dissipative channel
We investigated the interplay between quantum projective measurements and a dissipation channel, and we proposed a formulation of the energy exchange fluctuation relation, where the energy scaling factor depends on the populations of the stationary density matrix reached by the open quantum system
Summary
The connection among statistical properties of out-ofequilibrium dynamical systems, thermodynamics quantities, and information theory has been deeply investigated in classical and quantum systems and codified in terms of fluctuation relations [1,2,3,4,5,6,7]. The Jarzynski equality [18,19] relates the exponentiated negative work done on a system, averaged over a statistically relevant ensemble of realizations of the system dynamics, with the change in the free energy between two equilibrium thermal states This framework has been extended to describe the transport of energy and matter between different systems with different temperatures and chemical potentials [20,21]. The fluctuation relations can be recast in terms of the characteristic function— Fourier transform of the probability distribution function— of the considered nonequilibrium quantity This contains the full information about the fluctuations statistics and is obtained from two-time quantum correlations rather than by a. Our results are representative of quantum systems with dimension larger than two subjected to dissipation dynamics
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