The authors analyze the energy transfer in a quantum system by experimentally accessing the energy exchange statistics of a quantum system subjected to stochastic projective measurements. Employing a nitrogen-vacancy spin in diamond interacting with a tunable dissipation channel, they demonstrate the validity of the energy exchange fluctuation relation for an open system.
The authors analyze the energy transfer in a quantum system by experimentally accessing the energy exchange statistics of a quantum system subjected to stochastic projective measurements. Employing a nitrogen-vacancy spin in diamond interacting with a tunable dissipation channel, they demonstrate the validity of the energy exchange fluctuation relation for an open system.
Abstract The experimental verification of quantum fluctuation relations for driven open quantum system is currently a challenge, due to the conceptual and operative difficulty of distinguishing work and heat. The nitrogen-vacancy (NV) center in diamond has been recently proposed as a controlled test bed to study fluctuation relations in the presence of an engineered dissipative channel, in absence of work (Hernández-Gómez et al 2020 Phys. Rev. Res. 2 023327). Here, we extend those studies to exploring the validity of quantum fluctuation relations in a driven-dissipative scenario, where the spin exchanges energy both with its surroundings because of a thermal gradient, and with an external work source. We experimentally prove the validity of the quantum fluctuation relations in the presence of cyclic driving in two cases, when the spin exchanges energy with an effective infinite-temperature reservoir, and when the total work vanishes at stroboscopic times—although the power delivered to the NV center is non-null. Our results represent the first experimental study of quantum fluctuation relation in driven open quantum systems.
Engineered dynamical maps that combine not only coherent, but also unital and dissipative transformations of quantum states, have demonstrated a number of technological applications, and promise to be a beneficial tool also in quantum thermodynamic processes. Here, we exploit control of a spin qutrit to investigate energy exchange fluctuations of an open quantum system. The qutrit engineer dynamics can be understood as an autonomous feedback process, where random measurement events condition the subsequent dissipative evolution. To analyze this dynamical process, we introduce a generalization of the Sagawa-Ueda-Tasaki relation for dissipative dynamics and verify it experimentally. Not only we characterize the efficacy of the autonomous feedback protocol, but also find that the characteristic function of energy variations G(η) becomes insensitive to the process details at a single specific value of its argument. This allows us to demonstrate that a fluctuation theorem of the Jarzynski type holds for this general dissipative feedback dynamics, while previous relations were limited to unital dynamics. Moreover, in addition to the feedback efficacy, we find a witness of unitality associated with the fixed point of the dynamics.
Inspired by the idea that quantum computers can be useful in advancing basic science, we use a quantum processor to experimentally validate a number of theoretical results in non-equilibrium quantum thermodynamics, that were not (or were very little) corroborated so far.In order to do so, we first put forward a novel method to implement the so called two-point measurement scheme, which is at the basis of the study of nonequilibrium energetic exchanges in quantum systems.Like previously established methods, our method uses an ancillary system, but at variance with them, it provides direct access to the energy exchange statistics, and is, accordingly more effective, at least when applied to small quantum systems.Using a quantum computer as a remotely programmable experimental platform, we first validate our ancilla-assisted two-point measurement scheme, and then apply it to (i) experimentally verify that fluctuation theorems are robust against projective measurements, a theoretical prediction, which was not validated so far; (ii) experimentally verify the so-called heat-engine fluctuation relation, by implementing a SWAP quantum heat engine; (iii) experimentally verify that the heat-engine fluctuation relation holds for measurement-fueled quantum heat engines, by implementing the design at the basis of the so-called quantum-measurement-cooling concept.For both engines, we report the measured average heat and work exchanged and single out their operation mode.Our experiments constitute an experimental basis for the understanding of the nonequilibrium energetics of quantum computation and for the implementation of energy-management devices on quantum processors.
We experimentally explore the validity of the Jarzynski and W\'ojcik quantum heat-exchange fluctuation relation by implementing an interferometric technique in liquid-state nuclear magnetic resonance setup and study the heat-exchange statistics between two coupled spin-1/2 quantum systems. We experimentally emulate two models---(i) the XY-coupling model, containing an energy conserving interaction between the qubits, and (ii) the XX-coupling model---and analyze the regimes of validity and violation of the fluctuation symmetry when the composite system is prepared in an uncorrelated initial state with individual spins prepared in local Gibbs thermal states at different temperatures. We further extend our analysis for heat exchange by incorporating correlation in the initial state. We support our experimental findings by providing exact analytical results. Our experimental approach is general and can be systematically extended to study heat statistics for more complex out-of-equilibrium many-body quantum systems.
Energy exchange statistics between two bodies at different thermal equilibria obey the Jarzynski-Wójcik fluctuation theorem. The corresponding energy scale factor is the difference of the inverse temperatures associated to the bodies at equilibrium. In this work, we consider a dissipative quantum dynamics leading the quantum system towards a possibly nonthermal, asymptotic state. To generalize the Jarzynski-Wójcik theorem to nonthermal states, we identify a sufficient condition I for the existence of an energy scale factor η^{*} that is unique, finite, and time independent, such that the characteristic function of the energy exchange distribution becomes identically equal to 1 for any time. This η^{*} plays the role of the difference of inverse temperatures. We discuss the physical interpretation of the condition I, showing that it amounts to an almost complete memory loss of the initial state. The robustness of our results against quantifiable deviations from the validity of I is evaluated by experimental studies on a single nitrogen-vacancy center subjected to a sequence of laser pulses and dissipation.
Rapid progress in the fabrication and manipulation of micro and nanoscale devices has made it necessary to extend the concepts of thermodynamics to small systems and finally to quantum systems. In such systems the extensive thermodynamic quantities, such as entropy, heat, and work, are not described by their average values alone but by distributions. \n \nRemarkably, it has been shown that the stochastic thermodynamic variables often obey fluctuation relations which usually appear in the form of relations between exponential averages. While the two-measurement protocol of thermodynamic variables, especially work, is now well studied in closed quantum systems, there have been conceptual and experimental problems in open quantum systems. \n \nIn this thesis, we theoretically study work statistics and fluctuation relations in open quantum systems. To calculate the work statistics, we use the quantum jump method and direct master equation calculations. We show that work definitions equivalent in closed systems can lead to mutually different results in the case of open quantum systems due to a different order of approximations. Moreover, we show that the fluctuation relations can be extended to nearly adiabatically driven systems by using the adiabatic renormalization procedure. \n \nLast, we focus on how a finite size of the environment affects the dynamics and work statistics of open quantum systems. This is important from the experimental point of view because a finite-size environment allows the detection of heat exchange between the system and the environment. We derive a master equation that takes into account these effects and develop a stochastic model that unravels the master equation. We explicitly show that the finite size of the environment influences the dynamics and the work statistics. We also show that the common fluctuation relations are still valid.