Role of quantum coherence in the thermodynamics of energy transfer

Full counting statistics and coherences: Fluctuation symmetry in heat transport with the unified quantum master equation

Recently, a "unified" quantum master equation was derived and shown to be of the Gorini-Kossakowski-Lindblad-Sudarshan form. This equation describes the dynamics of open quantum systems in a manner that forgoes the full secular approximation and retains the impact of coherences between eigenstates close in energy. We implement full counting statistics with the unified quantum master equation to investigate the statistics of energy currents through open quantum systems with nearly degenerate levels. We show that, in general, this equation gives rise to dynamics that satisfy fluctuation symmetry, a sufficient condition for the Second Law of Thermodynamics at the level of average fluxes. For systems with nearly degenerate energy levels, such that coherences build up, the unified equation is simultaneously thermodynamically consistent and more accurate than the fully secular master equation. We exemplify our results for a "V" system facilitating energy transport between two thermal baths at different temperatures. We compare the statistics of steady-state heat currents through this system as predicted by the unified equation to those given by the Redfield equation, which is less approximate but, in general, not thermodynamically consistent. We also compare results to the secular equation, where coherences are entirely abandoned. We find that maintaining coherences between nearly degenerate levels is essential to properly capture the current and its cumulants. On the other hand, the relative fluctuations of the heat current, which embody the thermodynamic uncertainty relation, display inconsequential dependence on quantum coherences.

Operational Definition of the Temperature of a Quantum State

Temperature is usually defined for physical systems at thermal equilibrium. Nevertheless one may wonder if it would be possible to attribute a meaningful notion of temperature to an arbitrary quantum state, beyond simply the thermal (Gibbs) state. In this Letter, we propose such a notion of temperature considering an operational task, inspired by the zeroth law of thermodynamics. Specifically, we define two effective temperatures for quantifying the ability of a quantum system to cool down or heat up a thermal environment. In this way we can associate an operationally meaningful notion of temperature to any quantum density matrix. We provide general expressions for these effective temperatures, for both single- and many-copy systems, establishing connections to concepts previously discussed in the literature. Finally, we consider a more sophisticated scenario where the heat exchange between the system and the thermal environment is assisted by a quantum reference frame. This leads to an effect of "coherent quantum catalysis," where the use of a coherent catalyst allows for exploiting quantum energetic coherences in the system, now leading to much colder or hotter effective temperatures. We demonstrate our findings using a two-level atom coupled to a single mode of the electromagnetic field.

Catalytic Leverage of Correlations and Mitigation of Dissipation in Information Erasure

Correlations are a valuable resource for quantum information processing and quantum thermodynamics. However, the preparation of some correlated states can carry a substantial cost that should be compared against its value. We show that classical correlations generated in information erasure can be catalytically exploited, which enables us to mitigate the resulting dissipation of heat and entropy. Because these correlations are a byproduct of erasure, they can be considered free. Our framework consists of a composition of two transformations, where an initial erasure transformation is followed by a catalytic mitigation of dissipation. Although we also show that maximum erasure with minimum dissipation and no correlations is theoretically possible, catalysts are always useful in practical erasure settings, where correlations are expected to take place.

Collective enhancement in dissipative quantum batteries

We study a quantum battery made out of N nonmutually interacting qubits coupled to a dissipative single electromagnetic field mode in a resonator. We quantify the charging energy, ergotropy, transfer rate, and power of the system, showing that collective enhancements are still present despite losses, and can even increase with dissipation. Moreover, we observe that a performance deterioration due to dissipation can be reduced by scaling up the battery size. This is useful for experimental realizations when controlling the quality of the resonator and the number of qubits are limiting factors.

Quantum Coherence of Atoms with Dipole–Dipole Interaction and Collective Damping in the Presence of an Optical Field

We investigate the effect of the interatomic distances and thermal reservoir on the coherence dynamics of the atoms considering the dipole–dipole interaction (DDI) and collective damping effect (CDE). We show that the control and protection of the coherence are very sensitive to the interatomic distances and reservoir temperature. Furthermore, we explore the distance effect between atoms and reservoir temperature on the time evolution of the total quantum correlation between the two atoms. The obtained results could be useful to execute these quantum phenomena and also considered as a good indication to implement realistic experiments with optimal conditions.

Enhancing the performance of an open quantum battery via environment engineering

We investigate the charging process of open quantum battery in the weak system-environment coupling regime. A method to improve the performance of open quantum battery in a reservoir environment, which described by a band-gap environment model or a two-Lorentzian environment model, is proposed by manipulating the spectral density of environment. We find that the optimal quantum battery, characterized by fast charging time and large ergotropy, in the band-gap environment can be obtained by increasing the weights of two Lorentzians and the spectral width of the second Lorentzian, which is in sharp contrast to the quantum battery in two-Lorentzian environment. Then we extend our discussion to multiple coupled reservoir environments, which are composed of N coupled dissipative cavities. We show that, the performance of quantum battery can be enhanced by increasing the coupling strength between the nearest-neighbor environments and decreasing the size of the environments. In particular, to fully charge and extract the total stored energy as work for quantum battery can be achieved by manipulating the coupling strength between the nearest-neighbor environments. Our results provide a practical approach for the realization of the optimal quantum batteries in future experiments.

Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath

We study a scheme of thermal management where a three-qubit system assisted with a coherent auxiliary bath (CAB) is employed to implement heat management on a target thermal bath (TTB). We consider the CAB/TTB being ensemble of coherent/thermal two-level atoms (TLAs), and within the framework of collision model investigate the characteristics of steady heat current (also called target heat current (THC)) between the system and the TTB. It demonstrates that with the help of the quantum coherence of ancillae the magnitude and direction of heat current can be controlled only by adjusting the coupling strength of system-CAB. Meanwhile, we also show that the influences of quantum coherence of ancillae on the heat current strongly depend on the coupling strength of system—CAB, and the THC becomes positively/negatively correlated with the coherence magnitude of ancillae when the coupling strength below/over some critical value. Besides, the system with the CAB could serve as a multifunctional device integrating the thermal functions of heat amplifier, suppressor, switcher and refrigerator, while with thermal auxiliary bath it can only work as a thermal suppressor. Our work provides a new perspective for the design of multifunctional thermal device utilizing the resource of quantum coherence from the CAB.

The tight Second Law inequality for coherent quantum systems and finite-size heat baths

In classical thermodynamics, the optimal work is given by the free energy difference, what according to the result of Skrzypczyk et al. can be generalized for individual quantum systems. The saturation of this bound, however, requires an infinite bath and ideal energy storage that is able to extract work from coherences. Here we present the tight Second Law inequality, defined in terms of the ergotropy (rather than free energy), that incorporates both of those important microscopic effects - the locked energy in coherences and the locked energy due to the finite-size bath. The former is solely quantified by the so-called control-marginal state, whereas the latter is given by the free energy difference between the global passive state and the equilibrium state. Furthermore, we discuss the thermodynamic limit where the finite-size bath correction vanishes, and the locked energy in coherences takes the form of the entropy difference. We supplement our results by numerical simulations for the heat bath given by the collection of qubits and the Gaussian model of the work reservoir.

Weak invariants in dissipative systems: action principle and Noether charge for kinetic theory

In non-equilibrium classical thermostatistics, the state of a system may be described by not only dynamical/thermodynamical variables but also a kinetic distribution function. This 'double structure' bears some analogy with that in quantum thermodynamics, where both dynamical variables and the Hilbert space are involved. Recently, the concept of weak invariants has repeatedly been discussed in the context of quantum thermodynamics. A weak invariant is defined in such a way that its value changes in time but its expectation value is conserved under time evolution prescribed by a kinetic equation. Here, a new aspect of a weak invariant is revealed for the classical Fokker-Planck equation as an example of classical kinetic equations. The auxiliary field formalism is applied to the construction of the action for the kinetic equation. Then, it is shown that the auxiliary field is a weak invariant and is the Noether charge. The action is invariant under the transformation generated by the weak invariant. The result may shed light on possible roles of the symmetry principle in the kinetic descriptions of non-equilibrium systems. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

Measurement Induced Synthesis of Coherent Quantum Batteries

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

Spin Isoenergetic Process and the Lindblad Equation

A general comment is made on the existence of various baths in quantum thermodynamics, and a brief explanation is presented about the concept of weak invariants. Then, the isoenergetic process is studied for a spin in a magnetic field that slowly varies in time. In the Markovian approximation, the corresponding Lindbladian operators are constructed without recourse to detailed information about the coupling of the subsystem with the environment called the energy bath. The entropy production rate under the resulting Lindblad equation is shown to be positive. The leading-order expressions of the power output and work done along the isoenergetic process are obtained.

Extractable Work, the Role of Correlations, and Asymptotic Freedom in Quantum Batteries

We investigate a quantum battery made of N two-level systems, which is charged by an optical mode via an energy-conserving interaction. We quantify the fraction of energy stored in the battery that can be extracted in order to perform thermodynamic work. We first demonstrate that this quantity is highly reduced by the presence of correlations between the charger and the battery or between the subsystems composing the battery. We then show that the correlation-induced suppression of extractable energy, however, can be mitigated by preparing the charger in a coherent optical state. We conclude by proving that the charger-battery system is asymptotically free of such locking correlations in the N→∞ limit.