arXiv subjects

Vasco Cavina

Publications and source records attributed to Vasco Cavina.

33 records · Page 2Linked to original sources

arXiv2022

Thermodynamic consistency of quantum master equations

Starting from a microscopic system-baths description, we derive the general conditions for a time-local quantum master equation (QME) to satisfy the first and second law of thermodynamics at the fluctuating level. Using counting statistics, we show that the fluctuating second law can be rephrased as a Generalized Quantum Detailed Balance condition (GQDB), i.e., a symmetry of the time-local generators which ensures the validity of the fluctuation theorem. When requiring in addition a strict system-bath energy conservation, the GQDB reduces to the usual notion of detailed balance which ensures QMEs with Gibbsian steady states. However, if energy conservation is only required on average, QMEs with non Gibbsian steady states can still maintain a certain level of thermodynamic consistency. Applying our theory to commonly used QMEs, we show that the Redfield equation breaks the GQDB, and that some recently derived approximation schemes based on the Redfield equation (which hold beyond the secular approximation and allow to derive a QME of Lindblad form) satisfy the GQDB and the average first law. We find that performing the secular approximation is the only way to ensure the first and second law at the fluctuating level.

quant-ph↗

arXiv2022

Noise-assisted and monitoring-enhanced quantum bath tagging

We analyze the capability of discriminating the statistical nature of a thermal bath by exploiting the interaction with an additional environment. We first shows that, at difference with the standard scenario where the additional environment is not present, the modified evolution induced by the mere presence of the extra bath allows to improve the discrimination task. We then also consider the possibility of continuously monitoring the additional environment and we discuss in detail how to obtain improved performances in the discrimination by considering different kinds of interaction, i.e. different jump operators, and different monitoring strategies corresponding to continuous homodyne and photo-detection. Our strategy can be in principle implemented in a circuit QED setup and paves the way to further developments of quantum probing via continuous monitoring.

quant-ph↗

arXiv2021

Maximum power heat engines and refrigerators in the fast-driving regime

We study the optimization of the performance of arbitrary periodically driven thermal machines. Within the assumption of fast modulation of the driving parameters, we derive the optimal cycle that universally maximizes the extracted power of heat engines, the cooling power of refrigerators, and in general any linear combination of the heat currents. We denote this optimal solution as ``generalized Otto cycle'' since it shares the basic structure with the standard Otto cycle, but it is characterized by a greater number of fast strokes. We bound this number in terms of the dimension of the Hilbert space of the system used as working fluid. The generality of these results allows for a widespread range of applications, such as reducing the computational complexity for numerical approaches, or obtaining the explicit form of the optimal protocols when the system-baths interactions are characterized by a single thermalization scale. In this case, we compare the thermodynamic performance of a collection of optimally driven non-interacting and interacting qubits. Remarkably, for refrigerators the non-interacting qubits perform almost as well as the interacting ones, while in the heat engine case there is a many-body advantage both in the maximum power, and in the efficiency at maximum power. Additionally, we illustrate our general results studying the paradigmatic model of a qutrit-based heat engine. Our results strictly hold in the semiclassical case in which no coherence is generated by the driving, and finally we discuss the non-commuting case.

quant-ph↗

arXiv2020

Discrimination of thermal baths by single qubit probes

Non-equilibrium states of quantum systems in contact with thermal baths help telling environments with different temperatures or different statistics apart. We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures. Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability. We also find that non-equilibrium states are not universally optimal, and detail the conditions in which it becomes convenient to wait for complete thermalisation of the probe. These concepts are illustrated in a linear optical simulation.

quant-ph↗

arXiv2020

Work statistics across a quantum phase transition

We investigate the statistics of the work performed during a quench across a quantum phase transition using the adiabatic perturbation theory. It is shown that all the cumulants of work exhibit universal scaling behavior analogous to the Kibble-Zurek scaling for the average density of defects. Two kinds of transformations are considered: quenches between two gapped phases in which a critical point is traversed, and quenches that end near the critical point. In contrast to the scaling behavior of the density of defects, the scaling behavior of the work cumulants are shown to be qualitatively different for these two kinds of quenches. However, in both cases the corresponding exponents are fully determined by the dimension of the system and the critical exponents of the transition, as in the traditional Kibble-Zurek mechanism (KZM). Thus, our study deepens our understanding about the nonequilibrium dynamics of a quantum phase transition by revealing the imprint of the KZM on the work statistics.

quant-ph↗

arXiv2019

Maximum power and corresponding efficiency for two-level heat engines and refrigerators: optimality of fast cycles

We study how to achieve the ultimate power in the simplest, yet non trivial, model of a thermal machine, namely a two-level quantum system coupled to two thermal baths. Without making any prior assumption on the protocol, via optimal control we show that, regardless of the microscopic details and of the operating mode of the thermal machine, the maximum power is universally achieved by a fast Otto-cycle like structure in which the controls are rapidly switched between two extremal values. A closed formula for the maximum power is derived, and finite-speed effects are discussed. We also analyse the associated efficiency at maximum power (EMP) showing that, contrary to universal results derived in the slow-driving regime, it can approach Carnot's efficiency, no other universal bounds being allowed.

quant-ph↗

arXiv2019

Quantum bath statistics tagging

The possibility of discriminating the statistics of a thermal bath using indirect measurements performed on quantum probes is presented. The scheme relies on the fact that, when weakly coupled with the environment of interest, the transient evolution of the probe toward its final thermal configuration, is strongly affected by the fermionic or bosonic nature of the bath excitations. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the Quantum Chernoff bound, we discuss how to achieve the greatest precision in this statistics tagging procedure, analyzing different models of probes and different initial preparations and by optimizing over the time of exposure of the probe.

quant-ph↗

arXiv2019

Optimal probabilistic work extraction beyond the free energy difference with a single-electron device

We experimentally realize protocols that allow to extract work beyond the free energy difference from a single electron transistor at the single thermodynamic trajectory level. With two carefully designed out-of-equilibrium driving cycles featuring kicks of the control parameter, we demonstrate work extraction up to large fractions of $k_BT$ or with probabilities substantially greater than 1/2, despite zero free energy difference over the cycle. Our results are explained in the framework of nonequilibrium fluctuation relations. We thus show that irreversibility can be used as a resource for optimal work extraction even in the absence of feedback from an external operator.

cond-mat.stat-mech↗

arXiv2018

Variational approach to the optimal control of coherently driven, open quantum system dynamics

Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using advanced tools from the calculus of variations and reformulating the control problem in the instantaneous Hamiltonian eigenframe, we develop a general technique for minimizing a wide class of cost functionals when the external control has access to full rotations of the system Hamiltonian. The method is then applied both to time and heat loss minimization problems and explicitly solved in the case of a two level system in contact with either bosonic or fermionic thermal environments.

quant-ph↗

arXiv2018

Entropy production and asymptotic factorization via thermalization: a collisional model approach

The Markovian evolution of an open quantum system is characterized by a positive entropy production, while the global entropy gets redistributed between the system and the environment degrees of freedom. Starting from these premises, we analyze the entropy variation of an open quantum system in terms of two distinct relations: the Clausius inequality, that provides an intrinsic bound for the entropy variation in terms of the heat absorbed by the system, and an extrinsic inequality, which instead relates the former to the corresponding entropy increment of the environment. By modeling the thermalization process with a Markovian collisional model, we compare and discuss the two bounds, showing that the latter is asymptotically saturated in the limit of large interaction time. In this regime not only the reduced density matrix of the system reaches an equilibrium configuration, but it also factorizes from the environment degrees of freedom. This last result is proven analytically when the system-bath coupling is sufficiently strong and through numerical analysis in the weak-coupling regime.

quant-ph↗

arXiv2018

Optimal thermodynamic control in open quantum systems

We apply advanced methods of control theory to open quantum systems and we determine finite-time processes which are optimal with respect to thermodynamic performances. General properties and necessary conditions characterizing optimal drivings are derived, obtaining bang-bang type solutions corresponding to control strategies switching between adiabatic and isothermal transformations. A direct application of these results is the maximization of the work produced by a generic quantum heat engine, where we show that the maximum power is directly linked to a particular conserved quantity naturally emerging from the control problem. Finally we apply our general approach to the specific case of a two level system, which can be put in contact with two different baths at fixed temperatures, identifying the processes which minimize heat dissipation. Moreover, we explicitly solve the optimization problem for a cyclic two-level heat engine driven beyond the linear-response regime, determining the corresponding optimal cycle, the maximum power, and the efficiency at maximum power.

quant-ph↗

arXiv2018

Bridging thermodynamics and metrology in non-equilibrium Quantum Thermometry

Single-qubit thermometry presents the simplest tool to measure the temperature of thermal baths with reduced invasivity. At thermal equilibrium, the temperature uncertainty is linked to the heat capacity of the qubit, however the best precision is achieved outside equilibrium condition. Here, we discuss a way to generalize this relation in a non-equilibrium regime, taking into account purely quantum effects such as coherence. We support our findings with an experimental photonic simulation.

quant-ph↗

arXiv2018

Geometrical bounds on irreversibility in open quantum systems

Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this approach can provide an upper and lower bound to the irreversible entropy production for open quantum systems as well. These provide insights on the thermodynamics of the information erasure. Limits of the applicability of our bounds are discussed, and demonstrated in a quantum photonic simulator.

quant-ph↗

arXiv2017

Slow dynamics and thermodynamics of open quantum systems

We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasi-static transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows to formally evaluate perturbations up to arbitrary order to the work and heat exchange associated to an arbitrary process. Within first order in the perturbation expansion, we identify a general formula for the efficiency at maximum power of a finite-time Carnot engine. We also clarify under which assumptions and in which limit one can recover previous phenomenological results as, for example, the Curzon-Ahlborn efficiency.

quant-ph↗

arXiv2016

Optimal processes for probabilistic work extraction beyond the second law

According to the second law of thermodynamics, for every transformation performed on a system which is in contact with an environment of fixed temperature, the extracted work is bounded by the decrease of the free energy of the system. However, in a single realization of a generic process, the extracted work is subject to statistical fluctuations which may allow for probabilistic violations of the previous bound. We are interested in enhancing this effect, i.e. we look for thermodynamic processes that maximize the probability of extracting work above a given arbitrary threshold. For any process obeying the Jarzynski identity, we determine an upper bound for the work extraction probability that depends also on the minimum amount of work that we are willing to extract in case of failure, or on the average work we wish to extract from the system. Then we show that this bound can be saturated within the thermodynamic formalism of quantum discrete processes composed by sequences of unitary quenches and complete thermalizations. We explicitly determine the optimal protocol which is given by two quasi-static isothermal transformations separated by a finite unitary quench.

quant-ph↗