Heat and Work Along Individual Trajectories of a Quantum Bit

Experimental Verification of Demon-Involved Fluctuation Theorems

The limit of energy saving in the control of small systems has recently attracted much interest due to the concept refinement of the Maxwell demon. Inspired by a newly proposed set of fluctuation theorems, we report the first experimental verification of these equalities and inequalities in an ultracold ^{40}Ca^{+} ion system, confirming the intrinsic nonequilibrium in the system due to involvement of the demon. Based on elaborately designed demon-involved control protocols, such as the Szilard engine protocol, we provide experimentally quantitative evidence of the dissipative information and observe tighter bounds of both the extracted work and the demon's efficacy than the limits predicted by the Sagawa-Ueda theorem. Our results substantiate a close connection between the physical nature of information and nonequilibrium processes at the microscale, which help to further understand the thermodynamic characteristics of information and the optimal design of nanoscale and smaller systems.

Lie Algebraic Quantum Phase Reduction

We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schrödinger equation. Because a perturbation is represented by unitary transformation in quantum dynamics, we calculate phase response curves with respect to generators of a Lie algebra. Our method shows that the continuous measurement yields phase clusters and alters the phase response curves. The observable clusters capture the phase dynamics of individual quantum oscillators, unlike indirect indicators obtained from density operators. Furthermore, our method can be applied to finite-level systems that lack classical counterparts.

Single-energy-measurement integral fluctuation theorem and nonprojective measurements

We study a Jarzysnki-type equality for work in systems that are monitored using nonprojective unsharp measurements. The information acquired by the observer from the outcome f of an energy measurement and the subsequent conditioned normalized state ρ[over ̂](t,f) evolved up to a final time t are used to define work, as the difference between the final expectation value of the energy and the result f of the measurement. The Jarzynski equality obtained depends on the coherences that the state develops during the process, the characteristics of the meter used to measure the energy, and the noise it induces into the system. We analyze those contributions in some detail to unveil their role. We show that in very particular cases, but not in general, the effect of such noise gives a factor multiplying the result that would be obtained if projective measurements were used instead of nonprojective ones. The unsharp character of the measurements used to monitor the energy of the system, which defines the resolution of the meter, leads to different scenarios of interest. In particular, if the distance between neighboring elements in the energy spectrum is much larger than the resolution of the meter, then a similar result to the projective measurement case is obtained, up to a multiplicative factor that depends on the meter. A more subtle situation arises in the opposite case in which measurements may be noninformative, i.e., they may not contribute to update the information about the system. In this case a correction to the relation obtained in the nonoverlapping case appears. We analyze the conditions in which such a correction becomes negligible. We also study the coherences, in terms of the relative entropy of coherence developed by the evolved post-measurement state. We illustrate the results by analyzing a two-level system monitored by a simple meter.

Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines

We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

Measurement-Based Quantum Thermal Machines with Feedback Control

We investigated coupled-qubit-based thermal machines powered by quantum measurements and feedback. We considered two different versions of the machine: (1) a quantum Maxwell's demon, where the coupled-qubit system is connected to a detachable single shared bath, and (2) a measurement-assisted refrigerator, where the coupled-qubit system is in contact with a hot and cold bath. In the quantum Maxwell's demon case, we discuss both discrete and continuous measurements. We found that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further found that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we used continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We found that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.

Nonequilibrium thermodynamics in cavity optomechanics

Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium. As an emerging field, nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes, particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations. Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability, excellent mechanical performance, and ability to operate deep in the quantum regime. Here, we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems. The experimental results in entropy production assessment, fluctuation theorems, heat transfer, and heat engines are highlighted.

Energetics of a Single Qubit Gate

Qubits are physical, a quantum gate thus not only acts on the information carried by the qubit but also on its energy. What is then the corresponding flow of energy between the qubit and the controller that implements the gate? Here we exploit a superconducting platform to answer this question in the case of a quantum gate realized by a resonant drive field. During the gate, the superconducting qubit becomes entangled with the microwave drive pulse so that there is a quantum superposition between energy flows. We measure the energy change in the drive field conditioned on the outcome of a projective qubit measurement. We demonstrate that the drive's energy change associated with the measurement backaction can exceed by far the energy that can be extracted by the qubit. This can be understood by considering the qubit as a weak measurement apparatus of the driving field.

Experimental Verification of Dissipation-Time Uncertainty Relation

Dissipation is vital to any cyclic process in realistic systems. Recent research focus on nonequilibrium processes in stochastic systems has revealed a fundamental trade-off, called dissipation-time uncertainty relation, that entropy production rate associated with dissipation bounds the evolution pace of physical processes [Phys. Rev. Lett. 125, 120604 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.120604]. Following the dissipative two-level model exemplified in the same Letter, we experimentally verify this fundamental trade-off in a single trapped ultracold ^{40}Ca^{+} ion using elaborately designed dissipative channels, along with a postprocessing method developed in the data analysis, to build the effective nonequilibrium stochastic evolutions for the energy transfer between two heat baths mediated by a qubit. Since the dissipation-time uncertainty relation imposes a constraint on the quantum speed regarding entropy flux, our observation provides the first experimental evidence confirming such a speed restriction from thermodynamics on quantum operations due to dissipation, which helps us further understand the role of thermodynamical characteristics played in quantum information processing.

Joint statistics of work and entropy production along quantum trajectories

In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the stochastic level by unravelling the system's evolution in terms of quantum jump trajectories. We here derive a general formula for computing the joint statistics of work and entropy production in Markovian driven quantum systems, whose instantaneous steady states are of Gibbs form. If the driven system remains close to the instantaneous Gibbs state at all times, then we show that the corresponding two-variable cumulant generating function implies a joint detailed fluctuation theorem so long as detailed balance is satisfied. As a corollary, we derive a modified fluctuation-dissipation relation (FDR) for the entropy production alone, applicable to transitions between arbitrary steady states, and for systems that violate detailed balance. This FDR contains a term arising from genuinely quantum fluctuations, and extends an analogous relation from classical thermodynamics to the quantum regime.

Thermodynamic Uncertainty Relation in Slowly Driven Quantum Heat Engines

Thermodynamic uncertainty relations express a trade-off between precision, defined as the noise-to-signal ratio of a generic current, and the amount of associated entropy production. These results have deep consequences for autonomous heat engines operating at steady state, imposing an upper bound for their efficiency in terms of the power yield and its fluctuations. In the present Letter we analyze a different class of heat engines, namely, those which are operating in the periodic slow-driving regime. We show that an alternative TUR is satisfied, which is less restrictive than that of steady-state engines: it allows for engines that produce finite power, with small power fluctuations, to operate close to reversibility. The bound further incorporates the effect of quantum fluctuations, which reduces engine efficiency relative to the average power and reliability. We finally illustrate our findings in the experimentally relevant model of a single-ion heat engine.

Unconditional Preparation of Squeezed Vacuum from Rabi Interactions

Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation, and communication. Here, we propose a method for the generation of very good approximations to highly squeezed vacuum states with low excess antisqueezing using only a few oscillator-qubit coupling gates through a Rabi-type interaction Hamiltonian. This interaction can be implemented with several different methods, which has previously been demonstrated in superconducting circuit and trapped-ion platforms. The protocol is compatible with other protocols manipulating quantum harmonic oscillators, thus facilitating scalable continuous-variable fault-tolerant quantum computation.

Experimental Assessment of Entropy Production in a Continuously Measured Mechanical Resonator

The information on a quantum process acquired through measurements plays a crucial role in the determination of its nonequilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate for a continuously monitored mesoscopic quantum system. We consider an optomechanical system subjected to continuous displacement Gaussian measurements and characterize the entropy production rate of the individual trajectories followed by the system in its stochastic dynamics, employing a phase-space description in terms of the Wigner entropy. Owing to the specific regime of our experiment, we are able to single out the informational contribution to the entropy production arising from conditioning the state on the measurement outcomes. Our experiment embodies a significant step towards the demonstration of full-scale control of fundamental thermodynamic processes at the mesoscopic quantum scale.

Topological transition in measurement-induced geometric phases

The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states-a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement.