A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that this additional energetic cost leads to a stronger bound on the work extractable after a single measurement from a system initially in thermal equilibrium [Phys. Rev. A 80, 012322 (2009)]. Here, we extend this bound to a large class of feedback-driven quantum engines operating periodically and in finite time. The bound thus implies a natural definition for the efficiency of information to work conversion in such devices. For a simple model consisting of a laser-driven two-level system, we maximize the efficiency with respect to the observable whose measurement is used to control the feedback operations. We find that the optimal observable typically does not commute with the Hamiltonian and hence would not be available in a classical two level system. This result reveals that periodic feedback engines operating in the quantum realm can exploit quantum coherences to enhance efficiency.
The impacts of quantum coherence on nonequilibrium thermodynamics become observable by dividing the heat and work into the conventional diagonal part and the other part relaying on the superpositions and the time derivative of Hamiltonian. Specializing to exactly-solvable dynamics of Larmor precession, we build a quantum Otto heat engine employing magnetic-driven atomic rotations. The coherence induced by the population transition guarantees the positive work output when the control protocol is time dependent. The time-dependent control of a quantum heat engine implements the correspondence be…
We show that quantum coherence can enhance the performance of a continuous quantum heat engine in the Lindblad description. We investigate the steady-state solutions of the particle-exchanging quantum heat engine, composed of degenerate double quantum dots coupled to two heat baths in parallel, where quantum coherence may be induced due to interference between relaxation channels. We find that the engine power can be enhanced by the coherence in the nonlinear response regime, when the symmetry of coupling configurations between dots and two baths is broken. In the symmetric case, the coherence…
We introduce a universal scheme to divide the power output of a periodically driven quantum heat engine into a classical contribution and one stemming solely from quantum coherence. Specializing to Lindblad-dynamics and small driving amplitudes, we derive general upper bounds on both, the coherent and the total power. These constraints imply that, in the linear-response regime, coherence inevitably leads to power losses. To illustrate our general analysis, we explicitly work out the experimentally relevant example of a single-qubit engine.
For self-sustained oscillators subject to noise the coherence, understood as a constancy of the instantaneous oscillation frequency, is one of the primary characteristics. The delayed feedback has been previously revealed to be an efficient tool for controlling coherence of noise-driven self-sustained oscillator. The effect of the delayed feedback control on coherence is stronger for a longer delay time. Meanwhile, the instantaneous frequency of a noise-free oscillator can exhibit multistability for long delay time. The impact of the delay-feedback--induced multistability on the oscillation co…
For noisy self-sustained oscillators, both reliability, stability of a response to a noisy driving, and coherence understood in the sense of constancy of oscillation frequency belong to the main characteristics. Though the both characteristics and techniques for controlling them received great attention of researchers, owing to their importance for neurons, lasers, clocks, electric generators, etc., these characteristics were previously considered separately. In this paper, strong quantitative relation between coherence and reliability is revealed for a limit cycle oscillator subject to a weak…
We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest to feedback with multiple (incommensurable) delay times: (1) two delay times provide more flexibility in control than the single one; (2) some dynamic systems posses an inherent internal delay (e.g., traveling-wave tube), and the introducing of the second delayed feedback is a natural measure for dealing with stray effects brought about by the inherent one.…
Thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and post-selection must be considered in the backwa…
We present a detailed thermodynamic analysis of a three-level quantum heat engine coupled continuously to hot and cold reservoirs. The system is driven by an oscillating external field and is described by the Markovian quantum master equation. We use the general form of the dissipator which is consistent with thermodynamics. We calculate the heat, power, and efficiency of the system for the heat-engine operating regime and also examine the thermodynamic uncertainty relation. The efficiency of the system is strongly dependent on the structure of the dissipator, and the correlations between diff…
The introduction of the quantum analogue of a Carnot engine based on a bath comprising of particles with a small amount of coherence initiated an active line of research on the harnessing of different quantum resources for the enhancement of thermal machines beyond the standard reversible limit, with an emphasis on non-thermal baths containing quantum coherence. In our work, we investigate the impact of coherence on the thermodynamic tasks of a collision model which is composed of a system interacting, in the continuous time limit, with a series of coherent ancillas of two baths at different t…
The heat engine, a machine that extracts useful work from thermal sources, is one of the basic theoretical constructs and fundamental applications of classical thermodynamics. The classical description of a heat engine does not include coherence in its microscopic degrees of freedom. By contrast, a quantum heat engine might possess coherence between its internal states. Although the Carnot efficiency cannot be surpassed, and coherence can be performance degrading in certain conditions, it was recently predicted that even when using only thermal resources, internal coherence can enable a quantu…
Feedback can be utilized to convert information into useful work, making it an effective tool for increasing the performance of thermodynamic engines. Using feedback reversibility as a guiding principle, we devise a method for designing optimal feedback protocols for thermodynamic engines that extract all the information gained during feedback as work. Our method is based on the observation that in a feedback-reversible process the measurement and the time-reversal of the ensuing protocol both prepare the system in the same probabilistic state. We illustrate the utility of our method with two …
The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics. In particular, we will show that rather the definition of heat has to be modified to account for the thermodynamic cost for maintaining coherence and entanglement. Our theoretical findings are numerically illus…
We show that finite system-reservoir coupling imposes a distinct quantum limit on the performance of a non-equilibrium quantum heat engine. Even in the absence of quantum friction along the isentropic strokes, finite system-reservoir coupling induces correlations that result in the generation of coherence between the energy eigenstates of the working system. This coherence acts to hamper the engine's power output, as well as the efficiency with which it can convert heat into useful work, and cannot be captured by a standard Born-Markov analysis of the system-reservoir interactions.
Producing a large current typically requires large dissipation, as is the case in electric conduction, where Joule heating is proportional to the square of the current. Stochastic thermodynamics offers a framework to study nonequilibrium thermodynamics of small fluctuating systems, and quite recently, microscopic derivations and universal understanding of the trade-off relation between the current and dissipation have been put forward. Here we establish a universal framework clarifying how quantum coherence affects the trade-off between the current and dissipation: a proper use of coherence en…
A cyclically working quantum mechanical engine that operates at a single temperature is proposed. Its energy input is delivered by a quantum measurement. The functioning of the engine does not require any feedback control. We analyze work, heat, and the efficiency of the engine for the case of a working substance that is governed by the laws of quantum mechanics and that can be adiabatically compressed and dilated. The obtained general expressions are exemplified for a spin in an adiabatically changing magnetic field and a particle moving in a potential with slowly changing shape.
Maxwell's demon is a special case of a feedback controlled system, where information gathered by measurement is utilized by driving a system along a thermodynamic process that depends on the measurement outcome. The demon illustrates that with feedback one can design an engine that performs work by extracting energy from a single thermal bath. Besides the fundamental questions posed by the demon - the probabilistic nature of the Second Law, the relationship between entropy and information, etc. - there are other practical problems related to feedback engines. One of those is the design of opti…
We report on a lossless information engine that converts nearly all available information from an error-free feedback protocol into mechanical work. Combining high-precision detection at resolution of 1 nm with ultrafast feedback control, the engine is tuned to extract the maximum work from information on the position of a Brownian particle. We show that the work produced by the engine achieves a bound set by a generalized second law of thermodynamics, demonstrating for the first time the sharpness of this bound. We validate a generalized Jarzynski equality for error-free feedback-controlled i…
In 1929, Leo Szilard invented a feedback protocol in which a hypothetical intelligence called Maxwell's demon pumps heat from an isothermal environment and transduces it to work. After an intense controversy that lasted over eighty years; it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can convert information to free energy in principle. Nevertheless, experimental demonstration of this information-to-energy conversion has been elusive. Here, we demonstrate that a nonequilibrium feedback manipulation of a Brownian particle ba…
We introduce an information heat engine that is autonomous (i.e., without any time-dependent parameter) but has separated measurement and feedback processes. This model serves as a bridge between the other types of information heat engines inspired by Maxwell's demon; from the original Szilard-engine type systems to the autonomous demonic setups. By analyzing our model on the basis of a general framework introduced in our previous paper [N. Shiraishi and T. Sagawa, Phys. Rev. E {\bf 91}, 012130 (2015).], we clarify the role of the separation of measurement and feedback in the integral fluctuat…
Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine's working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or he…
It has recently been shown that the Jarzynski equality gets modified, when there are experimental errors in computing work. This modified result also holds good in presence of feedback. In this work, we use a simple toy model, that of a Szilard engine, to prove these results both in the presence and in absence of feedback.
We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control--single and multiple delay feedback, linear frequency filter, etc.--the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an "uncertainty principle" can be formulated: the loss of reliability occurs when cohere…
We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such system and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some …
Using a stochastic nonlinear phase oscillator model, we study the effect of event-triggered feedback on the statistics of interevent intervals. Events are associated with the entering of a new cycle. The feedback is modeled by an instantaneous increase (positive feedback) or decrease (negative feedback) of the oscillators frequency, whenever an event occurs followed by an exponential decay on a slow timescale. In contrast to previous works, we also consider positive feedback that leads to various novel effects. For instance, besides the known excitable and oscillatory regime, that are separate…
