Impurity reveals distinct operational phases in quantum thermodynamic cycles.

The ability of the internal states of a working fluid to be in a coherent superposition is one of the basic properties of a quantum heat engine. It was recently predicted that in the regime of small engine action, this ability can enable a quantum heat engine to produce more power than any equivalent classical heat engine. It was also predicted that in the same regime, the presence of such internal coherence causes different types of quantum heat engines to become thermodynamically equivalent. Here, we use an ensemble of nitrogen vacancy centers in diamond for implementing two types of quantum heat engines, and experimentally observe both effects.

We propose an arbitrary driven spin as the working fluid of a quantum Otto cycle in the presence of internal friction. The role of total allocated time to the adiabatic branches of the cycle, generated by different control field profiles, on the extractable work and the thermal efficiency are analyzed in detail. The internal friction is characterized by the excess entropy production and quantitatively determined by studying the closeness of an actual unitary process to an infinitely long one via quantum relative entropy. It is found that the non-ideal, finite-time adiabatic transformations negatively effect the work output and the thermal efficiency of the quantum heat engine. The non-monotone dependence of the work output, thermal efficiency, entropy production and the internal friction on the total adiabatic time are elucidated. It is also found that almost frictionless adiabatic transformations with small entropy production can be obtained in a short adiabatic time.

We study how a quantum heat engine performs across the critical value of an\nexternal parameter, pertaining to the quantum phase transition. Considering a\ntwo-ion system subjected to a magnetic field, we show that the system performs\nin a quantum Otto cycle above a critical value of the magnetic field, while\nbelow such critical point, it does not operate in a heat cycle at all.\nMoreover, at the critical point, its interaction with an ancillary ion\ndeteriorates the performance of the system as a heat engine. We further show\nthat a strong interaction between the constituent ions of an ion-based system\nis crucial for it to work in a heat-work cycle, while the coupling to the\nancillary system must be minimized.\n

When incomplete information about the control parameters is quantified as a prior distribution, a subtle connection emerges between quantum heat engines and their classical analogues. We study the quantum model where the uncertain parameters are the intrinsic energy scales and compare it with the classical models where the intermediate temperature is the uncertain parameter. The prior distribution quantifying the incomplete information has the form π(x)∝1/x in both the quantum and the classical models. The expected efficiency calculated in the near-equilibrium limit approaches the value of one third of Carnot efficiency.

Recently, the thermodynamics of open quantum systems driven by light fields has been investigated in the framework of quantum heat engines, whose output work can be measured as a spectroscopic signal. In this work, we investigate a four-level quantum heat engine that generates cascaded entangled photon pairs, treating the hot bath as an incoherent thermal pump and focusing on the correlation statistics of the output work and photon indistinguishability. We show that the dissipative nonequilibrium dynamics of this thermodynamic open quantum system can be reconstructed by correlation measurements under carefully mediated optical control. Comparing our findings with the traditional coherently pumped model, we find that the thermal pumping has the potential to generate nonclassical correlations resulting in photon indistinguishability, displaying an advantage in probing the nonequilibrium effects induced by the baths at different temperatures. Our work also demonstrates that incoherent pumping can optimize such correlations in output work beyond the classical limit. Lastly, we show that nonclassical correlations and resonant power at steady state cannot be simultaneously maximized in the weak coupling regime. Published by the American Physical Society 2024

This work establishes a quantum heat engine considering qubits as the external heat transfer mediums. The authors find that the efficiency and the power output of the quantum heat engine are closely dependent on the microproperties of qubits, and consequently relate the irreversible heat transfer with quantum effects. The equivalent conditions between the quantum heat engines and the classical endoreversible Carnot heat engines are revealed

We investigate two coupled spins 1/2 in a magnetic field as the working substance of the quantum Otto cycle. In the quantum adiabatic strokes, finite-time parametric transformations are employed either in the coupling strength or in the magnetic field. The operation regimes, where the mode of the cycle is a refrigerator or a heat engine, are explored. The role of the total allocated time to the quantum adiabatic stages on the performance of the quantum Otto refrigerator and the heat engine is investigated in detail. The finite-time adiabatic transformations are found to increase the Shannon entropy which is quantum in origin. The effect known as the inner friction is found to negatively effect the performances of the quantum heat engine and the refrigerator. The strong frictional losses are also found to induce inactive operation regimes where the mode of the cycle is neither a refrigerator nor a heat engine.

Two special coupled spins, one is an arbitrary spin-s and the other is a fixed spin-1/2, are proposed as the working substance of the quantum Otto and Carnot cycles. The quantum adiabatic stages of the cycles are considered the simultaneous changes of the frequencies of the spins and the interaction strength in which all the energy gaps of the working substance are changed by the same ratios in the two quantum adiabatic stages. The role of quantum interactions and the spin-s on the performance of the quantum cycles is investigated in detail. It is found that the thermal efficiencies of the cycles are independent of the spin-s and the interaction strength and are also equivalent to their classical counterparts. The work output of the cycles is found to be significantly enhanced by the quantum interactions. Compared to the uncoupled case, the coupled working substance with a smaller spin-s is found to produce more useful work in the weak coupling regime, while the harvested work with a smaller spin-s is less in the strong coupling regime. The concept of local thermodynamics and the role of inner friction are also addressed for the proposed quantum Otto and Carnot cycles.

A quantum heat engine of a specific type is studied. This engine contains a single particle confined in the infinite square well potential with variable width and consists of three processes: the isoenergetic process (which has no classical analogs) as well as the isothermal and adiabatic processes. It is found that the engine possesses exotic properties in its performance. The efficiency takes the maximum value when the expansion ratio of the engine is appropriately set, and, in addition, the lower the temperature is, the higher the maximum efficiency becomes, highlighting aspects of the influence of quantum effects on thermodynamics. A comment is also made on the relevance of this engine to that of Carnot.

Laser and photocell quantum heat engines (QHEs) are powered by thermal light and governed by the laws of quantum thermodynamics. To appreciate the deep connection between quantum mechanics and thermodynamics we need only recall that in 1901 Planck introduced the quantum of action to calculate the entropy of thermal light, and in 1905 Einstein's studies of the entropy of thermal light led him to introduce the photon. Then in 1917, he discovered stimulated emission by using detailed balance arguments. Half a century later, Scovil and Schulz-DuBois applied detailed balance ideas to show that maser photons were produced with Carnot quantum efficiency (see Fig. 1A). Furthermore, Shockley and Quiesser invoked detailed balance to obtain the efficiency of a photocell illuminated by "hot" thermal light (see Fig. 2A). To understand this detailed balance limit, we note that in the QHE, the incident light excites electrons, which can then deliver useful work to a load. However, the efficiency is limited by radiative recombination in which the excited electrons are returned to the ground state. But it has been proven that radiatively induced quantum coherence can break detailed balance and yield lasing without inversion. Here we show that noise-induced coherence enables us to break detailed balance and get more power out of a laser or photocell QHE. Surprisingly, this coherence can be induced by the same noisy (thermal) emission and absorption processes that drive the QHE (see Fig. 3A). Furthermore, this noise-induced coherence can be robust against environmental decoherence.Fig. 1.(A) Schematic of a laser pumped by hot photons at temperature T(h) (energy source, blue) and by cold photons at temperature T(c) (entropy sink, red). The laser emits photons (green) such that at threshold the laser photon energy and pump photon energy is related by Carnot efficiency (4). (B) Schematic of atoms inside the cavity. Lower level b is coupled to the excited states a and β. The laser power is governed by the average number of hot and cold thermal photons, and . (C) Same as B but lower b level is replaced by two states b(1) and b(2), which can double the power when there is coherence between the levels.Fig. 2.(A) Schematic of a photocell consisting of quantum dots sandwiched between p and n doped semiconductors. Open circuit voltage and solar photon energy ℏν(h) are related by the Carnot efficiency factor where T(c) is the ambient and T(h) is the solar temperature. (B) Schematic of a quantum dot solar cell in which state b is coupled to a via, e.g., solar radiation and coupled to the valence band reservoir state β via optical phonons. The electrons in conduction band reservoir state α pass to state β via an external circuit, which contains the load. (C) Same as B but lower level b is replaced by two states b(1) and b(2), and when coherently prepared can double the output power.Fig. 3.(A) Photocell current j = Γρ(αα) (laser photon flux P(l)/ℏ(ν(l))) (in arbitrary units) generated by the photovoltaic cell QHE (laser QHE) of Fig. 1C (Fig. 2C) as a function of maximum work (in electron volts) done by electron (laser photon) E(α) - E(β) + kT(c) log(ρ(αα)/ρ(ββ)) with full (red line), partial (brown line), and no quantum interference (blue line). (B) Power of a photocell of Fig. 2C as a function of voltage for different decoherence rates , 100γ(1c). Upper curve indicates power acquired from the sun.

Heat engines used to output useful work have important practical significance, which, in general, operate between heat baths of infinite size and constant temperature. In this paper, we study the efficiency of a heat engine operating between two finite-size heat sources with initial temperature difference. The total output work of such heat engine is limited due to the finite heat capacity of the sources. We firstly investigate the effects of different heat capacity characteristics of the sources on the heat engine’s efficiency at maximum work (EMW) in the quasi-static limit. Moreover, it is found that the efficiency of the engine operating in finite-time with maximum power of each cycle is achieved follows a simple universality as , where is the Carnot efficiency determined by the initial temperature of the sources. Remarkably, when the heat capacity of the heat source is negative, such as the black holes, we show that the heat engine efficiency during the operation can surpass the Carnot efficiency determined by the initial temperature of the heat sources. It is further argued that the heat engine between two black holes with vanishing initial temperature difference can be driven by the energy fluctuation. The corresponding EMW is proved to be .

We demonstrate a genuine quantum feature of heat: the power emitted by a qubit (quantum two-level system) into a reservoir under continuous driving shows peaks as a function of frequency $f$. These resonant features appear due to the accumulation of the dynamical phase during the driving. The position of the $n$th maximum is given by $f=f_{\rm M}/n$, where $f_{\rm M}$ is the mean frequency of the qubit in the cycle, and their positions are independent of the form of the drive and the number of heat baths attached, and even the presence or absence of spectral filtering. We show that the waveform of the drive determines the intensity of the peaks, differently for odd and even resonances. This quantum heat is expected to play a crucial role in the performance of driven thermal devices such as quantum heat engines and refrigerators. We also show that by optimizing the cycle protocol, we recover the favorable classical limit in fast driven systems without the use of counter-diabatic drive protocols and we demonstrate an entropy preserving non-unitary process. We propose that this non-trivial quantum heat can be detected by observing the steady-state power absorbed by a resistor acting as a bolometer attached to a driven superconducting qubit.

Entangled states are an important resource for quantum information processing and for the fundamental understanding of quantum physics. An intriguing open question would be whether entanglement can improve the performance of quantum heat engines in particular. One of the promising platforms to address this question is to use entangled atoms as a non-thermal bath for cavity photons, where the cavity mirror serves as a piston of the engine. Here we theoretically investigate a photonic quantum engine operating under an effective reservoir consisting of quantum-correlated pairs of atoms. We find that maximally entangled Bell states alone do not help extract useful work from the reservoir unless some extra populations in the excited states or ground states are taken into account. Furthermore, high efficiency and work output are shown for the non-maximally entangled superradiant state, while negligible for the subradiant state due to lack of emitted photons inside the cavity. Our results provide insights in the role of quantum-correlated atoms in a photonic engine and present new opportunities in designing a better quantum heat engine.

Quantum interference is at the heart of what sets the quantum and classical worlds apart. We demonstrate that quantum interference effects involving a many-body working medium is responsible for genuinely nonclassical features in the performance of a quantum heat engine. The features with which quantum interference manifests itself in the work output of the engine depends strongly on the extensive nature of the working medium. While identifying the class of work substances that optimize the performance of the engine, our results shed light on the optimal size of such media of quantum workers to maximize the work output and efficiency of quantum energy machines.

We present a consistent optimization procedure for the optical measurements in open quantum systems using recently developed incoherent control protocol. Assigning an effective hot bath for the two-entangled-photon pump we recast the transmission of classical probe as a work in a quantum heat engine framework. We demonstrate that maximum work in such a heat engine can exceed that for the classical two-photon and one-photon pumps, while efficiency at maximum power can be attributed to conventional boundaries obtained for the three-level maser heat engine. Our results pave the way for incoherent control and optimization of optical measurements in open quantum systems that involve two-photon processes with quantum light.