Abstract We propose a quantum Otto heat engine using a finite-size Dicke-Stark model as the working substance. In the extended coherent state space, the complete energy spectrum and eigenstates are obtained through numerical calculations. Within the infinite-time and finite-time thermodynamics frameworks, we find that the output work, efficiency, and power can be optimized by adjusting the Stark field strength, the qubit–boson coupling strength, stroke times, and number of atoms. Our results reveal that output work and efficiency are maximized near the coupling strength at the superradiant phase transition (SPT). Tuning the Stark field strength modifies the energy level structure and SPT, effectively suppressing entropy generation and quantum friction during nonequilibrium evolution. We also show that asymmetric heat engines—where the two isochoric strokes operate with different Stark field strengths and durations—further improve engine performance. These results may guide future implementations of efficient quantum heat engines.
Abstract We propose a quantum Otto heat engine using a finite-size Dicke-Stark model as the working substance. In the extended coherent state space, the complete energy spectrum and eigenstates are obtained through numerical calculations. Within the infinite-time and finite-time thermodynamics frameworks, we find that the output work, efficiency, and power can be optimized by adjusting the Stark field strength, the qubit–boson coupling strength, stroke times, and number of atoms. Our results reveal that output work and efficiency are maximized near the coupling strength at the superradiant phase transition (SPT). Tuning the Stark field strength modifies the energy level structure and SPT, effectively suppressing entropy generation and quantum friction during nonequilibrium evolution. We also show that asymmetric heat engines—where the two isochoric strokes operate with different Stark field strengths and durations—further improve engine performance. These results may guide future implementations of efficient quantum heat engines.
Quantum heat machines, encompassing heat engines, refrigerators, heaters, and accelerators, represent the forefront of quantum thermodynamics, offering a novel paradigm for converting heat energy into useful mechanical work. Leveraging quantum mechanical principles, these machines promise superior efficiency and performance compared to classical counterparts, with potential applications in renewable energy and quantum computing. This paper investigates a quantum Otto engine operating in both ideal and finite-time scenarios, employing a two-level system interacting with a harmonic oscillator within the framework of the anisotropic quantum Rabi-Stark model (AQRSM) as the working medium. This model is notable for exhibiting both first-order and continuous quantum phase transitions. By focusing on quantum heat engines, our study reveals that these phase transitions critically modulate the efficiency and power of AQRSM-based engines, outperforming quantum engines fueled by working medium with harmonic spectrum. Additionally, we explore the impacts of quantum friction and conduct limit cycle analysis in finite-time operations, providing insights into optimizing quantum heat engines for practical implementation.
Abstract This paper proposes a theoretical model for a heat engine operating on the Otto cycle, employing a two-qubit Heisenberg chain as its working substance. This system is subjected to an external, time-dependent homogeneous magnetic field and a symmetric cross-spin interaction. The interaction is configured to occur along two distinct orientations, contingent upon the direction of Zeeman energy and symmetric interaction: either exclusively along the X -direction or exclusively along the Z -direction. Furthermore, the thermal reservoirs integral to the Otto engine are considered to engage with the working substance via two discrete modes: a localized interaction or a collective interaction. The two qubits exhibit weak coupling to a non-equilibrium thermal environment during the isochoric heating and cooling strokes, thereby validating the application of a Markovian model as a suitable approximation for describing the time evolution of the working substance. This study investigates the influence of various system parameters on the thermodynamic quantities and the resultant power output. A principal finding is that refrigeration functionality is the predominant operational characteristic when the system engages in collective interaction with the reservoirs. Conversely, localized interactions facilitate dual operational modes, with the sign of the Zeeman energy determining the function as either a refrigerator or a heat engine. Significantly, positive power output is achieved in the engine regime, and we find that the choice of interaction axis acts as a powerful amplification mechanism for the thermodynamic output, while the system-environment coupling scheme proves to be the most decisive factor in determining the machine’s fundamental purpose.
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cycle, which are dependent on the time duration along each process. With these, we derive the analytical expressions for the thermodynamic quantities of the two-level heat engine, such as total work, thermodynamic efficiency, entropy production, and work fluctuations, in which effects of coherence, squeezing, inner friction and finite-time heat exchange are included. We then numerically determine the thermodynamic quantities and the fluctuations using the parameters employed in the experimental implementation. Our results clarify the role of coherence and squeezing in the performance and fluctuations in the quantum Otto engines.
We consider the finite-time operation of a quantum heat engine whose working substance is composed of a two-level atomic system. The engine cycle, consisting of two quantum adiabatic and two quantum isochoric (constant-frequency) processes and working between two heat reservoirs at temperatures Th and Tc(<Th), is a quantum version of the classical Otto cycle. By optimizing the power output with respect to two frequencies, we obtain the efficiency at maximum power output (EMP) and analyze numerically the effects of the times taken for two adiabatic and two isochoric processes on the EMP. In the absence of internally dissipative friction, we find that the EMP is bounded from the upper side by a function of the Carnot efficiency ${\ensuremath{\eta}}_{C}$, ${\ensuremath{\eta}}_{+}={\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})\mathrm{ln}(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$, with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$. This analytic expression is confirmed by our exact numerical result and is identical to the one derived in an engine model based on a mesoscopic or macroscopic system. If the internal friction is included, we find that the EMP decreases as the friction coefficient increases.
Abstract A scheme is theoretically proposed to investigate a quantum Otto engine (QOE) based on cavity quantum electrodynamics (QED) systems, where the working substance consists of a single‐mode optical cavity coupled to either one or two identical two‐level atoms, corresponding to the Jaynes–Cummings (JC) and Tavis–Cummings (TC) models, respectively. These results show that quantum coherence can enhance the efficiency of the quantum Otto heat engine (QOHE) and that the QOE can operate in various thermodynamic modes, such as a heat engine, refrigerator, or heater. Building on these two cavity QED models, it is further demonstrated that increasing the number of atoms leads to an exponential enhancement in the work output of the QOHE. Finally, a localized quantum engine is analyzed by tracing out one of the atoms in the TC model and show that the local system can achieve an efficiency comparable to that of the global system. This work establishes a novel theoretical framework for understanding and optimizing the performance of quantum heat engines in cavity QED platforms.
We demonstrate that under specific conditions, a finite-time quantum Otto engine, employing a spin-1/2 particle as the working substance, despite undergoing incomplete Otto cycles, can achieve higher efficiency than an ideal quantum Otto engine. A finite-time quantum Otto engine refers to an Otto engine where the two isochoric strokes are prematurely terminated before reaching thermal equilibrium with their respective hot and cold baths. We observe that the enhancement of efficiency of a finite-time quantum Otto engine over the ideal one can be realized by adjusting the initial temperature of the working substance within the temperature range of the hot and cold baths. We also find that incorporating an auxiliary qubit, and activating specific interactions between the single-qubit working substance and the auxiliary one, can enhance the efficiency of a finite-time as well as an ideal quantum Otto engine. Furthermore, we analyze the impact of glassy disorder within the system-bath coupling during the two isochoric strokes on the efficiency of a finite-time quantum Otto engine. We find that as strength of disorder increases, efficiency of a finite-time quantum Otto engine tends to decrease, albeit with relatively modest reduction even for strong disorder. However, the advantage in efficiency of the finite-time quantum Otto engine over the ideal one, obtained by tuning the initial state temperature, and the efficiency enhancement obtained by incorporating an auxiliary over the without-auxiliary scenario, persists even in presence of substantial disorder. Additionally, we show that while this disorder does not affect the ideal efficiency, it does influence the duration of isochoric strokes needed for an Otto engine to reach ideal efficiency. This stroke duration remains nearly constant until a specific disorder strength, beyond which it increases rapidly.