We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.
We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.
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 demonstrate how the reciprocating heat cycle of a quantum Otto engine (QOE) can be implemented using a single ion and an always-on thermal environment. The internal degree of freedom of the ion is chosen as the working fluid, while the motional degree of freedom can be used as the cold bath. We show, that by adiabatically changing the local magnetic field, the work efficiency can be asymptotically made unity. We propose a projective measurement of the internal state of the ion that mimics the release of heat from the working fluid during the engine cycle. In our proposal, the coupling to the hot and the cold baths need not be switched off and on in an alternate fashion during the engine cycle, unlike other existing proposals of QOE. This renders the proposal experimentally feasible using the available tapped-ion engineering technology.
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.
Abstract We investigate the phenomenon of partial thermalization in the context of the efficiency at maximum power (EMP) for a quantum Otto engine. This engine utilizes Bose-Einstein Condensation in a cubic potential. The occurrence of partial thermalization is observed during a finite-time isochoric process, preventing the system from reaching an equilibrium state with the reservoirs and leaving it in a state of residual coherence. The engine’s performance can be evaluated based on its power output and EMP. The cubic potential is employed to induce energy excitation during the expansion and compression phases. The total energy is determined by the work done over a complete cycle. Utilizing Fourier’s law for heat conduction, we have determined that the power output is explicitly influenced by the duration of the heating and cooling strokes as well as the engine’s efficiency. Specifically, a longer stroke time and higher efficiency result in reduced power output. To calculate EMP, we optimize power by varying the compression ratio (κ), and we have found that EMP is also influenced by the isochoric heating and cooling processes. When varying the duration of the isochoric process, EMP shows a slight decrease as isochoric time increases due to entropy production. However, significant improvements in the EMP of the Otto Engine can be achieved by extending the cooling stroke time beyond the heating stroke time.
Abstract Finite-time quantum heat engines operating with working substances of quantum nature are of practical relevance as they can generate finite-power. However, they encounter energy losses due to quantum friction, which is particularly pronounced in many-body systems with non-trivial coherences in their density operator. Strategies such as shortcuts to adiabaticity and fast routes to thermalization have been developed although the associated cost requirements remain uncertain. In this study, we theoretically investigate the finite-time operation of a trapped-atom Otto engine with light-induced dipole–dipole interactions and projection measurements in one of the isochoric processes. The investigation reveals that when atoms are sufficiently close to each other and their dipoles are oriented perpendicularly, light-induced dipole–dipole interactions generate strong coherent interactions. This has enhanced engine efficiency to near unity and accelerate the thermalization process by sixtyfold. The interactions also boost engine performance during finite-unitary strokes despite the significant quantum friction induced by the time-dependent driving field. Furthermore, the projection measurement protocol effectively erases quantum coherences developed during both the finite-unitary expansion and finite thermalization stages and allows finite-time engine operation with an output power. This setup presents a compelling avenue for further investigation of finite-time many-body quantum heat engines and provides an opportunity to explore the full potential of photon-mediated dipole–dipole interactions.
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.