Multiparameter quantum Otto engines raise an optimization problem absent in single-parameter cycles: which small quench vector maximizes the quadratic approximation to the exact output work in a multidimensional control space? We develop a local response theory for sudden-quench Otto engines with quantum working media described by linearly controlled Hamiltonians. We show that the local quadratic work decomposes into a thermal-bias gain and a quadratic response cost, whose competition determines the quench vector that maximizes the local quadratic work at a prescribed quench amplitude. We illustrate the theory in a minimal two-level working medium, where radial and transverse quenches play distinct roles, and in a finite interacting XYZ spin chain, where the resulting quench vector is determined by the balance between thermal-bias and response cost. Our results provide a practical local criterion for designing small multiparameter quenches in sudden-quench quantum Otto engines.
Multiparameter quantum Otto engines raise an optimization problem absent in single-parameter cycles: which small quench vector maximizes the quadratic approximation to the exact output work in a multidimensional control space? We develop a local response theory for sudden-quench Otto engines with quantum working media described by linearly controlled Hamiltonians. We show that the local quadratic work decomposes into a thermal-bias gain and a quadratic response cost, whose competition determines the quench vector that maximizes the local quadratic work at a prescribed quench amplitude. We illustrate the theory in a minimal two-level working medium, where radial and transverse quenches play distinct roles, and in a finite interacting XYZ spin chain, where the resulting quench vector is determined by the balance between thermal-bias and response cost. Our results provide a practical local criterion for designing small multiparameter quenches in sudden-quench quantum Otto engines.
We apply a simple sudden-quench approximation for the unitary work strokes of a quantum Otto engine in order to provide a general analysis of its performance, applicable to arbitrary quantum models with two-body interactions. This work extends recent results for an interaction-driven Otto cycle to generic many-body interacting quantum models, providing universal bounds on their operation efficiency. From this, we demonstrate that the net work of such an engine cycle is determined entirely by interparticle correlations. Applications are demonstrated for a handful of paradigmatic many-body quantum models, including an engine-with a spin-1/2 Fermi gas with contact two-body interactions as its working medium-in which we leverage control over spin polarization to greatly enhance its performance compared to the unpolarized case. We then extend the analysis of interaction-driven quantum Otto engine cycles to systems where control is exerted over the strength of arbitrary quantum operators that might be present in the system Hamiltonian (such as one-body, or three-body, etc.), finding that the general principles derived for the sudden quench with two-body interactions apply universally. As an example, this is demonstrated for a conventional volumetric Otto cycle, where beneficial net work is generated by leveraging the control over the frequency of an external trap, which is a one-body operator. However, we emphasize that the results derived here apply universally to all Otto engine cycles operating under a sudden-quench protocol.
Advances in experimental control of interacting quantum many-body systems with multiple tunable parameters-such as ultracold atomic gases and trapped ions-are driving rapid progress in quantum thermodynamics and enabling the design of quantum thermal machines. In this work, we utilize a sudden quench approximation as a means to investigate the operation of a quantum thermodynamic Otto cycle in which multiple parameters are simultaneously controllable. The method applies universally to many-body systems where such control is available, and therefore provides general principles for investigating their operation as a working medium in quantum thermal machines. We investigate application of this multi-parameter quench protocol in an experimentally realistic one-dimensional Bose gas, as well as in the transverse-field Ising model. We find that such a multi-parameter Otto cycle, when operating as an engine, outperforms not only its constituent single-parameter Otto cycles in terms of the net work and efficiency, but also the combined net work of its constituent engine cycles when added together independently. We also find that a similar multi-parameter enhancement applies to the coefficient of performance when the Otto cycle operates as a refrigerator.
Abstract We undertake a theoretical study of a finite-time quantum Otto engine cycle driven by inter-particle interactions in a weakly interacting one-dimensional (1D) Bose gas in the quasicondensate regime. Utilizing ac-field approach, we simulate the entire Otto cycle, i.e. the two work strokes and the two equilibration strokes. More specifically, the interaction-induced work strokes are modelled by treating the working fluid as an isolated quantum many-body system undergoing unitary evolution. The equilibration strokes, on the other hand, are modelled by treating the working fluid as an open quantum system tunnel-coupled to another quasicondensate which acts as either the hot or cold reservoir, albeit of finite size. We find that, unlike a uniform 1D Bose gas, a harmonically trapped quasicondensate cannot operate purely as aheatengine; instead, the engine operation is enabled by additionalchemicalwork performed on the working fluid, facilitated by the inflow of particles from the hot reservoir. The microscopic treatment of dynamics during equilibration strokes enables us to evaluate the characteristic operational time scales of this Ottothermochemicalengine, crucial for characterizing its power output, without any ad hoc assumptions about typical thermalization timescales. We analyse the performance and quantify the figures of merit of the proposed Otto thermochemical engine, finding that it offers a favourable trade-off between efficiency and power output, particularly when the interaction-induced work strokes are implemented via a sudden quench. We further demonstrate that in the sudden quench regime, the engine operates with an efficiency close to the near-adiabatic (near maximum efficiency) limit, while concurrently achieving maximum power output.
We study a quantum Otto heat engine whose working substance is an anisotropic two-qubit Heisenberg XYZ model. Independent local magnetic fields are used to control each spin individually. The influence of the longitudinal coupling, anisotropy, transverse coupling, and local fields on the net work output and efficiency is systematically examined. Reducing the longitudinal coupling is found to markedly improve both the maximum work and the peak efficiency. The engine performance reaches an optimum at a particular value of the anisotropy parameter. A local work analysis clarifies how work is produced during the cycle. Because of the asymmetric local fields and the intrinsic spin-spin interaction, the two qubits play markedly different thermodynamic roles; the interaction term itself contributes crucially to the total work. We further analyze the variation of quantum entanglement, quantified by concurrence, along the cycle. The results indicate that a pronounced change in entanglement between the hot and cold isomagnetic strokes is closely correlated with the efficiency enhancement. This work offers new insight into the operating principles and control of quantum Otto heat engines.
The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov–Curzon–Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero.
We study quantum Otto thermal machines with a two-spin working system coupled by anisotropic interaction. Depending on the choice of different parameters, the quantum Otto cycle can function as different thermal machines, including a heat engine, refrigerator, accelerator, and heater. We aim to investigate how the anisotropy plays a fundamental role in the performance of the quantum Otto engine (QOE) operating in different timescales. We find that while the engine's efficiency increases with the increase in anisotropy for the quasistatic operation, quantum internal friction and incomplete thermalization degrade the performance in a finite-time cycle. Further, we study the quantum heat engine (QHE) with one of the spins (local spin) as the working system. We show that the efficiency of such an engine can surpass the standard quantum Otto limit, along with maximum power, thanks to the anisotropy. This can be attributed to quantum interference effects. We demonstrate that the enhanced performance of a local-spin QHE originates from the same interference effects, as in a measurement-based QOE for their finite-time operation.