We propose two algorithmic quantum Otto refrigerators (AQOR) in which the standard isochoric cooling stroke is replaced by two distinct heat-bath algorithmic cooling (HBAC) protocols based on the partner-pairing algorithm (PPA). For each protocol, we derive closed-form expressions for the target qubit's asymptotic polarization and explicitly incorporate the work performed by HBAC into the coefficient of performance (COP). We further quantify the thermodynamic cost of the HBAC stroke and Landauer's bound for both protocols. Our analytical COP curves reveal parameter regimes where the AQOR surpasses the conventional Otto refrigerator. Furthermore, we show that, by tuning the auxiliary qubit's transition frequency and adjusting external control parameters, both protocols achieve enhanced COP and extend the operational window across a wider range of bath temperature differences. Therefore, the AQORs present a tradeoff between achieving high performance in specific regimes and maintaining enhanced applicability. These results demonstrate that algorithmic cooling can be seamlessly integrated into Otto cycles to realize quantum thermal machines with improved practicality on near-term hardware.
We propose two algorithmic quantum Otto refrigerators (AQOR) in which the standard isochoric cooling stroke is replaced by two distinct heat-bath algorithmic cooling (HBAC) protocols based on the partner-pairing algorithm (PPA). For each protocol, we derive closed-form expressions for the target qubit's asymptotic polarization and explicitly incorporate the work performed by HBAC into the coefficient of performance (COP). We further quantify the thermodynamic cost of the HBAC stroke and Landauer's bound for both protocols. Our analytical COP curves reveal parameter regimes where the AQOR surpasses the conventional Otto refrigerator. Furthermore, we show that, by tuning the auxiliary qubit's transition frequency and adjusting external control parameters, both protocols achieve enhanced COP and extend the operational window across a wider range of bath temperature differences. Therefore, the AQORs present a tradeoff between achieving high performance in specific regimes and maintaining enhanced applicability. These results demonstrate that algorithmic cooling can be seamlessly integrated into Otto cycles to realize quantum thermal machines with improved practicality on near-term hardware.
Quantum refrigerators (QRs) are pivotal in exploring thermodynamic behavior at microscopic scales. This study investigates a quantum Otto refrigerator using a bosonic gas confined in a cubic potential, operating under finite-time thermalization. We derive key thermodynamic quantities analytically, including the coefficient of performance (COP), cooling power, entropy, and cooling rate. Additionally, we investigate how partial thermalization during the isochoric heating and cooling stages influences overall system performance. The findings reveal a trade-off between COP and cooling power, emphasizing the importance of thermalization duration. Notably, by extending the cooling time relative to heating, the COP can be significantly improved, offering a practical approach to optimizing QR performance under realistic conditions.
Experimental demonstration of a truly quantum mechanical solid-state heat engine or refrigerator remains elusive up to now. Here, a four-stroke quantum refrigerator that can be realized using a superconducting qubit coupled alternately to two resonators with embedded reservoirs is analyzed theoretically. Besides being a practically feasible thermal machine, this concept presents a number of fundamentally interesting features. At high frequencies, the system exhibits nearly coherent dynamics, leading to quantum oscillations in cooling power versus operation frequency. At intermediate frequencies, an ideal Otto cycle can be realized. In the nearly adiabatic regime, the cooling power is quadratic in frequency and can be separated to classical and quantum contributions. Interestingly, it is shown here that quantum coherence leads always to performance that is inferior as compared to that arising from purely classical dynamics. Furthermore, in the nearly adiabatic regime the efficiency of the refrigerator exceeds clearly that of the standard Otto cycle.
Abstract For an Otto cycle there always exists a trade-off between the cycle efficiency and the output power due to the requirement of cycle length. The shortcut to adiabatic (STA) technology provides an effective way to deal with the difficulty of zero-output power in conventional Otto cycle. In this paper, the Otto cycle of three-qubit system as the working substance with counterdiabatic driving has been investigated. It is demonstrated that the tripartite Otto cycle as a universal machine, in the suitable regimes of external control parameter, could work as a quantum heat engine (QHE), refrigerator or heat pump. And, the performances of QHE and refrigerator with and without STA, such as the power and efficiency of QHE and the coefficient of performance (COP) and figure of merit (FOM) of refrigerator, have been investigated. It shows the application of STA scheme can lead to an effective enhancement in the performances of Otto cycle, including achievements of a high QHE’s/refrigerator’s power associated with a moderate QHE’s efficiency/COP of refrigerator. Especially, it is interesting that even in a short-time cycle the optimization of control parameters could arise a remarkable improvement in the efficiency (or COP) of STA QHE (refrigerator), approaching the ideal efficiency or COP of conventional Otto cycle with quasi-static process. Finally, with the aid of parameter optimization the trade-off regions between the efficiency and the power (the COP and the FOM) of STA Otto engine (refrigerator) have been advised.
Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.
The performance of a quantum Otto refrigerator coupled to a squeezed cold reservoir has been evaluated using the χ figure of merit. We have shown that squeezing can enhance the coefficient of performance (COP) dramatically, surpassing the Carnot COP defined by the initial temperatures of the heat baths. Furthermore, when the squeezing parameter approaches its maximum value, the work input vanishes while the cooling rate remains finite, in apparent contravention of the second law of thermodynamics. To explain this phenomenon, we have shown that squeezing renders the thermal bath into a nonequilibrium state and the temperature of the bath becomes frequency dependent. Thereby, a correlation to the Carnot COP has been deduced. The results reveal that the COP under the maximum χ figure of merit is of the Curzon-Ahlborn style that cannot surpass the actual Carnot COP, and is thus consistent with the second law of thermodynamics.
We suggest alternative quantum Otto engines, using heat bath algorithmic cooling with a partner pairing algorithm instead of isochoric cooling and using quantum swap operations instead of quantum adiabatic processes. Liquid state nuclear magnetic resonance systems in a single entropy sink are treated as working fluids. The extractable work and thermal efficiency are analyzed in detail for four-stroke and two-stroke types of alternative quantum Otto engines. The role of the heat bath algorithmic cooling in these cycles is to use a single entropy sink instead of two so that a single incoherent energy resource can be harvested and processed using an algorithmic quantum heat engine. Our results indicate a path to programmable quantum heat engines as analogs of quantum computers beyond traditional heat engine cycles. We find that for our NMR system example implementation of quantum algorithmic heat engine stages yields more power due to increased cycle speeds.