Performance analysis of an irreversible quantum heat engine working with harmonic oscillators

Abstract

The cycle model of a regenerative quantum heat engine working with many noninteracting harmonic oscillators is established. The cycle consists of two isothermal and two constant-frequency processes. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The inherent regenerative losses in the two constant-frequency processes are calculated. The expressions of several important performance parameters such as the efficiency, power output, and rate of the entropy production are derived for several interesting cases. Especially, the optimal performance of the cycle in high-temperature limit is discussed in detail. The maximum power output and the corresponding parameters are calculated. The optimal region of the efficiency and the optimal ranges of the temperatures of the working substance in the two isothermal processes are determined.

Quantum thermodynamics

“…These reservoirs model the bath that inputs energy into the working fluid (hot bath) and another that accepts energy from the working fluid (cold bath). Two main classes of quantum systems have been studied as working fluids, namely discrete quantum systems and continuous variable quantum systems [155][156][157][158]. This study of continuous variable systems complements various models of finite level systems [159,160] and hybrid models [161,162] studied as quantum engines.…”

“…The quantum analogue of the Carnot engine consists of a working fluid, which can be a particle in a box [166], qubits [18,159], multiple level atoms [157] or harmonic oscillators [155,156]. We emphasize that for all such engines, the efficiency of the engine is strictly bounded by the Carnot efficiency [167].…”

Lipkin-Meshkov-Glick model in a quantum Otto cycle

“…QHEs can extract more work from heat baths relative to classical heat engines [4,5]; they can operate beyond the classical Carnot bound without breaking the second law by exploiting quantum resources; such as entangled [6] or quantum coherent heat reservoirs [7,8], or by regenerative steps [9]. In comparison to non-interacting working substances, such as a two level (qubit) [4,5] or a multilevel atom [10], or a simple harmonic oscillator [11], QHEs with interacting working substances, in particular coupled spins, are found to be more efficient and capable to harvest more work [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Physical realizations of QHEs are proposed for a single ion [34,35], Paul trap [9], ultracold atoms [36], optomechanical systems [37], quantum dots [38], circuit and cavity quantum electrodynamic systems [7,39,40].…”

“…Since the recognition of three level maser as a heat engine [1], quantum heat engines (QHEs) have been attracted much interest recently [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40]. QHEs use quantum matter as their working substance to harvest work from classical or quantum resources through the quantum generalizations of classical thermodynamical cycles, such as Carnot, Otto, Brayton or Diesel cycles [2,3].…”

The 1st Law of Thermodynamics for the Mean Energy of a Closed Quantum System in the Aharonov-Vaidman Gauge

“…Such research includes a substantial body of literature discussing-for example-quantum heat engines (e.g., [14][15][16][17][18]), thermodynamics of open quantum systems (e.g., [19]), entanglement and work (e.g., [20]), quantum thermometry and heat baths (e.g., [21,22]), quantum refrigerators (e.g., [23,24]), Rényi entropy flow [25], qubit and qutrit work extraction (e.g., [26,27]), and quantum measurement control of thermodynamics [28].…”