The quantum heat engine and heat pump: An irreversible thermodynamic analysis of the three-level amplifier (original) (raw)

Three-level quantum amplifier as a heat engine: A study in finite-time thermodynamics

Physical Review E, 1994

The finite-rate performance of a quantum heat engine, constructed from a three-level amplifier, is analyzed. Consistent definitions of thermodynamical quantities in terms of quantum observables are postulated. The performance is analyzed in steady state, where the operation of the amplifier only infiuences the surroundings. Quantum master equations describe the irreversible dynamics induced by the coupling of the working medium to the reservoirs. It is shown that the standard assumption of field-independent dissipation is inconsistent with thermodynamics. Field-dependent relaxation equations, based upon the semigroup approach, and consistent with thermodynamics, are formulated. These equations are valid if the time scale of the external field is slow compared to that associated with the bath Buctuations. The steady-state values of the thermodynamical quantities are evaluated. The power is found to have maxima as a function of important controls, such as the field amplitude, frequency, and the coupling with the baths. The existence and locations of these maxima differ from those obtained in the standard treatment, where the dissipation is field independent. The irreversible nature of engine operation is due to the finite rate of heat transfer and a genuine "quantum-&iction" loss term due to dephasing.

Quantum heat engines, the second law and Maxwell's daemon

The European Physical Journal D, 2006

We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle. Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference between the hotter source and the cooler sink before any work can be extracted through the engines. The size of this minimum temperature difference is dictated by that of the energy gaps of the quantum engines involved. Our new quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. Inspired and motivated by the Rabi oscillations, we further introduce some modifications to the quantum heat engines with single-mode cavities in order to, while respecting the second law, extract more work from the heat baths than is otherwise possible in thermal equilibria. Some of the results above are also generalisable to quantum heat engines of an infinite number of energy levels including 1-D simple harmonic oscillators and 1-D infinite square wells.

Quantum thermodynamic cycles and quantum heat engines

Physical Review E, 2007

In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.

quantum refrigerators and the iii-law of thermodynamics

Quantum thermodynamics addresses the emergence of thermodynamical laws from quantum mechanics. The III-law of thermodynamics has been mostly ignored. There are seemingly two independent formulation of the third law of thermodynamics, both originally stated by Nernst. The first is known as Nernst heat theorem, which is purely static, and implies that the entropy flow from any substance at the absolute zero is zero. And the second formulation known as the unattainability principle practically state that no refrigerator can cool a system to absolute zero at finite time. We explore the dynamic version which is the vanishing of rate of temperature decrease of a cooled quantum bath when T → 0. The III-law is then quantified dynamically by evaluating the characteristic exponent ξ of the cooling process:

Irreversible performance of a quantum harmonic heat engine

New Journal of Physics, 2006

The unavoidable irreversible loss of power in a heat engine is found to be of quantum origin. Following thermodynamic tradition, a model quantum heat engine operating in an Otto cycle is analysed, where the working medium is composed of an ensemble of harmonic oscillators and changes in volume correspond to changes in the curvature of the potential well. Equations of motion for quantum observables are derived for the complete cycle of operation. These observables are sufficient to determine the state of the system and with it all thermodynamical variables. Once the external controls are set, the engine settles to a limit cycle. Conditions for optimal work, power and entropy production are derived. At high temperatures and quasistatic operating conditions, the efficiency at maximum power coincides with the endoreversible result η q = 1 − √ T c /T h . The optimal compression ratio varies from C = √ T h /T c in the quasistatic limit where the irreversibility is dominated by heat conductance to C = (T h /T c ) 1/4 in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions, the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.

Quantum refrigerators and the third law of thermodynamics

Physical Review E, 2012

The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process dT (t) dt ∼ −T ζ when approaching absolute zero, T → 0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled two-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat-driven refrigerator (absorption refrigerator) is compared to a power-driven refrigerator. When optimized, both cases lead to the same exponent ζ , showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined.

Heat machines and quantum systems: towards the third law

We analyze cooling more generally based on the process of "algorithmic cooling". We review previous results that show that using this algorithm it is impossible to set the probability of ground-state for a register of spins below some bound. We generalize these results, arguing that this implies that in any sensible refrigeration scheme it is impossible to cool a finite quantum system beyond a certain minimal (non-zero) temperature. This iii temperature approaches zero in the macroscopic limit. Our results therefore indicate that in the quantum domain the laws of thermodynamics are subtly different. The third law or unattainability principle, while still valid, can be improved upon by providing bounds on the asymptotic behavior of rates or a minimal temperature above zero. These bounds take into account limitations beyond just a "finite

Introduction to Quantum Thermodynamics: History and Prospects

Thermodynamics in the Quantum Regime, 2018

Quantum Thermodynamics is a continuous dialogue between two independent theories: Thermodynamics and Quantum Mechanics. Whenever the two theories have addressed the same phenomena new insight has emerged. We follow the dialogue from equilibrium Quantum Thermodynamics and the notion of entropy and entropy inequalities which are the base of the II-law. Dynamical considerations lead to nonequilibrium thermodynamics of quantum Open Systems. The central part played by completely positive maps is discussed leading to the Gorini-Kossakowski-Lindblad-Sudarshan "GKLS" equation. We address the connection to thermodynamics through the system-bath weak-coupling-limit WCL leading to dynamical versions of the I-law. The dialogue has developed through the analysis of quantum engines and refrigerators. Reciprocating and continuous engines are discussed. The autonomous quantum absorption refrigerator is employed to illustrate the III-law. Finally, we describe some open questions and perspectives.

Quantum Refrigerator and the III-law of Thermodynamics

2012

The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to the absolute zero. The III-law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process dT (t) dt ∼ −T ζ when approaching the absolute zero, T → 0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled 2-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat driven refrigerator (absorption refrigerator) is compared to a power driven refrigerator. When optimized both cases lead to the same exponent ζ, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat baths models are considered, a bath composed of harmonic oscillators and a bath composed from ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the III-law are discussed. In the appendix the theory of periodicaly driven open systems and its implication to thermodynamics is outlined. − − − ≥0 FIG. 1: A quantum heat pump designated by the Hamiltonian Hs coupled to a work reservoir with temperature Tw, a hot reservoir with temperature T h and a cold reservoir with temperature Tc. The heat and work currents are indicated. In steady state J h + Jc + P = 0.

Quantum thermodynamic cooling cycle

2001

The quantum-mechanical and thermodynamic properties of a 3-level molecular cooling cycle are derived. An inadequacy of earlier models is rectified in accounting for the spontaneous emission and absorption associated with the coupling to the coherent driving field via an environmental reservoir.