Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1709.08353 · Quantum

Quantum and classical dynamics of a three-mode absorption refrigerator

Stefan Nimmrichter, Jibo Dai, Alexandre Roulet, Valerio Scarani

Published Dec 11, 2017• 32 citations
arXivHTMLPDF

Abstract

We study the quantum and classical evolution of a system of three harmonic modes interacting via a trilinear Hamiltonian. With the modes prepared in thermal states of different temperatures, this model describes the working principle of an absorption refrigerator that transfers energy from a cold to a hot environment at the expense of free energy provided by a high-temperature work reservoir. Inspired by a recent experimental realization with trapped ions, we elucidate key features of the coupling Hamiltonian that are relevant for the refrigerator performance. The coherent system dynamics exhibits rapid effective equilibration of the mode energies and correlations, as well as a transient enhancement of the cooling performance at short times. We find that these features can be fully reproduced in a classical framework.

DOI
10.22331/q-2017-12-11-37

Related papers

Coherence and decoherence in quantum absorption refrigerators

Michael Kilgour, Dvira Segal

Absorption refrigerators transfer thermal energy from a cold reservoir to a hot reservoir using input energy from a third, so-called work reservoir. We examine the operation of quantum absorption refrigerators when coherences between eigenstates survive in the steady state limit. In our model, the working medium comprises a discrete, four-level system. Several studies on related setups have demonstrated the performance-enhancing potential of steady-state eigenbasis quantum coherences. By contrast, in our model such coherences generally quench the cooling current in the refrigerator, while minimally affecting the coefficient of performance (cooling efficiency). We rationalize the behavior of the four-level refrigerator by studying three-level model systems for energy transport and refrigeration. Our calculations further illuminate the shortcomings of secular quantum master equations and the necessity of employing dynamical equations of motion that retain couplings between population and coherences.

arXiv:1804.10585•Physical review. E•Jul 16, 2018•61 citations

Quantum refrigerators and the third law of thermodynamics

Amikam Levy, Robert Alicki, Ronnie Kosloff

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.

arXiv:1205.1347•Physical Review E•Jun 26, 2012•191 citations

Small quantum absorption refrigerator in the transient regime: Time scales, enhanced cooling, and entanglement

Jonatan Bohr Brask, Nicolas Brunner

A small quantum absorption refrigerator, consisting of three qubits, is discussed in the transient regime. We discuss time scales for coherent dynamics, damping, and approach to the steady state, and we study cooling and entanglement. We observe that cooling can be enhanced in the transient regime, in the sense that lower temperatures can be achieved compared to the steady-state regime. This is a consequence of coherent dynamics but can occur even when this dynamics is strongly damped by the dissipative thermal environment, and we note that precise control over couplings or timing is not needed to achieve enhanced cooling. We also show that the amount of entanglement present in the refrigerator can be much larger in the transient regime compared to the steady state. These results are of relevance to future implementations of quantum thermal machines.

arXiv:1508.02025•Physical Review E•Dec 1, 2015•100 citations

Quantum refrigerator embedded in spin-star environments: Scalings of temperature and refrigeration time

Sukrut Mondkar, Aparajita Bhattacharyya, Ujjwal Sen

We examine a quantum absorption refrigerator that comprises three qubits, each of which is connected with a separate spin-star environment, with the three qubit-bath units coupled through an effective six-body interaction. The refrigerator exhibits the feature of transient cooling, i.e., lowering of the temperature of the first qubit in sufficiently small timescales, rather than steady-state refrigeration. A key advantage of our model is that the symmetries of the Hamiltonian enable a semi-analytic solution of the reduced density matrices of the refrigerator qubits, even in the presence of a large number of environmental spins. We derive the condition for autonomous refrigeration and analyze how the optimal cold-qubit temperature scales with the number of bath spins. We find a power-law scaling towards a constant asymptotic value. We also find the scaling of the minimum time required for optimal cooling as a function of the number of bath spins. Furthermore, we quantify the non-Markovianity of the cold-qubit dynamics using a restricted Breuer-Laine-Piilo information-backflow measure and observe that stronger backflow correlates with lower transient minimum temperatures across the sampled parameter regime. The transient-cooling performance is found to be robust under broad parameter variations. Compared to a conventional Markovian three-qubit refrigerator, the CSQAR achieves lower cold-qubit temperatures on shorter timescales. We further analyze the heat currents associated with the three qubits and their respective baths.

arXiv:2505.04374•Physical Review A•Jul 17, 2026•0 citations

Coherence-assisted single-shot cooling by quantum absorption refrigerators

Mark T. Mitchison, Mischa P. Woods, Javier Prior +1 more

The extension of thermodynamics into the quantum regime has received much attention in recent years. A primary objective of current research is to find thermodynamic tasks which can be enhanced by quantum mechanical effects. With this goal in mind, we explore the finite-time dynamics of absorption refrigerators composed of three quantum bits (qubits). The aim of this finite-time cooling is to reach low temperatures as fast as possible and subsequently extract the cold particle to exploit it for information processing purposes. We show that the coherent oscillations inherent to quantum dynamics can be harnessed to reach temperatures that are colder than the steady state in orders of magnitude less time, thereby providing a fast source of low-entropy qubits. This effect demonstrates that quantum thermal machines can surpass classical ones, reminiscent of quantum advantages in other fields, and is applicable to a broad range of technologically important scenarios.

arXiv:1504.01593•New Journal of Physics•Nov 27, 2015•155 citations

Necessarily transient quantum refrigerator

Sreetama Das, Avijit Misra, Amit Kumar Pal +2 more

We show that it is possible to construct a quantum absorption refrigerator that provides refrigeration only in the transient regime, by using three interacting qubits, each of which is also interacting with a local heat bath. Though the machine does not provide any effective cooling in the steady state, significant cooling of a qubit can be achieved much before the system reaches its steady state. We also demonstrate a scenario where the temperature of the qubit that has to be cooled, decreases monotonically to its minimum steady-state temperature. This facilitates bypassing of precise time control in cooling. We study the behaviour of the ratio of the heat currents of the machine for both the scenarios. The results remain qualitatively unchanged for different models of thermal baths. We also comment on the temporal behaviour of bipartite and multipartite quantum correlations present in the system, when transient cooling without steady-state cooling takes place.

arXiv:1606.06985•Europhysics Letters (EPL)•Feb 21, 2019•23 citations
We study the quantum and classical evolution of a system of three harmonic modes interacting via a trilinear Hamiltonian. With the modes prepared in thermal states of different temperatures, this model describes the working principle of an absorption refrigerator that transfers energy from a cold to a hot environment at the expense of free energy provided by a high-temperature work reservoir. Inspired by a recent experimental realization with trapped ions, we elucidate key features of the coupling Hamiltonian that are relevant for the refrigerator performance. The coherent system dynamics exhibits rapid effective equilibration of the mode energies and correlations, as well as a transient enhancement of the cooling performance at short times. We find that these features can be fully reproduced in a classical framework.
Absorption refrigerators transfer thermal energy from a cold reservoir to a hot reservoir using input energy from a third, so-called work reservoir. We examine the operation of quantum absorption refrigerators when coherences between eigenstates survive in the steady state limit. In our model, the working medium comprises a discrete, four-level system. Several studies on related setups have demonstrated the performance-enhancing potential of steady-state eigenbasis quantum coherences. By contrast, in our model such coherences generally quench the cooling current in the refrigerator, while minimally affecting the coefficient of performance (cooling efficiency). We rationalize the behavior of the four-level refrigerator by studying three-level model systems for energy transport and refrigeration. Our calculations further illuminate the shortcomings of secular quantum master equations and the necessity of employing dynamical equations of motion that retain couplings between population and coherences.
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.
A small quantum absorption refrigerator, consisting of three qubits, is discussed in the transient regime. We discuss time scales for coherent dynamics, damping, and approach to the steady state, and we study cooling and entanglement. We observe that cooling can be enhanced in the transient regime, in the sense that lower temperatures can be achieved compared to the steady-state regime. This is a consequence of coherent dynamics but can occur even when this dynamics is strongly damped by the dissipative thermal environment, and we note that precise control over couplings or timing is not needed to achieve enhanced cooling. We also show that the amount of entanglement present in the refrigerator can be much larger in the transient regime compared to the steady state. These results are of relevance to future implementations of quantum thermal machines.
We examine a quantum absorption refrigerator that comprises three qubits, each of which is connected with a separate spin-star environment, with the three qubit-bath units coupled through an effective six-body interaction. The refrigerator exhibits the feature of transient cooling, i.e., lowering of the temperature of the first qubit in sufficiently small timescales, rather than steady-state refrigeration. A key advantage of our model is that the symmetries of the Hamiltonian enable a semi-analytic solution of the reduced density matrices of the refrigerator qubits, even in the presence of a large number of environmental spins. We derive the condition for autonomous refrigeration and analyze how the optimal cold-qubit temperature scales with the number of bath spins. We find a power-law scaling towards a constant asymptotic value. We also find the scaling of the minimum time required for optimal cooling as a function of the number of bath spins. Furthermore, we quantify the non-Markovianity of the cold-qubit dynamics using a restricted Breuer-Laine-Piilo information-backflow measure and observe that stronger backflow correlates with lower transient minimum temperatures across the sampled parameter regime. The transient-cooling performance is found to be robust under broad parameter variations. Compared to a conventional Markovian three-qubit refrigerator, the CSQAR achieves lower cold-qubit temperatures on shorter timescales. We further analyze the heat currents associated with the three qubits and their respective baths.
The extension of thermodynamics into the quantum regime has received much attention in recent years. A primary objective of current research is to find thermodynamic tasks which can be enhanced by quantum mechanical effects. With this goal in mind, we explore the finite-time dynamics of absorption refrigerators composed of three quantum bits (qubits). The aim of this finite-time cooling is to reach low temperatures as fast as possible and subsequently extract the cold particle to exploit it for information processing purposes. We show that the coherent oscillations inherent to quantum dynamics can be harnessed to reach temperatures that are colder than the steady state in orders of magnitude less time, thereby providing a fast source of low-entropy qubits. This effect demonstrates that quantum thermal machines can surpass classical ones, reminiscent of quantum advantages in other fields, and is applicable to a broad range of technologically important scenarios.
We show that it is possible to construct a quantum absorption refrigerator that provides refrigeration only in the transient regime, by using three interacting qubits, each of which is also interacting with a local heat bath. Though the machine does not provide any effective cooling in the steady state, significant cooling of a qubit can be achieved much before the system reaches its steady state. We also demonstrate a scenario where the temperature of the qubit that has to be cooled, decreases monotonically to its minimum steady-state temperature. This facilitates bypassing of precise time control in cooling. We study the behaviour of the ratio of the heat currents of the machine for both the scenarios. The results remain qualitatively unchanged for different models of thermal baths. We also comment on the temporal behaviour of bipartite and multipartite quantum correlations present in the system, when transient cooling without steady-state cooling takes place.