The Quantum Refrigerator: The quest for absolute zero

Abstract

The scaling of the optimal cooling power of a reciprocating quantum refrigerator is sought as a function of the cold bath temperature as $T_c\to 0$. The working medium consists of noninteracting particles in a harmonic potential. Two closed-form solutions of the refrigeration cycle are analyzed, and compared to a numerical optimization scheme, focusing on cooling toward zero temperature. The optimal cycle is characterized by linear relations between the heat extracted from the cold bath, the energy level spacing of the working medium and the temperature. The scaling of the optimal cooling rate is found to be proportional to $T_c^{3/2}$ giving a dynamical interpretation to the third law of thermodynamics.

References in corpus (7)

• Quantized thermal conductance of dielectric quantum wires
• Irreversible Performance of a Quantum Harmonic Heat Engine
• Performance of discrete heat engines and heat pumps in finite time
• The Quantum Four Stroke Heat Engine: Thermodynamic Observables in a Model with Intrinsic Friction
• A Discrete Four Stroke Quantum Heat Engine Exploring the Origin of Friction
• Characteristics of the Limit Cycle of a Reciprocating Quantum Heat Engine
• Notes on the Third Law of Thermodynamics.I

Cited by in corpus (55)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Quantum Thermodynamics
• Fast optimal frictionless atom cooling in harmonic traps
• Shortcuts to adiabaticity
• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• The quantum harmonic Otto cycle
• Controlling open quantum systems: Tools, achievements, and limitations
• The Quantum Absorption Refrigerator
• Quantum Refrigerator and the III-law of Thermodynamics
• Quantum Supremacy of Many-Particle Thermal Machines
• Superadiabatic population transfer in a three-level superconducting circuit
• Scaling-up quantum heat engines efficiently via shortcuts to adiabaticity
• Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
• Optimal refrigerator
• The smallest refrigerators can reach maximal efficiency
• Thermodynamic limits of dynamic cooling
• Shortcuts to adiabaticity using flow fields
• An efficient non-linear Feshbach engine
• Shortcut-to-adiabaticity quantum Otto refrigerator
• Short Time Cycles of Purely Quantum Refrigerators
• Occurrence of discontinuities in the performance of finite-time quantum Otto cycles
• Optimal control of quantum thermal machines using machine learning
• Enabling quantum non-Markovian dynamics by injection of classical colored noise
• Quantum heat engine based on level degeneracy
• Floquet-engineered quantum state manipulation in a noisy qubit
• Optimal Efficiency of a Noisy Quantum Heat Engine
• Irreversible Work and Internal Friction in a Quantum Otto Cycle of a Single Arbitrary Spin
• Work and Efficiency of Quantum Otto Cycles in Power Law Trapping Potentials
• Quantum heat engines: limit cycles and exceptional points
• Quantum speed limit constraints on a nanoscale autonomous refrigerator
• Fast driving between arbitrary states of a quantum particle by trap deformation
• Simulating spin chains using a superconducting circuit: gauge invariance, superadiabatic transport, and broken time-reversal symmetry
• Dynamical Casimir effect and minimal temperature in quantum thermodynamics
• Resonant shortcuts for adiabatic rapid passage with only $z$-field control
• Thermodynamics of quantum feedback cooling
• A third-order exceptional point effect on the dynamics of a single particle in a time-dependent harmonic trap
• The minimal temperature of Quantum Refrigerators
• Counter-diabatic driving for fast spin control in a two-electron double quantum dot
• Multi-spin counter-diabatic driving in many-body quantum Otto refrigerators
• Speeding up adiabatic passage with an optimal modified Roland-Cerf protocol
• Exact Delta Kick Cooling, Time-Optimal Control of Scale-Invariant Dynamics, and Shortcuts to Adiabaticity Assisted by Kicks
• Friction-free quantum machines
• Shortcuts to adiabaticity for an interacting Bose-Einstein condensate via exact solutions of the generalized Ermakov equation
• Thermodynamics of a minimal algorithmic cooling refrigerator
• Quantum Work Fluctuations in connection with Jarzynski Equality
• Nonadiabatic energy fluctuations of scale-invariant quantum systems in a time-dependent trap
• The interplay between cycle geometry and performance of sudden refrigerators
• An Exponential Bound in the Quest for Absolute Zero
• Anisotropy-assisted thermodynamic advantage of a local-spin thermal machine
• Quantum Pontryagin Principle under Continuous Measurements and Feedback
• Effective Scaling Approach to Frictionless Quantum Quenches in Trapped Bose Gases
• A shortcut to adiabaticity in a cavity with a moving mirror
• Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
• The EPR Paradox Implies A Minimum Achievable Temperature
• Irreversible Work Reduction by Disorder in Many-Body Quantum Systems