Ehrenfest Dynamics and Frictionless Cooling Methods

Abstract

Recently introduced methods which result in shortcuts to adiabaticity, particularly in the context of frictionless cooling, are rederived and discussed in the framework of an approach based on Ehrenfest dynamics. This construction provides physical insights into the emergence of the Ermakov equation, the choice of its boundary conditions, and the use of minimum uncertainty states as indicators of the efficiency of the procedure. Additionally, it facilitates the extension of frictionless cooling to more general situations of physical relevance, such as optical dipole trapping schemes. In this context, we discuss frictionless cooling in the short-time limit, a complementary case to the one considered in the literature, making explicit the limitations intrinsic to the technique when the full three-dimensional case is analyzed.

9 pages, 4 figures, v2: To appear in Physical Review A. (some minor typos corrected and some references added)

References in corpus (8)

• Shortcuts to adiabaticity by counter-diabatic driving
• Single ion heat engine with maximum efficiency at maximum power
• Fast atomic transport without vibrational heating
• Shortcut to adiabaticity for an interacting Bose-Einstein condensate
• Fast optimal transition between two equilibrium states
• Generating shortcuts to adiabaticity in quantum and classical dynamics
• Inverted Oscillator
• Squeezing and robustness of frictionless cooling strategies

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• Exact Delta Kick Cooling, Time-Optimal Control of Scale-Invariant Dynamics, and Shortcuts to Adiabaticity Assisted by Kicks
• Shortcuts to Adiabaticity Assisted by Counterdiabatic Born-Oppenheimer Dynamics
• Quantum inverted harmonic potential
• Ehrenfest approach to open double-well dynamics
• Self-accelerating Parabolic Cylinder Waves in 1-D
• The time-dependent quantum harmonic oscillator: a pedagogical approach via the Lewis-Riesenfeld dynamical invariant method
• Black hole production at lepton colliders