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Semi-classical evaporative cooling: classical and quantum distributions

A. A. Arvizu-Velazquez, A. A. del Río-Lima, S. Dondé-Rodríguez, F. J. Poveda-Cuevas

Abstract

A unified semiclassical framework is presented to describe the evaporative cooling of trapped atomic gases, accounting for both classical and quantum statistics. By combining global thermodynamics with phase-space distributions, general analytic expressions for the particle number and internal energy are derived for a broad family of confining potentials. Building on these results, a recursive evaporation protocol is formulated based on truncated energy distributions, enabling stepwise mapping between successive thermodynamic states and revealing the system's degree of freedom governance over cooling efficiency. Numerical simulations of the systems highlight the contrasting behavior of classical and quantum systems as they approach degeneracy, with particularly distinctive signatures in quadrupole traps, due to their nonstandard phase-space scaling. The results provide a versatile theoretical tool for modeling evaporative cooling across experimentally relevant geometries and offer quantitative guidance for optimizing cooling trajectories in ultracold atomic systems.

Semi-classical evaporative cooling: classical and quantum distributions

Abstract

A unified semiclassical framework is presented to describe the evaporative cooling of trapped atomic gases, accounting for both classical and quantum statistics. By combining global thermodynamics with phase-space distributions, general analytic expressions for the particle number and internal energy are derived for a broad family of confining potentials. Building on these results, a recursive evaporation protocol is formulated based on truncated energy distributions, enabling stepwise mapping between successive thermodynamic states and revealing the system's degree of freedom governance over cooling efficiency. Numerical simulations of the systems highlight the contrasting behavior of classical and quantum systems as they approach degeneracy, with particularly distinctive signatures in quadrupole traps, due to their nonstandard phase-space scaling. The results provide a versatile theoretical tool for modeling evaporative cooling across experimentally relevant geometries and offer quantitative guidance for optimizing cooling trajectories in ultracold atomic systems.
Paper Structure (10 sections, 37 equations, 2 figures, 1 table)

This paper contains 10 sections, 37 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Thermodynamics of trapped atomic gases
  3. The Ideal Gas Limit
  4. Semiclassical distribution for trapped gases
  5. Thermodynamic variables for confining potentials
  6. Evaporative cooling
  7. Evaporative cooling protocol
  8. Applied evaporative cooling protocol
  9. Numerical results and discussion
  10. Conclusions

Figures (2)

  • Figure 1: Scheme protocol of evaporation. (a) We start with a gas distribution at temperature $T_0$ and with $N_0$ atoms. Then, (b) a cut is made in said distribution, discarding those higher-energy atoms. After this process, (c) the system re-thermalizes to a new temperature, $T_1$, and a new number, $N_1$, where both will be lower than the initial conditions.
  • Figure 2: Sample temperature is a function of the cut-off energy for a system confined in a box, harmonic, and quadrupole potential. They all have an initial temperature of $50 \mu$K, a cut-off energy of $\eta_0=0.5$mK, and a fixed step of $\Delta \eta= 0.1 ~\mu \mathrm{K}$.