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

Physical Review A

Quantum kinetic theory for evaporative cooling of trapped atoms: Growth of Bose-Einstein condensate

Makoto Yamashita, Masato Koashi, Nobuyuki Imoto

Published Mar 1, 1999• 25 citations
Publisher

Abstract

Evaporative cooling of trapped atoms is studied based on the quantum kinetic theory. We extend the classical analysis of Luiten et al. [Phys. Rev. A 53, 381 (1996)] to treat Bose statistics of alkali-metal atoms. Dynamics in evaporative cooling process is described by a kinetic equation for the truncated Bose-Einstein distribution function under the assumption that the system is close to the thermal equilibrium. This approach is applicable to the ``slow'' evaporative cooling normally adopted in most experiments for the efficient production of Bose-Einstein condensates. Time-evolution calculations explain the current experiment well with sodium atoms using a slow evaporative cooling and demonstrate a rapid growth of condensate in the cooling process.

DOI
10.1103/physreva.59.2243

Related papers

Kinetics for evaporative cooling of a trapped gas

Kirstine Berg‐Sørensen

We discuss the kinetic theory for evaporative cooling of a dilute collisional gas in a trap. The analysis in O. J. Luiten et al., Phys. Rev. A 53, 381 (1996) is extended to incorporate a time-dependent trap strength and truncation energy. We employ the equations obtained to predict the efficiency of evaporative cooling of sodium atoms in a Ioffe trap and realize that a time-dependent trap strength can be crucial for the cooling. The calculations are classical in the sense that no effects of quantum statistics are taken into account: nevertheless the results of the calculations are useful in order to reveal experimental routes towards a Bose-Einstein condensate of sodium atoms.

Physical Review A•Feb 1, 1997•24 citations

Kinetic evolution of trapped Bose gas in evaporative cooling

Makoto Yamashita, Masato Koashi, N. Imoto

Summary form only given.The successful demonstrations of Bose-Einstein condensation (BEG) with alkali atoms in a magnetic trap have opened up a new field of quantum physics. The evaporative cooling that enables six-order increase of phase space density is the essential technique for achieving the BEC transition in these experiments. However, at low temperatures, this cooling method is strongly affected by Bose statistics of alkali atoms, since evaporation occurs through the scattering process between trapped atoms. The quantum kinetics of nonequilibrium gas has been the subject of considerable interest for classic gas on the basis of truncated Boltzman distribution. We extend this method to treat the quantum statistics.

Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations

Quantum kinetic theory. VI. The growth of a Bose-Einstein condensate

M. D. Lee, Crispin W. Gardiner

A detailed analysis of the growth of a Bose-Einstein condensate is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose-stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. [Phys. Rev. Lett. 79, 1793 (1997); 81, 5266 (1998)]. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan, Svistunov, and Shlyapnikov (Zh. Eksp. Teor. Fiz. 101, 528 (1992) [Sov. Phys. JETP 75, 387 (1992)]), for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modeling of growth implicitly gives a model of the spatial shape of the density profile of the condensate-vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi-shaped condensate. Our method gives substantially different results for condensate numbers and temperatures obtained from phenomenological fits, but fits the published column density data very well.

arXiv:cond-mat/9912420•Physical Review A•Aug 11, 2000•52 citations

Dynamics of evaporative cooling and growth of a Bose-Einstein condensate

Makoto Yamashita

The dynamics of evaporative cooling of magnetically trapped 87 Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. The theoretical optimization of the cooling trajectory clarifies that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against serious three-body recombination loss. The number of condensed atoms is expected to be largely enhanced by the optimization as compared with the typical value produced by the conventional evaporative cooling, where the frequency of the radio-frequency magnetic field is swept exponentially. Next, we precisely examine how the growth of a condensate depends on the experimental parameters of evaporative cooling in this inefficient exponential-sweep cooling. We find that, due to large nonlinear three-body loss, the number of condensed atoms finally becomes insensitive to the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. This result opens up the experimental possibility that the final number of condensed atoms can be well stabilized against the shot-to-shot fluctuations of experimental conditions in evaporative cooling.

Laser Physics•Jan 1, 2004•0 citations

Dynamics of evaporative cooling in magnetically trapped atomic hydrogen

Makoto Yamashita, Masato Koashi, T. Mukai +2 more

We study the evaporative cooling of magnetically trapped atomic hydrogen on the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is described by the coupled differential equations, considering both the evaporation and dipolar spin relaxation processes. The numerical time-evolution calculations quantitatively agree with the recent experiment of Bose-Einstein condensation with atomic hydrogen. It is demonstrated that the balance between evaporative cooling and heating due to dipolar relaxation limits the number of condensates to $9\ifmmode\times\else\texttimes\fi{}{10}^{8}$ and the corresponding condensate fraction to a small value of 4% as observed experimentally.

arXiv:cond-mat/0007179•Physical Review A•Aug 9, 2000•13 citations

Simulation Method for Evaporative Cooling of Trapped Bose Gases at Finite Temperatures

Emiko Arahata, Tetsuro Nikuni

Abstract We have devised a simulation method for studying the evaporative cooling process of trapped Bose-Einstein condensates at finite temperatures, leveraging the Zaremba-Nikuni-Griffin (ZNG) formalism. This framework incorporates the generalized Gross-Pitaevskii (GP) equation and a semiclassical kinetic equation governing the behavior of the thermal cloud. Our approach builds upon the numerical techniques pioneered by Jackson and Zaremba, which involve simulating the kinetic equation using test particles. A pivotal aspect of our method lies in emulating the evaporative cooling process by selectively removing test particles with high energy. Through extensive simulations, we demonstrate the efficacy of our approach in accurately describing condensate growth during evaporative cooling. Furthermore, we extend our simulations to investigate the formation of vortex lattices during evaporative cooling in the presence of a rotating thermal cloud. This comprehensive analysis provides valuable insights into the intricate dynamics of trapped Bose-Einstein condensates undergoing evaporative cooling processes.

arXiv:2310.03250•Springer proceedings in physics•Jan 1, 2026•0 citations
Evaporative cooling of trapped atoms is studied based on the quantum kinetic theory. We extend the classical analysis of Luiten et al. [Phys. Rev. A 53, 381 (1996)] to treat Bose statistics of alkali-metal atoms. Dynamics in evaporative cooling process is described by a kinetic equation for the truncated Bose-Einstein distribution function under the assumption that the system is close to the thermal equilibrium. This approach is applicable to the ``slow'' evaporative cooling normally adopted in most experiments for the efficient production of Bose-Einstein condensates. Time-evolution calculations explain the current experiment well with sodium atoms using a slow evaporative cooling and demonstrate a rapid growth of condensate in the cooling process.
We discuss the kinetic theory for evaporative cooling of a dilute collisional gas in a trap. The analysis in O. J. Luiten et al., Phys. Rev. A 53, 381 (1996) is extended to incorporate a time-dependent trap strength and truncation energy. We employ the equations obtained to predict the efficiency of evaporative cooling of sodium atoms in a Ioffe trap and realize that a time-dependent trap strength can be crucial for the cooling. The calculations are classical in the sense that no effects of quantum statistics are taken into account: nevertheless the results of the calculations are useful in order to reveal experimental routes towards a Bose-Einstein condensate of sodium atoms.
Summary form only given.The successful demonstrations of Bose-Einstein condensation (BEG) with alkali atoms in a magnetic trap have opened up a new field of quantum physics. The evaporative cooling that enables six-order increase of phase space density is the essential technique for achieving the BEC transition in these experiments. However, at low temperatures, this cooling method is strongly affected by Bose statistics of alkali atoms, since evaporation occurs through the scattering process between trapped atoms. The quantum kinetics of nonequilibrium gas has been the subject of considerable interest for classic gas on the basis of truncated Boltzman distribution. We extend this method to treat the quantum statistics.
A detailed analysis of the growth of a Bose-Einstein condensate is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose-stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. [Phys. Rev. Lett. 79, 1793 (1997); 81, 5266 (1998)]. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan, Svistunov, and Shlyapnikov (Zh. Eksp. Teor. Fiz. 101, 528 (1992) [Sov. Phys. JETP 75, 387 (1992)]), for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modeling of growth implicitly gives a model of the spatial shape of the density profile of the condensate-vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi-shaped condensate. Our method gives substantially different results for condensate numbers and temperatures obtained from phenomenological fits, but fits the published column density data very well.
The dynamics of evaporative cooling of magnetically trapped 87 Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. The theoretical optimization of the cooling trajectory clarifies that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against serious three-body recombination loss. The number of condensed atoms is expected to be largely enhanced by the optimization as compared with the typical value produced by the conventional evaporative cooling, where the frequency of the radio-frequency magnetic field is swept exponentially. Next, we precisely examine how the growth of a condensate depends on the experimental parameters of evaporative cooling in this inefficient exponential-sweep cooling. We find that, due to large nonlinear three-body loss, the number of condensed atoms finally becomes insensitive to the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. This result opens up the experimental possibility that the final number of condensed atoms can be well stabilized against the shot-to-shot fluctuations of experimental conditions in evaporative cooling.
We study the evaporative cooling of magnetically trapped atomic hydrogen on the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is described by the coupled differential equations, considering both the evaporation and dipolar spin relaxation processes. The numerical time-evolution calculations quantitatively agree with the recent experiment of Bose-Einstein condensation with atomic hydrogen. It is demonstrated that the balance between evaporative cooling and heating due to dipolar relaxation limits the number of condensates to $9\ifmmode\times\else\texttimes\fi{}{10}^{8}$ and the corresponding condensate fraction to a small value of 4% as observed experimentally.
Abstract We have devised a simulation method for studying the evaporative cooling process of trapped Bose-Einstein condensates at finite temperatures, leveraging the Zaremba-Nikuni-Griffin (ZNG) formalism. This framework incorporates the generalized Gross-Pitaevskii (GP) equation and a semiclassical kinetic equation governing the behavior of the thermal cloud. Our approach builds upon the numerical techniques pioneered by Jackson and Zaremba, which involve simulating the kinetic equation using test particles. A pivotal aspect of our method lies in emulating the evaporative cooling process by selectively removing test particles with high energy. Through extensive simulations, we demonstrate the efficacy of our approach in accurately describing condensate growth during evaporative cooling. Furthermore, we extend our simulations to investigate the formation of vortex lattices during evaporative cooling in the presence of a rotating thermal cloud. This comprehensive analysis provides valuable insights into the intricate dynamics of trapped Bose-Einstein condensates undergoing evaporative cooling processes.