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Physical Review A

Collisionless motion and evaporative cooling of atoms in magnetic traps

E.L. Surkov, Jook T. M. Walraven, Georgy V. Shlyapnikov

Published May 1, 1996• 40 citations
Publisher

Abstract

We analyze the collisionless motion of atoms in magnetic traps in relation to evaporative cooling. For the example of a long Ioffe quadrupole trap we investigate both the regular and stochastic regimes of motion. We emphasize a strong influence of the regime of collisionless motion on the process of evaporative cooling. For evaporation of atoms across an axial potential barrier the stochastic motion of atoms at energies above the barrier enables three-dimensional evaporation, i.e., particles acquiring in elastic collisions a total enery higher than the barrier height ${\mathit{E}}_{0}$ escape from the trap. The regular motion leads to axial evaporation: only atoms which due to collisions acquire an axial energy higher than ${\mathit{E}}_{0}$ leave the trap. The rate of axial evaporation is smaller by a factor \ensuremath{\sim}\ensuremath{\eta}=${\mathit{E}}_{0}$/T\ensuremath{\gg}1, where T is the gas temperature. This has important consequences for evaporative cooling, which we discuss in relation to trapped atomic hydrogen. \textcopyright{}1996 The American Physical Society.

DOI
10.1103/physreva.53.3403

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We present an analytical and numerical analysis of collisionless motion of neutral particles in magnetostatic traps. We treat the example of an idealized Ioffe quadrupole trap, emphasizing that the essential features of coupling between the degrees of freedom are of general relevance for static traps. In common situations the coupling between axial and radial motion predominantly occurs in a regular way. The coupling is weak, in particular, when the frequency of axial oscillations ${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$ is much smaller than the radial frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{\ensuremath{\rho}}}$ and the particle energy is much lower than the Zeeman energy in the center of the trap. Then, under an adiabatic change of the potential parameters, the quantity ${\mathit{scrE}}_{\mathit{z}}$/${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$, where ${\mathit{scrE}}_{\mathit{z}}$ is a characteristic axial energy, is an approximate adiabatic invariant. If ${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$ is decreasing and ${\mathrm{\ensuremath{\Omega}}}_{\mathit{p}}$ is constant, then the characteristic radial energy ${\mathit{scrE}}_{\mathrm{\ensuremath{\rho}}}$ will remain constant while ${\mathit{scrE}}_{\mathit{z}}$ decreases proportionally to ${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$. This implies one-dimensional adiabatic cooling, which is an interesting option for gravitational studies of light atoms such as hydrogen and antihydrogen.

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Atomic hydrogen in magnetostatic traps

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Evaporation-limited loading of an atomic trap

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Recently, we have experimentally demonstrated a continuous loading mechanism for an optical dipole trap from a guided atomic beam [M. Falkenau, V. V. Volchkov, J. R\"uhrig, A. Griesmaier, and T. Pfau, Phys. Rev. Lett. 106, 163002 (2011)]. The observed evolution of the number of atoms and temperature in the trap are consequences of the unusual trap geometry. In the present paper, we develop a model based on a set of rate equations to describe the loading dynamics of such a mechanism. We consider the collision statistics in the nonuniform trap potential that leads to two-dimensional evaporation. The comparison between the resulting computations and experimental data allows to identify the dominant loss process and suggests ways to enhance the achievable steady-state atom number. Concerning subsequent evaporative cooling, we find that the possibility of controlling axial and radial confinement independently allows faster evaporation ramps compared to single beam optical dipole traps.

arXiv:1202.6167•Physical Review A•Feb 21, 2012•6 citations
We analyze the collisionless motion of atoms in magnetic traps in relation to evaporative cooling. For the example of a long Ioffe quadrupole trap we investigate both the regular and stochastic regimes of motion. We emphasize a strong influence of the regime of collisionless motion on the process of evaporative cooling. For evaporation of atoms across an axial potential barrier the stochastic motion of atoms at energies above the barrier enables three-dimensional evaporation, i.e., particles acquiring in elastic collisions a total enery higher than the barrier height E0{\mathit{E}}_{0}E0​ escape from the trap. The regular motion leads to axial evaporation: only atoms which due to collisions acquire an axial energy higher than E0{\mathit{E}}_{0}E0​ leave the trap. The rate of axial evaporation is smaller by a factor \ensuremath{\sim}\ensuremath{\eta}=E0{\mathit{E}}_{0}E0​/T\ensuremath{\gg}1, where T is the gas temperature. This has important consequences for evaporative cooling, which we discuss in relation to trapped atomic hydrogen. \textcopyright{}1996 The American Physical Society.
We present an analytical and numerical analysis of collisionless motion of neutral particles in magnetostatic traps. We treat the example of an idealized Ioffe quadrupole trap, emphasizing that the essential features of coupling between the degrees of freedom are of general relevance for static traps. In common situations the coupling between axial and radial motion predominantly occurs in a regular way. The coupling is weak, in particular, when the frequency of axial oscillations ${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$ is much smaller than the radial frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{\ensuremath{\rho}}}$ and the particle energy is much lower than the Zeeman energy in the center of the trap. Then, under an adiabatic change of the potential parameters, the quantity scrEz{\mathit{scrE}}_{\mathit{z}}scrEz​/${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$, where scrEz{\mathit{scrE}}_{\mathit{z}}scrEz​ is a characteristic axial energy, is an approximate adiabatic invariant. If ${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$ is decreasing and ${\mathrm{\ensuremath{\Omega}}}_{\mathit{p}}$ is constant, then the characteristic radial energy ${\mathit{scrE}}_{\mathrm{\ensuremath{\rho}}}$ will remain constant while scrEz{\mathit{scrE}}_{\mathit{z}}scrEz​ decreases proportionally to ${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$. This implies one-dimensional adiabatic cooling, which is an interesting option for gravitational studies of light atoms such as hydrogen and antihydrogen.
We apply kinetic theory to the problem of evaporative cooling of a dilute collisional gas in a trap. Assuming ``sufficient ergodicity'' (phase-space distribution only a function of energy) and s-wave collisions with an energy-independent cross section, an equation for the evolution of the energy distribution of trapped atoms is derived for arbitrary trap shapes. Numerical integration of this kinetic equation demonstrates that during evaporation the gas is accurately characterized by a Boltzmann distribution of atom energies, truncated at the trap depth. Adopting the assumption of a truncated Boltzmann distribution, closed expressions are obtained for the thermodynamic properties of the gas as well as for the particle and energy loss rates due to evaporation. We give analytical expressions both for power-law traps and for a realistic trapping potential (Ioffe quadrupole trap). As an application, we discuss the evaporative cooling of trapped atomic hydrogen gas. \textcopyright{} 1996 The American Physical Society.
This chapter begins with an introductory summary of basic properties of spin-polarised hydrogen. It discusses the properties of atomic quantum gases at ultra-low temperatures with atomic hydrogen as a primary example. Building on the extensive experience of various research groups with the low temperature gas phase of atomic hydrogen, many interesting aspects could be illustrated with well established experimental and theoretical results. As for many traps the single-particle motion is non-ergodic, interatomic collisions are usually essential to assure ‘sufficient ergodicity’. The chapter also discusses a number of thermodynamic properties relevant for the description of evaporative cooling using the truncated exponential energy distribution as a starting point. It considers the case of plain evaporative cooling. In forced evaporative cooling the escape threshold is lowered with decreasing temperature, thus allowing the evaporation to proceed at a desired rate.
Ultra-cold Collisions and Evaporative Cooling of Caesium in a Magnetic Trap Angharad Mair Thomas, Jesus College, Oxford University DPhil Thesis, Hilary Term 2004 Caesium-133 atoms have been evaporatively cooled in a magnetic trap to temperatures as low as 8 nK producing a final phase-space density within a factor of 4 of that required for the onset of Bose-Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3,mF = −3 state remain in the magnetic trap. A decrease in the one-dimensional evaporative cooling efficiency at very low temperatures is observed as the trapped sample enters the collisionally thick (hydrodynamic) regime. Different evaporation trajectories are experimentally studied leading to a greater understanding of one-dimensional evaporation, inelastic collisions and the hydrodynamic regime. A theoretical simulation accurately reproduces the experimental data and indicates that the reduction in the evaporative cooling efficiency as the cloud enters the hydrodynamic regime is the main obstacle to the realization of Bose-Einstein condensation in the F = 3,mF = −3 state. In addition, we report measurements of the two-body inelastic collision rate coefficient for caesium atoms as a function of magnetic field and collision energy. The positions of three previously identified resonances are confirmed, with reduced uncertainties, at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) Gauss. The resonance centred at 118.46Gauss is also investigated as a function of temperature, thus demonstrating the dependence of the inelastic Feshbach resonance on collision energy. The importance of including partial waves of a higher basis in theoretical
We have evaporatively cooled caesium atoms in a magnetic trap to temperatures as low as 8 nK and produced a final phase space density within a factor of four of that required for the onset of Bose–Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3, m F = −3 state remain in the magnetic trap. We observe a decrease in the one-dimensional evaporative cooling efficiency at very low temperatures as the trapped sample enters the collisionally thick (hydrodynamic) regime. To alleviate this problem we propose a modified trapping scheme where three-dimensional evaporation is possible. In addition, we report measurements of the two-body inelastic collision rates for caesium atoms as a function of magnetic field. We confirm the positions, with reduced uncertainties, of three previously identified resonances at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) G.
Recently, we have experimentally demonstrated a continuous loading mechanism for an optical dipole trap from a guided atomic beam [M. Falkenau, V. V. Volchkov, J. R\"uhrig, A. Griesmaier, and T. Pfau, Phys. Rev. Lett. 106, 163002 (2011)]. The observed evolution of the number of atoms and temperature in the trap are consequences of the unusual trap geometry. In the present paper, we develop a model based on a set of rate equations to describe the loading dynamics of such a mechanism. We consider the collision statistics in the nonuniform trap potential that leads to two-dimensional evaporation. The comparison between the resulting computations and experimental data allows to identify the dominant loss process and suggests ways to enhance the achievable steady-state atom number. Concerning subsequent evaporative cooling, we find that the possibility of controlling axial and radial confinement independently allows faster evaporation ramps compared to single beam optical dipole traps.