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arXiv:physics/9910043 · Physical Review A

Atomic dynamics in evaporative cooling of trapped alkali-metal atoms in strong magnetic fields

Olli H. Pakarinen, Kalle‐Antti Suominen

Published Jul 20, 2000• 5 citations
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Abstract

We investigate how the nonlinear Zeeman shift affects the dynamics of rf field-induced evaporative cooling in magnetic traps. We demonstrate for the ${}^{87}\mathrm{Rb}$ $F=2$ trapping state with wave-packet simulations how the cooling stops when the rf field frequency goes below a certain limit. We examine the applicability of semiclassical models for the strong-field case as an extension of our previous work [Phys. Rev. A 58, 3983 (1998)]. Our results verify many of the aspects observed in a recent ${}^{87}\mathrm{Rb}$ experiment [Phys. Rev. A 60, R1759 (1999)].

DOI
10.1103/physreva.62.025402

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arXiv:0709.2841•Journal of Physics B Atomic Molecular and Optical Physics•Oct 2, 2007•27 citations
We investigate how the nonlinear Zeeman shift affects the dynamics of rf field-induced evaporative cooling in magnetic traps. We demonstrate for the 87Rb{}^{87}\mathrm{Rb}87Rb F=2F=2F=2 trapping state with wave-packet simulations how the cooling stops when the rf field frequency goes below a certain limit. We examine the applicability of semiclassical models for the strong-field case as an extension of our previous work [Phys. Rev. A 58, 3983 (1998)]. Our results verify many of the aspects observed in a recent 87Rb{}^{87}\mathrm{Rb}87Rb experiment [Phys. Rev. A 60, R1759 (1999)].
Radio-frequency-induced evaporative cooling of 87Rb{}^{87}\mathrm{Rb}87Rb atoms in the F=2,F=2,F=2, m=2m=2m=2 ground state in a magnetic trap with a high bias field is found to be hampered, and eventually interrupted, by the presence of nonlinear Zeeman shifts. An experiment studying evaporation at a fixed adjustable rf frequency was used to illustrate this effect. These nonlinear shifts prevent us from reaching quantum degeneracy in the F=2,F=2,F=2, m=2m=2m=2 ground state; however, evaporation in the F=1,F=1,F=1, $m=\ensuremath{-}1$ ground state is not adversely affected, and we can produce a Bose-Einstein condensate (BEC). Our analysis shows that this effect can play a role in many BEC experiments.
Magnetically trapped neutral atoms can be cooled with the evaporation technique. This is typically done by using a radio-frequency (rf) field that adiabatically couples trapped and untrapped internal atomic states for atoms with kinetic energies above a value set by the field frequency. The rf field can also induce nonadiabatic changes of internal atomic spin states (F,M)(F,M)(F,M) that lead to heating and enhanced loss of atoms. In this paper we use wave-packet simulations to show that the evaporation process can induce these nonadiabatic transitions, which change the internal spin state of doubly spin-polarized (2,2) trapped atoms. We also verify the validity of a multistate Landau-Zener model in describing the nonadiabatic dynamics. In addition, we calculate exchange relaxation rate coefficients for collisions between atoms in the (2,M)(2,M)(2,M) states of 23Na{}^{23}\mathrm{Na}23Na atoms. Large exchange relaxation coefficients for 23Na{}^{23}\mathrm{Na}23Na as compared to 87RbF=2{}^{87}\mathrm{Rb} F=287RbF=2 suggest that evaporative cooling of (2,2) Na will be more difficult than for the corresponding state of Rb.
A theoretical investigation for implementing a scheme of forced evaporative cooling in radio-frequency (rf) adiabatic potentials is presented. Supposing the atoms to be trapped in a combination of a dc magnetic field and a rf field at frequency ${\ensuremath{\omega}}_{1}$, the cooling procedure is facilitated using a second rf source at frequency ${\ensuremath{\omega}}_{2}$. This second rf field produces a controlled coupling between the spin states dressed by ${\ensuremath{\omega}}_{1}$. The evaporation is then possible in a pulsed or continuous mode. In the pulsed case, atoms with a given energy are transferred into untrapped dressed states by abruptly switching off the ${\ensuremath{\omega}}_{2}$ coupling. In the continuous case, it is possible for energetic atoms to adiabatically follow the doubly dressed states and escape out of the trap. Our results also show that when ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are separated by at least the Rabi frequency associated with ${\ensuremath{\omega}}_{1}$, additional evaporation zones appear which can make this process more efficient.
We demonstrate a way to circumvent the interruption of evaporative cooling observed at high bias field for 87Rb{}^{87}\mathrm{Rb}87Rb atoms trapped in the (F=2,m=+2)(F=2,m=+2)(F=2,m=+2) ground state. Our scheme uses a three-frequency rf knife achieved by mixing two rf frequencies. This compensates part of the nonlinearity of the Zeeman effect, allowing us to achieve Bose-Einstein condensation where the standard one-frequency rf knife evaporation method did not work. We are able to get efficient evaporative cooling, provided that the residual detuning between the transition and the rf frequencies is smaller than the power broadening of the rf transitions at the end of the evaporation ramp.
The dynamics of atom trapping in a radio-frequency-dressed-state potential formed by static and radio frequency (rf) fields has been studied using the Direct Simulation Monte Carlo (DSMC) technique. Using the simulations, a case of formation of a toroidal trap for cold 87Rb^{87}Rb87Rb atoms is investigated for atoms trapped in a static quadrupole magnetic trap and exposed to an rf-field with temporally increasing amplitude and decreasing frequency. We first calculate the adiabatic rf-dressed potential for an atom interacting with these fields and then apply DSMC algorithm to simulate the motion of the atom in this time dependent adiabatic potential. In the simulations the Landau-Zener (LZ) transition probability is calculated to know if the atom is in the trappable or untrappable dressed state. The results show that, initially at lower rf-field strength, the rf-field ejects atoms from the trap and leads to evaporative cooling of the atom cloud. However at higher rf-field strength, the atoms make LZ transition to the trappable dressed state which results in a toroidal shape to the atom cloud. The results of numerical simulations show a qualitative agreement with the experimental observations.
We observe the spontaneous evaporation of atoms confined in a bubble-like radio frequency (rf)-dressed trap (Zobay and Garraway 2001 Phys. Rev. Lett. 86 1195; 2004 Phys. Rev. A 69 023605). The atoms are confined in a quadrupole magnetic trap and are dressed by a linearly polarized rf field. The evaporation is related to the presence of holes in the trap, at the positions where the rf coupling vanishes, due to its vectorial character. The final temperature results from a competition between residual heating and evaporation efficiency, which is controlled via the height of the holes with respect to the bottom of the trap. The experimental data are modelled by a Monte Carlo simulation predicting a small increase in phase-space density limited by the heating rate. This increase was within the phase-space density determination uncertainty of the experiment.