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arXiv:physics/9807052 · Physical Review A

Nonadiabatic dynamics in evaporative cooling of trapped atoms by a radio-frequency field

Kalle‐Antti Suominen, Eite Tiesinga, Paul S. Julienne

Published Nov 1, 1998• 17 citations
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Abstract

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 $(F,M)$ 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 $(2,M)$ states of ${}^{23}\mathrm{Na}$ atoms. Large exchange relaxation coefficients for ${}^{23}\mathrm{Na}$ as compared to ${}^{87}\mathrm{Rb} F=2$ suggest that evaporative cooling of (2,2) Na will be more difficult than for the corresponding state of Rb.

DOI
10.1103/physreva.58.3983

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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.
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.
Nonadiabatic decay rates for a radio-frequency-dressed magnetic trap are calculated using Fermi's golden rule: that is, we examine the probability for a single atom to make transitions out of the dressed trap and into a continuum in the adiabatic limit, where perturbation theory can be applied. This approach can be compared to the semiclassical Landau-Zener theory of a resonant dressed atom trap, and it is found that, when carefully implemented, the Landau-Zener theory overestimates the rate of nonadiabatic spin-flip transitions in the adiabatic limit. This indicates that care is needed when determining requirements on trap Rabi frequency and magnetic-field gradient in practical atom traps.
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)].
We investigate sympathetic cooling fermions 40 K by evaporatively cooling bosonic 87 Rb atoms in a magnetic trap with microwave and radio frequency induced evaporations in detail. The mixture of bosonic and fermionic atoms is prepared in their polarized spin states | F = 9/2, m F = 9/2〉 for 40 K and | F = 2, m F = 2〉 for 87 Rb, which is trapped in Quadrupole—Ioffe—Configuration trap. Comparing microwave with radio frequency evaporatively cooling bosonic 87 Rb atoms with sympathetically cooling Fermi gas 40 K, we find that the presence of rubidium atoms in the |2, 1〉 Zeeman states, which are generated in the evaporative process, gives rise to a significant loss of 40 K due to inelastic collisions. Thus, the rubidium atoms populated in the |2, 1〉 Zeeman states should be removed in order to effectively perform sympathetically cooling 40 K with the evaporatively cooled 87 Rb atoms.
Using a Direct Simulation Monte Carlo technique, we have studied the time evolution of a cold atom cloud interacting with a time dependent radio frequency (rf) dressed state potential. Exposure of a cloud of 87Rb^{87}Rb87Rb atoms, trapped in a quadrupole magnetic trap, to a time dependent rf-field with increasing amplitude and decreasing frequency, shows a variation in the number of trapped atoms and the overall shape of the atom cloud. It is shown by simulations that, initially at lower rf-field strength, the rf-field results in ejection of atoms from the trap, leading to evaporative cooling of the atom cloud. Later, at higher rf-field strength, the atoms undergo the non-adiabatic Landau-Zener (LZ) transitions, which leads to their trapping in an rf-dressed state potential of toroidal shape. The results of simulations explain the experimentally observed results. The simulations can be useful to predict the atom cloud dynamics and trapping geometries with other forms of the potential.