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arXiv:1705.00681 · Physical Review A

Nonadiabatic losses from radio-frequency-dressed cold-atom traps: Beyond the Landau-Zener model

Kathryn Burrows, Hélène Perrin, B. M. Garraway

Published Aug 30, 2017• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.96.023429

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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.
Cold atom traps are a promising tool for investigating and manipulating atomic behaviour. Radio frequency (RF) dressed cold atom traps allow high versatility of trapping potentials, which is important for potential applications, particularly in atom interferometry. This thesis investigates non-adiabatic spin flip transitions which can lead to losses of atoms from RF-dressed cold atom traps. We develop two models for the adiabatic potentials associated with RF-dressed traps, for the cases in which gravity does and doesn't have a significant effect. Within these two models we use first order perturbation theory to calculate decay rates for the number of dressed spin flip transitions per unit time. Our obtained decay rates are dependent on the atomic energy. For RF-dressed cold atom traps in which spin flip transitions lead to losses of atoms from the trap, we are able to predict ow non-adiabatic transitions decrease the trapped atom number. We achieve this by modelling the atomic distribution of energies for several different scenarios. The thesis concludes with a comparison to experimental data, including modelling how atomic energies are affected by noise in the currents generating the trapping magnetic fields.
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.
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.
We calculate the rates of inelastic collisions for ultracold alkali-metal atoms in radio-frequency-dressed traps, using coupled-channel scattering calculations on accurate potential energy surfaces. We identify a radio-frequency-induced loss mechanism that does not exist in the absence of radio frequency (rf) radiation. This mechanism is not suppressed by a centrifugal barrier in the outgoing channel, and can be much faster than spin relaxation, which is centrifugally suppressed. We explore the dependence of the rf-induced loss rate on singlet and triplet scattering lengths, hyperfine splittings, and the strength of the rf field. We interpret the results in terms of an adiabatic model of the collision dynamics, and calculate the corresponding nonadiabatic couplings. The loss rate can vary by 10 orders of magnitude as a function of singlet and triplet scattering lengths. 87Rb^{87}\mathrm{Rb}87Rb is a special case, where several factors combine to reduce rf-induced losses; as a result, they are slow compared to spin-relaxation losses. For most other alkali-metal pairs, rf-induced losses are expected to be much faster and may dominate.
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.
We study the hyperfine spectrum of atoms of 87Rb^{87}\mathrm{Rb}87Rb dressed by a radio-frequency field and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap, and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant sidebands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum using a semiclassical model in the low-field limit and the rotating-wave approximation for alkali-metal-like species, in general, and 87Rb^{87}\mathrm{Rb}87Rb atoms, in particular. As a proof of concept, we demonstrate how the spectral signal of a dressed atomic ensemble enables an accurate determination of the dressing configuration and the probing microwave field.