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arXiv:physics/9707025 · Physical Review A

Time-dependent control of ultracold atoms in magnetic traps

Nikolay V. Vitanov, Kalle‐Antti Suominen

Published Dec 1, 1997• 49 citations
arXivHTMLPDF

Abstract

With radio-frequency fields one can control ultracold atoms in magnetic traps. These fields couple the atomic spin states, and are used in evaporative cooling that can lead to Bose-Einstein condensation in the atom cloud. Also, they can be used in controlled release of the condensate from the trap, thus providing output couplers for atom lasers. In this paper we show that the time-dependent multistate models for these processes have exact solutions that are polynomials of the solutions of the corresponding two-state models. This allows simple, in many cases analytic, descriptions for the time-dependent control of the magnetically trapped ultracold atoms.

DOI
10.1103/physreva.56.r4377

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With radio-frequency fields one can control ultracold atoms in magnetic traps. These fields couple the atomic spin states, and are used in evaporative cooling that can lead to Bose-Einstein condensation in the atom cloud. Also, they can be used in controlled release of the condensate from the trap, thus providing output couplers for atom lasers. In this paper we show that the time-dependent multistate models for these processes have exact solutions that are polynomials of the solutions of the corresponding two-state models. This allows simple, in many cases analytic, descriptions for the time-dependent control of the magnetically trapped ultracold atoms.
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.
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 have calculated the time-dependent dynamics of two ultracold Na atoms in an atom trap where a time-dependent magnetic field B(t)B(t)B(t) moves a Feshbach resonance state across the energy threshold for a binary collision. Our coupled-channel scattering calculations, which reproduce the observed properties of such resonances in sodium atom collisions, can be reduced to an effective two-channel configuration-interaction model for one bound state and one continuum. The model is adapted to describe the time-dependent dynamics induced by B(t)B(t)B(t) for two atoms trapped either in a strongly confining single well of an optical lattice or in an optical potential in the presence of a Bose-Einstein condensate. We show that a simple Landau-Zener curve crossing model gives quantitative agreement with exact calculations of field-induced transition rates. If B(t)B(t)B(t) sweeps the resonance across threshold from above, two atoms in the ground state of the trap potential can be efficiently converted to translationally cold dimer molecules. If the resonance is swept from below, the atoms can be removed from the ground state and placed in hot vibrational levels of the trap. Our calculations reproduce the rapid atom loss rates observed in a Na Bose-Einstein condensate due to sweeping a Feshbach resonance state through the binary collision threshold.
In this work, the RF-dressed potentials generated using a static magnetic field of a quadrupole trap and various radio frequency (RF) fields have been theoretically investigated for trapping and manipulating of cold atoms in a two-dimensional (2D) geometry. In this scheme, the RF fields of some particular polarizations and phases are shown to give rise to some novel static and time-dependent anisotropic two-dimensional potentials that are useful to trap and manipulate the cold atoms in the 2D geometry. The generated time-dependent 2D potentials, rotating on a circular ring, can be used to control the rotation and the oscillation of the cold-atom cloud on the path of the circular ring. The ultracold atoms trapped in these potentials may be used to investigate interesting physics phenomena, such as tunnelling and superfluidity.
We describe a proof-of-principle experiment on a fully permanent magnet atom chip. We study ultracold atoms and produce a Bose-Einstein condensate. The magnetic trap is loaded efficiently by adiabatic transport of a magnetic trap via the application of uniform external fields. Radio frequency spectroscopy is used for in-trap analysis and to determine the temperature of the atomic cloud. The formation of a Bose-Einstein condensate is observed in time-of-flight images and as a narrow peak appearing in the radio frequency spectrum.
PACS 67.85.-d – Ultracold gases, trapped gases Abstract.- We demonstrate that atoms in magnetically insensitive hyperfine states (m=0) can be trapped efficiently by a Bose-Einstein Condensate of the same atomic species occupying a different hyperfine state. The latter is trapped magnetically. Hyperfine state changing collisions, and therefore loss of the trapped (m=0) atoms, are shown to be strongly inhibited in case of a low density of the confined atomic cloud. We monitor the transition from a ’soft ’ to a ’hard’ effective potential by studying the backaction of the trapped (m=0) atoms onto the condensate which provides their confinement. The controlled outcoupling of the trapped atoms by shaping the condensate’s wavefunction is explored. We observe a pulsed emission of atoms from the trapping region reminiscent of an atom laser. Trapped ultracold atomic gases offer outstanding possibilities to model complex quantum systems. A paradigm is the Mott-Insulator phase transition demonstrated with atoms trapped in a lattice potential [1]. Thus, a key ingredient for advancing the possibilities to explore the