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International Journal of Modern Physics B

SCHRÖDINGER MODAL STRUCTURE OF A SODIUM ATOM BETWEEN PARALLEL PLATES

S. Al‐Awfi

Published Apr 30, 2004• 2 citations
Publisher

Abstract

We investigate the vibrational energy eigenvalues and eigenfunctions of the neutral sodium atom trapped by the optical dipole potential due to a cavity mode. Our model is based on the optical confinement of a sodium atom between parallel plates with its dipole moment vector fixed in the axial direction of the cavity. The negative detuning situation and suitable parameters are taken in order to maintain a sufficiently deep central well of the optical dipole potential to allow many quasi harmonics trapped states of the atom.

DOI
10.1142/s0217979204024811

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The dynamics of atoms subject to laser light propagating between perfectly conducting parallel plates is investigated. In the semiclassical approximation the motion of atoms in this context is governed by a van der Waals--type potential, together with a dynamic dipole potential that comes into play as soon as a cavity mode is excited. In addition, the atoms become subject to an average dissipative (spontaneous) force associated with the cavity mode that always acts parallel to the plates. We show that, by a suitable choice of field intensity and detuning, the total transverse potential can be used to confine atoms in transverse vibrational states, while their motion in the parallel direction is controlled by the dissipative force. Significant variations of the characteristics of the system with atom velocity, dipole orientation, and type of excited cavity mode are emphasized. These features are illustrated using typical parameters for the case of sodium atoms between parallel plates with subwavelength separations.
We describe a relatively large volume dipole laser trap for the confinement of sodium atoms. Two counterpropagating beams, tuned below resonance, with foci separated by approximately one con focal parameter, provide radial confinement via the dipole force and axial confinement by balancing the radiation pressures of the two beams.1 Identical circular polarization for both beams prevents optical pumping and serves to maintain a two-state system. Alternation of the two beams2 is necessary to avoid the effects of standing-wave heating. Additionally, the trapping cycle is alternated with a Doppler cooling cycle2 to achieve low temperatures and long confinement times. Trapping beams of 100 mW focused to 50-μm spot radii and detuned ~2 GHz below the F = 2 to F′= 3 transition of the D2 line provide a well depth of 50 mK and a confinement volume of 10-4 cm3. Analysis of atomic motion and escape mechanisms as well as progress toward the experimental realization of this trap is presented.
Summary form only given. A new regime in cavity QED is realized in which single atoms interact with the cavity field for very long times (i.e., many Rabi cycles) and in which the atomic kinetic energy is comparable to or smaller than the dipole coupling energy. The mechanical effects of just a few-photon light field should therefore enable single atoms to be trapped in effective potential wells. We consider such a situation in the far detuned dispersive regime of cavity QED, where a single atom is confined in the lower (quantized) bound states of the effective optical potential formed around an antinode of the standing wave cavity field.
In the absence of external modes, cavity dimensions and dipole location are the main factors that increase, reduce and disallow dipole decay rate in the Cavity QED. The presence of external modes with short cavity length, high atom velocity and high intensity is con- sidered as a reasonable source of constrain to the dipole vector in a fixed direction. As a result, only two orthogonal directions can be as- sumed: π polarization and σ polarization. These directions can be used to illustrate the variations of Cavity QED effects with dipole adjust- ment. Thus the distribution of the dipole decay rate across the plates separation is independent of the excited cavity mode. In contrast, dur- ing the passage of a slow atom between the plates, the dipole can ad- just itself along a local electric field direction. In this work, it has been proven that the average dipole adjustment is determined at every point parallel to the direction of the electric mode vector of the excit- ed cavity mode. Also the subordination was shown to lead to observ- able changes in the dipole decay rate. The above cases have been explored for situations involving sodium atoms between conducting plates of the sub-wavelength range.