A simple result of scalar diffraction theory is used to derive the round trip phase accrual of a plane wave in dye laser oscillators containing gratings. This is used to determine configurations where the standing wave condition is satisfied at the feedback wavelength throughout an angle scan. We find that at least one such exactly synchronous configuration always exists regardless of oscillator type.
We consider quantized motion of neutral atoms cooled below the recoil limit in a quadrupole magnetostatic trap. Because of Majorana transitions to untrapped levels near the point of zero field at the trap center, all quantum levels have a nonzero decay rate. The Schrodinger equation associated with the potential gAB S (S is the total atomic spin) takes the form of coupled equations in r when the spinor components are expanded in spherical harmonics. We integrate the multichannel problem numerically to obtain asymptotic phase shifts, resonance energies, and widths. For S = 1/2, the lowest levels have widths somewhat less than their spacing. Thus the trap quantum-level structure might possibly be observable if the atoms are sufficiently cold, namely, in the 0.1-,uK regime for most atoms and attainable trap field gradients. The width decreases rapidly with increasing Mj, the angular momentum about the symmetry axis. Spectroscopic linewidths of a few hertz are possible if there is enough population in the lowest levels with a few Mj quanta. The decay rate of the lowest levels, however, is probably too rapid for studying Bose-Einstein condensation in such a trap.
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