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Quantum Electronics and Laser Science Conference

Forces on three-level atoms including trapped-state contribution

M. S. Shahriar, Philip Hemmer, N. P. Bigelow, Mara Goff Prentiss

Published May 12, 1991• 1 citation
OpenAlex

Abstract

In this paper we present a new calculation of the force on a stationary three-level atom in a bichromatic standing-wave light field (see Fig. 1). Contrary to other theoretical treatments,1 which ignore optical pumping into the trapped state, we find that a stationary atom experiences no force when there is no difference frequency detuning (i.e., when Δ = 0). However, when there is a nonzero differential detuning (Δ ≠ 0) there can be force components that vary in both the wavelength of the optical fields and their beat wavelength. This stimulated force can be much larger than the maximum spontaneous force associated with this system. To obtain a simple physical interpretation of this force, the problem is treated in a basis that is formed from symmetric |+〉 and antisymmetric |−〉 linear combinations of the atomic ground states2 (see Fig. 1).

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arXiv:1307.7156•Physical Review A•Oct 16, 2013•24 citations
In this paper we present a new calculation of the force on a stationary three-level atom in a bichromatic standing-wave light field (see Fig. 1). Contrary to other theoretical treatments,1 which ignore optical pumping into the trapped state, we find that a stationary atom experiences no force when there is no difference frequency detuning (i.e., when Δ = 0). However, when there is a nonzero differential detuning (Δ ≠ 0) there can be force components that vary in both the wavelength of the optical fields and their beat wavelength. This stimulated force can be much larger than the maximum spontaneous force associated with this system. To obtain a simple physical interpretation of this force, the problem is treated in a basis that is formed from symmetric |+〉 and antisymmetric |−〉 linear combinations of the atomic ground states2 (see Fig. 1).
We present a calculation of the force on a stationary three-level atom excited by a nearly resonant Raman light field, which may be composed of an arbitrary combination of standing- and traveling-wave fields. The effects of the ground-state coherences are explicitly included and are shown to play a crucial role in the nature of the force on the atom. We show that the force contains terms that vary on length scales both shorter and longer than the optical wavelength and that the magnitude of these terms can be made arbitrarily large.
Rectified dipole forces1 offer the possibility of providing deep potential wells for neutral atoms. In the intense standing wave, a two-level atom can experience a large dipole force due to the large intensity gradient. However, this force changes sign on the optical wavelength scale, preventing the formation of deep potential wells. If a second, nearly commensurate, standing wave is added, its ac Stark shift causes the effective detuning of the first field to vary on the optical wavelength scale. The resulting change in sign of the detuning can counteract the change in sign of the intensity gradient, causing the force to maintain its sign over many wavelengths (i.e., the force becomes rectified), thereby forming a deep potential well. This rectified force is periodic with the beat wavelength between the two laser fields. In a three-level atom the same basic mechanism applies, but with the advantage that the two frequencies of the bichromatic standing wave can now be tuned dose to resonance with the two transitions of the atom.
A sodium atomic beam is deflected by two optical standing-wave fields which excite near resonance Raman transitions. Observed deflections are consistent with theoretical predictions of a long-range dc component of the force on a three-level atom in the \ensuremath{\Lambda} configuration. The low laser intensities (and small detunings) used, combined with observed evidence of damping in the three-level \ensuremath{\Lambda} system, may ultimately lead to the design of high-density, all optical traps wherein the atoms would be mostly in the dark state.
On the previous work of acquiring an unidirectional dipole force over macro-quantitative optical wavelengths by imposing two standing waves of two different frequencies on an atom in the reference[1],the fluctuation of the rectified dipole-force is derived and calculated by means of quantum aggressive theory.The results show that DI from the interaction between atomic dipole's zero-point fluctuation and the gradient of the light field amplitude has great magnitude being the dominant factor of the fluctuation and varies as the space extremely similar with the rectified dipole force;DS from the interaction between the atomic dipole and zero-point vacuum's vibration is so small that it can be neglected.The heating effect of the atom from the fluctuations is harmful for the atom's trapping by means of dipole force.
Stimulated optical forces offer a simple and efficient method for providing optical forces far in excess of the saturated radiative force. The bichromatic force, using a counterpropagating pair of two-color beams, has so far been the most effective of these stimulated forces for deflecting and slowing atomic beams. We have numerically studied the evolution of a two-level system under several different bichromatic and polychromatic light fields, while retaining the overall geometry of the bichromatic force. New insights are gained by studying the time-dependent trajectory of the Bloch vector, including a better understanding of the remarkable robustness of bi- and polychromatic forces with imbalanced beam intensities. We show that a four-color polychromatic force exhibits great promise. By adding new frequency components at the third harmonic of the original bichromatic detuning, the force is increased by nearly 50% and its velocity range is extended by a factor of 3, while the required laser power is increased by only 33%. The excited-state fraction, crucial to possible application to molecules, is reduced from 41% to 24%. We also discuss some important differences between polychromatic forces and pulse trains from a high-repetition-rate laser.