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Physical Review A

High-velocity dark states in velocity-selective coherent population trapping

M. T. Widmer, M. R. Doery, M. J. Bellanca, Walter F. Buell, T. H. Bergeman, H. Metcalf

Published Feb 1, 1996• 5 citations
Publisher

Abstract

We have observed long-lived dark states in velocity-selective coherent population trapping (VSCPT) in a one-dimensional lin-angle-lin configuration with metastable He atoms using the $J=1\ensuremath{\Rightarrow}1$ transition at $\ensuremath{\lambda}=1.083$ \ensuremath{\mu}m. These states are characterized by two peaks in the atomic momentum distribution at $\ifmmode\pm\else\textpm\fi{}Q\ensuremath{\hbar}k(Q=\mathrm{positive}\mathrm{integer})$, where $k$ is the magnitude of the optical wave vector. VSCPT states previously observed are characterized by $Q=1$, but we have observed long-lived states with $Q=2$. Optical Bloch equation calculations show that these high-velocity dark states appear at higher $Q$ for greater light intensity.

DOI
10.1103/physreva.53.946

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We have observed long-lived dark states in velocity-selective coherent population trapping (VSCPT) in a one-dimensional lin-angle-lin configuration with metastable He atoms using the J=1\ensuremath⇒1J=1\ensuremath{\Rightarrow}1J=1\ensuremath⇒1 transition at \ensuremathλ=1.083\ensuremath{\lambda}=1.083\ensuremathλ=1.083 \ensuremath{\mu}m. These states are characterized by two peaks in the atomic momentum distribution at \ifmmode±\else\textpm\fiQ\ensuremathℏk(Q=positiveinteger)\ifmmode\pm\else\textpm\fi{}Q\ensuremath{\hbar}k(Q=\mathrm{positive}\mathrm{integer})\ifmmode±\else\textpm\fiQ\ensuremathℏk(Q=positiveinteger), where kkk is the magnitude of the optical wave vector. VSCPT states previously observed are characterized by Q=1Q=1Q=1, but we have observed long-lived states with Q=2Q=2Q=2. Optical Bloch equation calculations show that these high-velocity dark states appear at higher QQQ for greater light intensity.
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We present a set of exploratory experimental studies of velocity-selective coherent population trapping (VSCPT) on the $2{}^{3}{S}_{1}\ensuremath{\rightarrow}2{}^{3}{P}_{1}$ transition of Helium, including the effect of an external magnetic field along the propagation direction of the light. We also investigate in detail the effects of the laser detuning and the atom-laser interaction time in determining the shape and width of the VSCPT velocity distribution. Our data corroborates some previous theory and calculations. We demonstrate that the only observable effect of a magnetic field applied along the direction of light propagation is to shift the center of the VSCPT peaks in the atomic velocity distribution by an amount proportional to the magnitude of the applied field. We present a semiclassical picture that describes the atomic motion of VSCPT in such a B field.
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We show theoretically that velocity-selective coherent population trapping in one dimension may be realized in atomic transitions other than Jg = 1 ↔ Je = 1. The atomic momentum distribution resulting from irradiation by counterpropagating σ+–σ− waves on the Jg = 3/2 ↔ Je = 1/2 and the Jg = 2 ↔ Je = 1 atomic transitions is investigated through solution of the optical Bloch equations and determination of the effective loss rates for atomic eigenstates. An inverted-W atomic level configuration is also used to investigate the features of velocity-selective coherent population trapping. The momentum distribution exhibits peaks at the ±ħk or the ±ħ2k and the 0 momenta, depending on the atomic transitions and the laser intensity. These structures, generated by atomic states that do not interact with the laser radiation, are stable when associated with eigenstates of the kinetic energy, or metastables; i.e., the structures last several hundred spontaneous lifetimes when generated by nonexact kinetic-energy eigenstates.
Atoms can be accumulated by velocity-selective coherent population trapping (VSCPT) in dark states of very highly monovelocity, resulting in very narrow distributions. The optical pumping process that permits the population accumulation proceeds by random walk in momentum space and is of limited efficiency. Several authors have predicted that damping forces can enhance VSCPT in carefully chosen laser fields. We present corroboration of this idea with measurements showing increased efficiency for VSCPT.
We study the mean-field dynamics of atoms in a velocity-selective coherent population trapping (VSCPT) configuration, under the influence of resonant dipole-dipole interactions. By elimination of the transverse electromagnetic field we derive a Heisenberg master equation for an arbitrary atomic operator. A closed equation of motion for the one-particle density matrix can be given by employing a time-dependent Hartree-Fock (TDHF) factorization of the two-particle density matrix, thereby neglecting two-particle correlations, i.e., collisional effects. In the case of bosons, the mean-field evolution mainly shows a quantum-statistical enhancement of the spontaneous emission rates, sensitive to the final-state occupation. The description is specialized to treat atoms with a J=1\ensuremath{\rightarrow}${\mathit{J}}^{\ensuremath{'}}$=1 transition in a one-dimensional ${\mathrm{\ensuremath{\sigma}}}^{+}$-${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ VSCPT configuration. The TDHF equations are integrated numerically. It is shown that for a density at which the gas is optically dense, the number of atoms, trapped in the dark state, is increased and its momentum width is decreased. \textcopyright{} 1996 The American Physical Society.