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Physical Review Letters

Radial Confinement of Light in an Ultracold Anisotropic Medium

Mukund Vengalattore, Mara Goff Prentiss

Published Dec 6, 2005• 28 citations
Publisher

Abstract

We demonstrate radial confinement and waveguiding of light in an ultracold anisotropic gas. The waveguiding medium is a laser cooled ensemble of rubidium atoms confined in a trap of large aspect ratio. A recoil induced resonance (RIR) is used to create strong dispersion and large gain in this ensemble. The combination of the anisotropic trap and the RIR give rise to a spatially varying group refractive index resulting in a slow-light optical waveguide. Waveguided pulses of light experience strong gain (approximately 50), low group velocities (c approximately 1500 m/s), and long group delays (delta approximately 7 micros) due to the enhanced path length.

DOI
10.1103/physrevlett.95.243601

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We demonstrate radial confinement and waveguiding of light in an ultracold anisotropic gas. The waveguiding medium is a laser cooled ensemble of rubidium atoms confined in a trap of large aspect ratio. A recoil induced resonance (RIR) is used to create strong dispersion and large gain in this ensemble. The combination of the anisotropic trap and the RIR give rise to a spatially varying group refractive index resulting in a slow-light optical waveguide. Waveguided pulses of light experience strong gain (approximately 50), low group velocities (c approximately 1500 m/s), and long group delays (delta approximately 7 micros) due to the enhanced path length.
We demonstrate optical nonlinearities due to the interaction of weak optical fields with the collective motion of a strongly dispersive ultracold gas. The combination of a recoil-induced resonance in the high gain regime and optical waveguiding within the dispersive medium enables us to achieve a collective atomic cooperativity of 275+/-50 even in the absence of a cavity. As a result, we observe optical bistability at input powers as low as 20 pW. The present scheme allows for dynamic optical control of the dispersive properties of the ultracold gas using very weak pulses of light. The experimental observations are in good agreement with a theoretical model.
A collection of ultracold atoms has an index of refraction that varies depending on the spatial density distribution of the gas. For many confined gases commonly found in ultracold atom experiments, there can be a substantial gradient in the spatial density distribution and hence the index of refraction. In addition, these gases can have a smaller spatial extent than that of the cross section of a laser beam that illuminates them. With a sufficient gradient in density under these conditions, the resulting index variation leads to frequency-dependent focusing or defocusing of incident near-resonant light as demonstrated by the calculations in this work. Nonintuitive intensity pattern formations result within the gas from the combination of refraction and diffraction of the incident light, including focusing effects that substantially increase the intensity of the light as compared to its incident value despite the nominally absorptive nature of the gas.
As evidenced by this book, there has been a flurry of activity over the last decade on tailoring the dispersive properties of optical materials [1]. What has captured the attention of the research community were some of the early results on creating spectral regions of large normal dispersion [2-4]. Large normal dispersion results in extremely small group velocities, where the group velocity is the approximate speed at which a pulse of light propagates through a material. We denote the group velocity by υg = c/ng, where c is the speed of light in vacuum and ng is known as the group index. In the early experiments, described in greater detail in Chapter 1, a dilute gas of atoms is illuminated by a control or coupling beamwhose frequency is tuned precisely to an optical transition of an atom. This control field modifies the absorption and dispersion properties of another atomic transition that shares a common energy level. A narrow transparencywindow is created on this second transition-a process known as electromagnetically induced transparency (EIT)—and within this window, υg takes on extremely small values. Many experiments have now observed υg ∼ 1 m/s or less, implying ng > 108. This result is remarkable, considering the fact that the refractive index n of a material rarely exceeds 3 in the visible part of the spectrum.What are the implications of such large group indices? What applications are enabled by this basic science discovery?
A Bose-Einstein condensate illuminated by a single off-resonant laser beam ("dressed condensate") shows a high gain for matter waves and light. We have characterized the optical and atom-optical properties of the dressed condensate by injecting light or atoms, illuminating the key role of long-lived matter wave gratings produced by the condensate at rest and recoiling atoms. The narrow bandwidth for optical gain gave rise to an extremely slow group velocity of an amplified light pulse ( approximately 1 m/s).
Measurements of the temperature dependence of trap loss collisions of laser-cooled rubidium atoms are presented. A significant suppression of the rate of collisions between ground- and excited-state atoms is observed for temperatures below $\\sim$70 mu\\mumuK. In such inelastic collisions, the atomic excitation takes place at long range and must survive against spontaneous decay to short range. Our results are consistent with recent predictions for the low temperature suppression of these collisions due to reduced survival of atomic excitation at low collision velocities.^ We report on measurements of trap loss collisions between ultracold Rb atoms which are confined in a magneto-optical trap. Both isotopes sp85\\sp{85}sp85Rb and sp87\\sp{87}sp87Rb have been studied over wide range of trap laser intensities and detunings. The trap loss collision rates exhibit variations over 3 orders of magnitude. We observe significant differences between the isotopes. At large detunings the ability of the trap to recapture products of the hyperfine-changing collisions is significantly diminished. This finding is supported by our numerical simulations of the recapture process. The trap loss rates due to collisions with room temperature background gas have also been measured.^ Using laser light tuned to a repulsive molecular potential, we have been able to suppress inelastic ground-state hyperfine changing collisions between ultracold sp87\\sp{87}sp87Rb atoms. Adiabatic excitation to the repulsive curve alters the atomic trajectories and prevents the atoms from approaching close enough for the hyperfine change to occur. Experimental results show suppressions up to $\\sim$50% and are in reasonable agreement with a simple Landau-Zener model.^ Finally, we have observed a significant cooperative effect in ultracold trap loss collisions induced by two separate lasers. One laser, tuned close to the atomic resonance, excites the atom pair to an attractive potential at long range. The resulting acceleration and deflection give rise to an enhancement in the collisional flux of ground-state atoms reaching short range, as probed by a second laser. Enhancements up to a factor of $\\sim$3 have been observed. ^
We report on a simple anisotropic magneto-optical trap for neutral atoms that produces a large sample of cold atoms confined in a cylindrically-shaped volume with a high aspect ratio (100:1). Due to the large number of trapped atoms, the laser beams that propagate along the optically thick axis of the trap to cool the atoms are substantially attenuated. We demonstrate that the resulting intensity imbalance produces a net force that spatially localizes the atoms. This limits both the trap length and the total number of trapped atoms. Rotating the cooling beams by a small angle relative to the trap axis avoids the problem of attenuation, and atoms can be trapped throughout the entire available trapping volume. Numerical and experimental results are reported that demonstrate the effects of absorption in an anisotropic trap, and a steady-state, line-center optical path length of 55 is measured for a probe beam propagating along the length of the trap.