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Optics Letters

Decreased damping of ultracold atoms in optical molasses: predictions and a possible solution

N. P. Bigelow, Mara Goff Prentiss

Published Dec 15, 1990• 8 citations
Publisher

Abstract

We derive expressions for the damping rate for a two-level atom trapped in the antinodes of an optical interference pattern. We find that the decay rate is much slower than the rate for untrapped atoms in optical molasses. Although the velocity of untrapped atoms decays exponentially in time, the velocity of trapped atoms decays only as t(-(1/2)). We show that the slow damping rate can be circumvented by the addition of a traveling-wave component to the molasses standing wave and discuss how these results can be extended to multilevel atoms.

DOI
10.1364/ol.15.001479

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Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations
We derive expressions for the damping rate for a two-level atom trapped in the antinodes of an optical interference pattern. We find that the decay rate is much slower than the rate for untrapped atoms in optical molasses. Although the velocity of untrapped atoms decays exponentially in time, the velocity of trapped atoms decays only as t(-(1/2)). We show that the slow damping rate can be circumvented by the addition of a traveling-wave component to the molasses standing wave and discuss how these results can be extended to multilevel atoms.
The force acting on a two-level atom in a low-intensity standing laser wave is calculated. On account of this force, atoms can be trapped at the loops (antinodes) of the field. By quantizing the atomic motion near the bottom of the sinusoidal potential, we have studied the atomic behavior when they are trapped in bound states as well as when they are in the free state. Laser cooling of neutral atoms was first suggested by T. Hansh and A. Schawlow in 1975. The principle involves the Doppler effect in a detuned laser beam. The absorption rate of a photon depends on the apparent frequency of the photon that is shifted ωv/c\omega v/cωv/c from ω\omegaω, where ω\omegaω is the frequency of the laser, v is the velocity of the atom, and c is the velocity of light. For a single laser beam detuned slightly below an atomic resonance frequency, the apparent frequency for atoms moving toward the laser is closer to resonance, which causes a higher absorption rate. And these atoms lose momentum when they absorb a photon from the beam. The velocity of atoms can be decreased from 10$\sp5$ cm/sec, the velocity they have when they escape from an oven, to 10$\sp2$ cm/sec (about 1mK) by a laser beam. For further cooling, counterpropagating beams are necessary. In this study we propose a new mechanism for supercooling, that is, cooling well below the Doppler cooling limit. Within a standing laser wave there exists a force called a "dipole force", which has a sinusoidal spatial dependence. Once atoms are trapped by the potential, their motion around the minimum of the potential well is that of a simple harmonic oscillator. Restricting our attention to the two lowest quantized states, we calculate transition rates between free states and bound states, from which the average residence times in the bound states can be obtained. This first quantum treatment of an atom trapped in the sinusoidal potential is restricted to the one-dimensional case. Generalization to higher dimensions is left for future research.
We observe quantum tunneling of cold sodium atoms from an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. For sufficiently large values of the acceleration, we observe an exponential decay in the number of atoms that remain trapped as a function of the interaction time. We show that this loss is due to quantum tunneling, and compare the decay rates with Landau-Zener theory. We also observe oscillations in the tunneling rate as a function of the acceleration which are due to quantum interference effects.
We describe a numerical implementation of our semiclassical laser-cooling theory [J. Javanainen, Phys. Rev. A 44, 5857 (1991)] for an arbitrary multilevel atom and light field. There is satisfactory agreement between experiments and temperatures obtained from Langevin-equation simulations of the motion of an atom subject to light-pressure force and the accompanying diffusion in three-dimensional (3D) optical molasses in which there are three orthogonal pairs of counterpropagating waves with a common linear polarization for the two beams in a pair, but orthogonal polarizations between the pairs. However, the velocity distribution of the atoms is anisotropic and may deviate strongly from a Gaussian, heterodyne spectra may have a sideband, and the atomic density may be a maximum at the maximum of the potential of the dipole forces of the molasses beams. Subsequent velocity-linearized analysis of atomic damping and diffusion shows that the damping tensor may have a negative eigenvalue corresponding to heating in large regions of space, even though the light is red tuned for cooling. It is also found that the position-averaged damping and diffusion tensors make a poor predictor of the temperature obtained in Langevin-equation simulations and real experiments. Based on additional simulations of a simple 1D model, we formulate a hypothesis that connects our findings. The key idea is that an atom trapped in a minimum of the potential of the dipole forces is subject to a weaker-than-average damping, and therefore tends to boil out of the trap.
A theoretical analysis is given for laser cooling of a two-level atom with magnetic sublevels in the presence of polarization gradients. The optical Bloch equations for the multilevel system are solved numerically for four combinations of polarizations in one-dimensional optical molasses. The light-pressure force on the atom as given by a simple two-level theory is recovered in the absence of polarization gradients, whereas a spatial variation of the polarization is found to lead to a strong cooling force for slow atoms. The increased cooling force is responsible for the recent observations of atoms cooled in optical molasses to temperatures an order of magnitude below the Doppler limit.
We develop a general scheme for studying the optical response of ultracold atoms driven into a regime of standing-wave electromagnetically induced transparency. We rely on full numerical solutions of the Maxwell-Liouville equations without invoking secular and adiabatic approximations and arbitrary initial state assumptions. These approximations and assumptions can conceal, e.g., significant loss and diffusion responsible for the decay of stationary light pulses in cold atomic samples. The complex decay dynamics of a stationary light pulse is here analyzed in terms of higher-order spin and optical coherences that arise from nonlinear interactions of the stationary light pulse with the two counterpropagating components of a standing-wave driving field. Specific results for stationary light pulses in cold 87Rb^{87}\mathrm{Rb}87Rb atoms have been discussed for temperature regimes where the residual Doppler broadening is negligible.
Summary form only given.We report the observation of short-time deviation from exponential decay in a quantum tunneling experiment. Our system consists of ultracold sodium atoms that are trapped in an accelerating periodic optical potential created by a standing wave of light. Atoms can escape the wells via quantum tunneling, and the number that remain is measured as a function of interaction time for a fixed value of the well depth and acceleration. To study tunneling in this system, sodium atoms are first trapped and cooled in a magneto-optical trap. The trapping beams as well as the magnetic field gradient are then turned off, and an accelerating far-detuned standing wave of light is turned on. A three-step acceleration is implemented to measure the loss due to tunneling. Once the final velocity is reached, the potential is turned off and the atomic fluorescence is imaged after a free drift time. We have measured the survival probability and found that the initial survival probability is flat and then crosses over to an exponential decay. The intermediate stage is characterized by a time-dependent loss rate. To analyze the short-time tunneling probability and the approach to exponential decay, we use a simple model of the band structure with a single (trapped) band separated by a bandgap from a free particle state. We find an analytic expression for the survival probability that is quadratic for the first few microseconds of evolution, with a crossover to exponential decay at long times. We show that this crossover time is related to the tunneling time. We also identify a new parameter regime where coherent oscillations of the survival probability are seen.