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Quantum Trapping of Atoms in Optical Molasses.

Kimie Takusagawa

Published Oct 1, 1992• 0 citations
OpenAlex

Abstract

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 $\omega v/c$ from $\omega$, where $\omega$ 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.

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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\sp5\sp5 cm/sec, the velocity they have when they escape from an oven, to 10\sp2\sp2\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 present a simple review of the basic physical processes allowing one to control, with laser beams, the velocity and the position of neutral atoms. The control of the velocity corresponds to a cooling of atoms, that is, a reduction of the atomic velocity spread around a given value. The control of the position means a trapping of atoms in real space. The best present performances will be given, in terms of the lowest temperatures and the highest densities. The corresponding highest quantum degeneracy will also be estimated. It is imposed by fundamental limits, which will be described briefly. We also give the general trends in this field of research and outline the new directions which look promising for observing quantum statistical effects in laser cooled atomic samples, but which are for the moment restricted by unsolved problems. Introducing the Simple Schemes The radiative forces acting on atoms in a light field can be split into two parts, a reactive one and a dissipative one. The dissipative force (radiation pressure), which basically involves scattering processes, is velocity dependent. We will see that this dependence leads to the Doppler cooling scheme and to the concept of optical molasses, and we will give the corresponding minimal achievable temperature. The dissipative force can be made position dependent, through a gradient of the magnetic field, so that the atoms are also trapped in the so-called magneto-optical trap.
In two recent experiments Verkerk et al. and our group have observed quantization of the center-of-mass motion of laser cooled atoms in sub-wavelength sized potential wells formed by the light field of a 1-dimensional optical molasses. Our 1-dimensional optical molasses consists of a pair of counterpropagating laser beams of orthogonal, linear polarization, creating a series of potential wells separated by {lambda}/4. Polarization gradient laser cooling reduces the thermal energy of the atoms until they are trapped in well resolved vibrational levels near the bottom of the wells. Transitions between these vibrational levels are seen in a high resolution spectrum of fluorescence, where they give rise to a Rayleigh peak centered at the laser frequency, and well resolved Raman sidebands shifted by a frequency {plus_minus}{omega}, typically on the order of 100 kHz. We find quantitative agreement between the measured level separation h{omega} and the results of a calculation of the bandstructure in the periodic optical potential. Based on the observed ratio of the strength of the blue to the red sideband we determine the temperature of the atoms, and find agreement with theoretical predictions. Based on the level spacing and temperature we find the atoms to be localized to {approx}/15, withmore » up to 50-60% of the population of the trapped atoms in the vibrational ground state. We observe intriguing differences between fluorescence radiated by localized atoms, and the fluorescence radiated by non-localized atoms in a 1-dimensional optical molasses composed of a pair of counterpropagating laser beams of opposite circular polarization. The prospect of observing quantum motion and spatial order in 2 and 3 dimensions, and the consequences for the spectrum of fluorescence, will be discussed.« less
Researchers in Germany and France have bound neutral atoms in regular two- and three-dimensional lattices induced by the interference patterns of several laser beams. The work builds on the techniques of magnetooptical trapping and sub-Doppler laser cooling and on previous work in which atoms were bound in onedimensional standing waves of light. The fields of light in these techniques are called optical molasses, because atoms within them experience viscous forces, which cool the atoms to temperatures on the order of microkelvins. In the new, “crystalline” molasses, the standing waves produce a stable, regular array of potential wells—a microscopic “egg carton”— and the atoms become localized at the bottoms of the wells.
We present a quantum treatment of laser cooling of neutral atoms. The cooling mechanism studied is the "Sisyphus" process for 1-dimensional optical molasses. We first derive the energy eigenstates for the atom moving in the potential associated with the light-shifts due to the laser. Then, taking into account optical pumping, we calculate the steady-state populations of these quantum levels in the secular approximation. This approach allows us to determine the atomic eigenfrequencies in the optical wells, as well as momentum and position distributions. In particular, the minimum r.m.s. atomic momentum is ≃ 6 single-photon momenta; this result was not accessible to previous semi-classical treatments.
Quantization of Atomic Motion. Atoms can be easily cooled to KE to below 0.2 MHz, below the light shifts in a weak standing wave. At low excitation rates, an optical standing wave may be viewed as producing a sinusoidal potential. Atoms are then confined in the lambda space between the planes of the standing wave, but have a deBroglie wavelength approx. lambda 10 or more. Thus their motion is quantized by the light field. We have evidence of this quantization of motion from direct rf spectroscopy of the vibrational states in the wells. The position of the rf peaks do not correspond to the calculated energy intervals, and do ot shift with laser parameters as expected.
Using six optical beams (+ and − directions on three orthogonal axes) tuned slightly to the red of resonance it is possible to cool sodium atoms to a few hundred microkelvin. The cooling occurs because the laser radiation pressure creates a damping force which reduces the atomic velocities to a rms value of ~60 cm/s, determined by random scattering. In this optical molasses, the laser beams propagate in all directions and the light acts as a viscous photon fluid which damps the atomic velocity. The resulting motion of the sodium atoms is diffusive until the atoms reach the edge of the laser beams where they escape. The process of atomic confinement by optical molasses can be modeled as a random walk in a viscous medium with a boundary. For a spherical volume of 0.2 cm3 the resulting confinement time is ~0.1 s for half of the atoms to escape. Direct time-of-flight measurement of the atomic temperature gives ~240 μK, which agrees with predictions of quantum limited cooling by resonance radiation pressure. With confinement times of 0.1 s and temperatures of ~240 μK this method provides a source of atoms sufficiently slow for even the highest resolution optical spectroscopy, collision studies, or optical traps.