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Physical Review A

Laser cooling to a single quantum state in a trap: One-dimensional results

Thomas Pellizzari, P. Marte, P. Zoller

Published Dec 1, 1995• 4 citations
Publisher

Abstract

Laser cooling in a trap is investigated for laser and trapping configurations which allow the existence of approximate ``dark states'' of the combined atom-plus-trap system, i.e., states that are decoupled from the laser light by quantum interference. We show that a one-dimensional (1D) free-particle dark state in angular momentum ${\mathit{J}}_{\mathit{g}}$=1 to ${\mathit{J}}_{\mathit{e}}$=1 transitions and in two counterpropagating laser fields survives as an approximate dark state in a ``flat-bottom'' trap of size much larger than the optical wavelength. Furthermore, we show the existence of approximate dark states in 1D harmonic-oscillator potentials. In the latter configuration we are able to provide analytical results.

DOI
10.1103/physreva.52.4709

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Laser cooling in a trap is investigated for laser and trapping configurations which allow the existence of approximate dark states'' of the combined atom-plus-trap system, i.e., states that are decoupled from the laser light by quantum interference. We show that a one-dimensional (1D) free-particle dark state in angular momentum ${\mathit{J}}_{\mathit{g}}$=1 to ${\mathit{J}}_{\mathit{e}}$=1 transitions and in two counterpropagating laser fields survives as an approximate dark state in a flat-bottom'' trap of size much larger than the optical wavelength. Furthermore, we show the existence of approximate dark states in 1D harmonic-oscillator potentials. In the latter configuration we are able to provide analytical results.
Laser cooling in a trap is investigated for configurations which allow the existence of "dark states" of the combined atom-plus-trap system, i.e., states which are decoupled from the laser light by quantum interference. Two examples of approximate dark states in a 1D flat bottom and 2D harmonic trap for angular momentum 1 to 1 transitions are discussed. A wave function simulation of the quantum master equation predicts that a significant fraction of the atoms are transferred to a single trap state.
We study the laser cooling of one atom in a harmonic trap beyond the Lamb-Dicke regime. By using sequences of laser pulses of different detunings we show that the atom can be confined into just one state of the trap, either the ground state or an excited state of the harmonic potential. The latter can be achieved because under certain conditions an excited state becomes a dark state. We study the problem in one and two dimensions. For the latter case a different cooling mechanism is possible, based on the destructive interference between the effects of laser fields in different directions, which allows the creation of a variety of dark states. For both, one- and two-dimensional cases, Monte Carlo simulations of the cooling dynamics are presented.
We show that by using an atomic-transition scheme including a common angular momentum J g = 1 atomic ground state and two excited states with angular momenta J e 1 = J e 2 = 1 or J e 1 = 0 and J e 2 = 1, one can construct an all-optical trap, where atoms are trapped and cooled towards a single nearly dark quantum state with a spatial dimension of the order of an optical wavelength. Single-atom calculations for two blue detuned counterpropagating σ + and σ − polarized light fields in one dimension predict that close to 100% of the atomic population will be transferred to the lowest quantum state.
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.
A detailed study of a robust and fast laser cooling scheme on a three level system is presented. A special laser configuration, applicable to trapped ions, atoms or cantilevers, designs a quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon processes. As a consequence cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very stable under fluctuations of the physical parameters such as laser intensity or detuning, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes, overcoming one of the limitations of current quantum information processing implementations. Its suitability as a cooling scheme for several ions in a trap or for a cloud of atoms in a dipole trap is shown.
We present a detailed analysis of a robust and fast laser cooling scheme [J. Cerrillo et al., Phys. Rev. Lett. 104, 043003 (2010)] on a three-level system. A special laser configuration, applicable to trapped ions, atoms, or cantilevers, designs a double-path quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon interactions. As a consequence, cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very flexible under constraints of the physical parameters such as laser intensity, detuning, or optical access, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes. Its suitability as a cooling scheme for several ions in a trap and three-dimensional cooling is shown.