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Physical Review Letters

Laser Cooling to a Single Quantum State in a Trap

Ralph Dum, P. Marte, Thomas Pellizzari, P. Zoller

Published Nov 21, 1994• 32 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.73.2829

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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.
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 Jg{\mathit{J}}_{\mathit{g}}Jg​=1 to Je{\mathit{J}}_{\mathit{e}}Je​=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.
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.
We analyze the laser cooling of trapped bosonic gases beyond the Lamb-Dicke limit. We use a quantum master equation formalism to study the cooling dynamics, and show that dark-state cooling methods similar to those previously proposed for a single trapped atom allow for the condensation of a collection of bosons into a single state of the trap, either the ground state or an excited state. Using Monte Carlo simulations we analyze the condensation dynamics for different dimensions, and two different cooling schemes; we also demonstrate the appearance of multistability and hysteresis phenomena.
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.
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.
Laser cooling has advanced to the point where atomic motion can no longer be described in terms of discrete particles moving on classical trajectories. Instead, de Broglie wave fields occupy quantum states of a potential created by the interaction between atoms and the light field. Atomic transitions between these quantum states are mediated by optical pumping, in much the same way as transitions were made between internal angular momentum states in Prof. Series' time. Some examples are studied here, with special emphasis on dark states.