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Physical Review Letters

How Large Photon Recoil Can Make Cold Atoms Lase

Klaus M. Gheri, Helmut Ritsch, Daniel F. Walls, V. I. Balykin

Published Jan 30, 1995• 9 citations
Publisher

Abstract

We calculate the weak probe field absorption spectrum for ultracold three-level atoms in a Raman gain configuration in the limit of the recoil shift exceeding the natural linewidth and the Doppler broadening. Our results show that even in the limit of very large recoil gain persists with its maximum shifted toward the red of the atomic line by the recoil energy, as is the spontaneous emission line. Some preliminary calculations suggest the possibility of a cw deep uv laser, based on cooled metastable helium atoms.

DOI
10.1103/physrevlett.74.678

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We calculate the weak probe field absorption spectrum for ultracold three-level atoms in a Raman gain configuration in the limit of the recoil shift exceeding the natural linewidth and the Doppler broadening. Our results show that even in the limit of very large recoil gain persists with its maximum shifted toward the red of the atomic line by the recoil energy, as is the spontaneous emission line. Some preliminary calculations suggest the possibility of a cw deep uv laser, based on cooled metastable helium atoms.
We present a review and extension of a recently made proposal [K. M. Gheri et al., Phys. Rev. Lett. 74, 678 (1995)] to utilize cold atoms in a Raman configuration as a uv-laser gain medium in the limit of the photon recoil shift exceeding the natural atomic linewidth and the Doppler broadening. A discussion of model assumptions is given as well as an analysis of the dependence of the gain on detunings and decay rates. Special emphasis is put on a calculation of the nonlinear gain that allows a self-consistent determination of the uv-laser intensity as a function of the model parameters. For a deep uv transition, the gain turns out to be of approximately the same order of magnitude as for comparable optical transitions including a significant enhancement through Raman coherences especially at weak laser intensities. Our calculations suggest the possibility of a cw deep uv laser, based on laser cooled metastable (e.g., helium) atoms.
A theory of pump-probe spectroscopy is developed in which optical fields drive two-photon Raman transitions between ground states of an ensemble of three-level atoms. Effects related to the recoil the atoms undergo as a result of their interactions with the fields are fully accounted for in this theory. The linear absorption coefficient of a weak probe field in the presence of two pump fields of arbitrary strength is calculated. For subrecoil cooled atoms, the spectrum consists of eight absorption lines and eight emission lines. In the limit that ${\ensuremath{\chi}}_{1}\ensuremath{\ll}{\ensuremath{\chi}}_{2},$ where ${\ensuremath{\chi}}_{1}$ and ${\ensuremath{\chi}}_{2}$ are the Rabi frequencies of the two pump fields, one recovers the absorption spectrum for a probe field interacting with an effective two-level atom in the presence of a single pump field. However, when ${\ensuremath{\chi}}_{1}\ensuremath{\gtrsim}{\ensuremath{\chi}}_{2},$ new interference effects arise that allow one to selectively turn on and off some of these recoil-induced resonances.
Based on the numerical solution of the quantum kinetic equation for the atomic density matrix, which makes it possible to accurately take into account the recoil effects in the interaction of atoms with field photons, we have studied the limits of laser cooling of atoms using closed optical transitions characterised by different recoil parameters (the ratio of the recoil energy to the natural linewidth). It is shown that for optical transitions with an insufficiently small recoil parameter, the polarisation effects, which lead to the possibility of sub-Doppler laser cooling, lose their efficiency and do not ensure an attainment of the temperature below the Doppler limit. The analysis performed allows one to outline the boundaries of the sub-Doppler theory of laser cooling of atoms.
Theoretical calculations are presented for the probe absorption spectra of atoms having magnetically degenerate ground states which are subjected to weak pump fields that produce spatial polarization gradients. Apart from the Raman resonance contribution to the spectrum which has been observed experimentally, we predict that additional resonant structures should appear as a result of the atomic recoil that occurs during the absorption or emission of radiation by the atoms. The width of the atomic recoil resonances is directly related to the Doppler width associated with the driven transition. For sub-Doppler cooled atoms, the width can be much narrower than the optical pumping rate that determines the width of the Raman signal.
The atomic-recoil effect leads to large (25%) asymmetries in a nearly ideal form of saturation spectroscopy based on Ca atoms that have been laser-cooled to . Starting with spectra from the more familiar Doppler-broadened domain, we show how the fundamental asymmetry between absorption and stimulated emission of light manifests itself when shorter spectroscopic pulses lead to the Fourier transform regime. These effects occur on frequency scales much larger than the size of the recoil shift itself, and have not been described before in saturation spectroscopy. These results directly impact precision spectroscopic measurements.
It is shown that, as a result of the atomic recoil associated with the absorption and emission of radiation, resonances can appear in nonlinear spectroscopy. The theory is illustrated by calculating the line shapes associated with nearly degenerate four-wave mixing and pump-probe spectroscopy when laser fields interact with an ensemble of two-level atoms. The recoil-induced resonances should be observable for atoms cooled below the Doppler limit of laser cooling, and the line shapes may provide a means for measuring the velocity distribution of these cooled atoms.