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Physical Review A

Probe-transmission spectrum of a blue-detuned optical lattice

Jingzhong Guo, J. Cooper

Published Sep 1, 1995• 6 citations
Publisher

Abstract

The probe-transmission spectrum of a one-dimensional optical lattice is calculated. The optical lattice consists of atoms that are cooled by a pair of counterpropagating, linearly polarized fields, whose frequency \ensuremath{\omega} is detuned to the blue side of an atomic transition. A weak probe field of frequency ${\mathrm{\ensuremath{\omega}}}^{\ensuremath{'}}$ is assumed to be propagating in the same direction as one of the cooling fields. It is shown that, owing to the existence of dark and gray states in the lattice, the probe-transmission spectrum exhibits interesting features that are qualitatively different from those of a ``normal'' optical lattice with red-detuned cooling fields. Examples of these features include subrecoil linewidths and reversed absorption-amplification sidebands. It is shown that by monitoring the magnitudes of resonance signals in the spectrum, one can gain information on the evolution of the dark-state population in the lattice.

DOI
10.1103/physreva.52.r1819

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Physical Review Letters•Jul 3, 1995•89 citations
The probe-transmission spectrum of a one-dimensional optical lattice is calculated. The optical lattice consists of atoms that are cooled by a pair of counterpropagating, linearly polarized fields, whose frequency \ensuremath{\omega} is detuned to the blue side of an atomic transition. A weak probe field of frequency \ensuremathω\ensuremath′{\mathrm{\ensuremath{\omega}}}^{\ensuremath{'}}\ensuremathω\ensuremath′ is assumed to be propagating in the same direction as one of the cooling fields. It is shown that, owing to the existence of dark and gray states in the lattice, the probe-transmission spectrum exhibits interesting features that are qualitatively different from those of a ``normal'' optical lattice with red-detuned cooling fields. Examples of these features include subrecoil linewidths and reversed absorption-amplification sidebands. It is shown that by monitoring the magnitudes of resonance signals in the spectrum, one can gain information on the evolution of the dark-state population in the lattice.
We present a calculation of the probe-transmission spectrum of a two-dimensional optical lattice, in which atoms are cooled by a pair of standing-wave fields with perpendicular polarizations within the plane of incidence. A probe laser is directed along the axis of one of the cooling fields, with a polarization parallel to the incident plane of the cooling fields. The calculated probe-transmission spectrum exhibits both sidebands, which originate from stimulated Raman transitions between different vibrational states of the atoms in the molasses, and a central resonance structure, which originates from Rayleigh resonances among these vibrational states. We also include in our calculation a possible misalignment of the probe field relative to the axis of the cooling field. It is shown that the effrects of the probe misalignment can lead to significant modifications to the central resonance signal.
We present a theoretical investigation of the temperature and of the magnetization of atoms in one-dimensional ``gray'' optical lattices. Such lattices consist of counterpropagating beams having crossed linear polarizations, tuned on the blue side of a J\ensuremath{\rightarrow}J or a J\ensuremath{\rightarrow}J-1 transition, and a static longitudinal magnetic field. The variation of the atomic temperature with the magnetic field recently observed (an increase at low magnetic field; a decrease towards an asymptotic value at high magnetic field) is found for any atomic transition admitting one or two uncoupled states. This change of behavior of the temperature results from a qualitative change of the cooling mechanism and is correlated with a transition from paramagnetism to antiparamagnetism in the optical lattice. \textcopyright{} 1996 The American Physical Society.
We study photonic band gaps in a one-dimensional optical lattice of laser-cooled trapped atoms. We solve for the self-consistent equilibrium positions of the atoms, accounting for the backaction of the atoms on the trapping beams. This solution depends strongly on the sign of the trapping laser detuning. For red-detuned trapping lasers, the resulting lattice exhibits a one-dimensional photonic band gap for frequencies between the trapping laser frequency and the atomic resonance. For blue detuning the stop band extends symmetrically about resonance, typically for hundreds of atomic linewidths, except for the small region between atomic resonance and the lattice frequency, which is excluded. We calculate the reflection spectrum for a lattice of Cs atoms for various trapping laser detunings and interpret its behavior as a function of the lattice size and density. For a mean density of 1011{10}^{11}1011 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, and 1000 planes, 55% reflection of a weak probe beam should be observed. We also consider Bragg scattering in a three-dimensional optical lattice as a means of probing the long-range order in the atomic density correlation function.
We present a detailed theoretical investigation of the absorption spectrum of a probe beam after transmission through a one-dimensional optical molasses obtained with circularly cross-polarized counterpropagating pump beams (corkscrew molasses). The study is performed for a Jg{\mathit{J}}_{\mathit{g}}Jg​=1\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=2 atomic transition and the external degrees of freedom are described by means of a Fokker-Planck equation in the regime where the stationary momentum distribution lies within the range of linearity of the cooling force. We analyze the stimulated Raman transitions occurring between differently populated and light-shifted ground-state Zeeman sublevels. In the case where the probe beam has the same polarization as the copropagating cooling beam, an additional narrow Rayleigh resonance appears for a probe frequency close to the pump frequency. Its width is equal to 2\ensuremath{\alpha}/M, where \ensuremath{\alpha} is the friction coefficient of the cooling force and M is the atomic mass. In the case where the probe beam has the same polarization as the counterpropagating cooling beam, a central recoil-induced resonance is expected. Its width is related to the Doppler width of the optical molasses.
We present a detailed theoretical investigation of the transmission spectrum of a probe beam interacting with atoms in a one-dimensional optical molasses obtained with linearly cross-polarized counterpropagating pump beams. The study is performed for a Jg{\mathit{J}}_{\mathit{g}}Jg​=1/2\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=3/2 atomic transition in the limit where the Hamiltonian part of the atom-field coupling is predominant over the relaxation part. We analyze the stimulated Raman transitions occurring between different vibrational levels of the atoms in the periodic potential created by the light shifts, and we show a dramatic lengthening of the damping time of coherences between such levels due to the Lamb-Dicke effect. Very narrow Rayleigh resonances with a shape sensitive to the probe polarization appear for a probe frequency close to the pump frequency. We interpret these resonances in terms of scattering of the pump waves on density and magnetization gratings, and show that they provide important information about the dynamics and localization of atoms at the bottom of the potential wells. Such information should also be accessed by phase-conjugation experiments. Finally, indications on the treatment of other atomic transitions are given.
We demonstrate a new type of optical lattice which confines atoms in nearly dark states. The lattice is formed by cooperation of an optical standing wave detuned to the blue with respect to an atomic $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1\ensuremath{\rightarrow}F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ transition and a homogeneous magnetic field. The atoms are predominantly localized where the light is purely $\ensuremath{\pi}$ polarized such that they are optically pumped to the mF=0{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0mF​=0 Zeeman component which is decoupled from the light field. We have observed quantized vibrations of the localized atoms by means of probe transmission spectroscopy. Our ``dark'' optical lattice works in two and three dimensions.