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Journal of the Optical Society of America B

Emission and absorption spectra of dark optical superlattices

Péter Horák, Helmut Ritsch

Published Aug 1, 1997• 1 citation
Publisher

Abstract

We calculate the spectrum of resonance fluorescence and the weak-field absorption spectrum obtained from atoms cooled and trapped in a one-dimensional dark optical superlattice, which is formed by a bichromatic laser field in double-Λ configuration. These spectra provide an experimentally accessible tool to gain important information about the trapping mechanism and the steady-state density matrix. A rate-equation approach is used to discuss the dependence of the spectra on various model parameters.

DOI
10.1364/josab.14.001967

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We calculate the spectrum of resonance fluorescence and the weak-field absorption spectrum obtained from atoms cooled and trapped in a one-dimensional dark optical superlattice, which is formed by a bichromatic laser field in double-Λ configuration. These spectra provide an experimentally accessible tool to gain important information about the trapping mechanism and the steady-state density matrix. A rate-equation approach is used to discuss the dependence of the spectra on various model parameters.
We show that the coherent part of the atomic fluorescence spectrum in a dark optical superlattice can be interpreted as a new type of Bragg scattering of the trapping lasers by the periodic atomic distribution. We explicitly solve the 1D problem to demonstrate that this built-in mechanism provides a diagnostic tool to determine the atomic position and energy distribution without any extra disturbance of the system. Hence, in principle, this method allows one to gain important information on atom-atom interactions and quantum statistics in the case of several atoms confined within a single optical (super)well.
We present the experimental realization of optical superlattices created by exposing laser cooled 85Rb{}^{85}\mathrm{Rb}85Rb atoms to a bichromatic standing-wave light field. The two light frequencies are tuned close to the D1{D}_{1}D1​ and D2{D}_{2}D2​ lines of 85Rb.{}^{85}\mathrm{Rb}.85Rb. The total optical potential seen by the atoms exhibits a modulation at the spatial beat period of the two light fields in addition to the typical periodicity on the scale of an optical wavelength. The bichromatic light field cools the atoms into the superlattice potential, resulting in a density modulation on a macroscopic scale. We have observed the density modulation directly in one- and three-dimensional superlattice configurations using an absorption imaging technique.
We investigate the resonance fluorescence emission and absorption spectra for a one-dimensional harmonically trapped two-level ion. The master equation is used to generate the atomic polarizations from which the spectra are derived. Because of their size, the final density matrix equations are investigated numerically. The calculations are carried out in the Lamb-Dicke limit of tight localization of the ion. Sharp peaks are found to appear in the spectra at frequencies detuned from line centre by steps of the trap frequency. The frequency of the peaks and their superposition with Rabi sidebands above saturation are analysed for a variety of parameter ranges. Moreover, new features of the absorption spectra of a weak probe such as sharp gain regions around the trap sidebands are also discussed.
We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\ensuremath{\Lambda}$ shaped and driven at two-photon resonance by a pair of lasers, which cool the center-of-mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb-Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second-order perturbation theory. We find that the spectrum of resonance fluorescence is composed of two narrow sidebands---the Stokes and anti-Stokes components of the scattered light---while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow-type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behavior of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two levels.
We examine the radiative properties of a two-level atom driven by a strong bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\delta}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{0}$+${\mathrm{\ensuremath{\delta}}}_{2}$, which can be asymmetrically placed about the atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and can have different Rabi frequencies ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$. Applying the optical Bloch equations for the bichromatic excitation, we derive an infinite set of equations of motion for the time evolution of the atomic variables. The equations are solved numerically by matrix inversion and Laplace transforms. Using the quantum regression theorem, we then solve for the steady-state total fluorescence intensity, and the resonance-fluorescence and absorption spectra. The spectra are found to depend on the frequency difference 2\ensuremath{\delta}=${\mathrm{\ensuremath{\delta}}}_{1}$+${\mathrm{\ensuremath{\delta}}}_{2}$, the average detuning \ensuremath{\Delta}=${\mathrm{\ensuremath{\omega}}}_{0}$-1/2(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$), and the Rabi frequencies of the driving fields. For ${\mathrm{\ensuremath{\Omega}}}_{1}$=${\mathrm{\ensuremath{\Omega}}}_{2}$=\ensuremath{\Omega}, the total fluorescent intensity displays a series of maxima for \ensuremath{\Delta}=\ifmmode\pm\else\textpm\fi{}n\ensuremath{\delta}\ensuremath{\mp}${\mathrm{\ensuremath{\Omega}}}^{2}$/4\ensuremath{\delta}, where the n are the odd integers. The intensity-dependent shift from the resonances n\ensuremath{\delta} is explained as an analog of the generalized Bloch-Siegert shift. The resonance-fluorescence spectrum for \ensuremath{\Delta}\ensuremath{\ne}0 appears to contain more peaks than that for \ensuremath{\Delta}=0.This is due to the splitting of the central peak and the even sidebands into doublets. The absorption spectrum of a weak-probe beam for \ensuremath{\Delta}=0 and equal Rabi frequencies consists of a symmetric series of dispersionlike sidebands separated from ${\mathrm{\ensuremath{\omega}}}_{0}$ by integer multiples of \ensuremath{\delta}, together with a central absorption peak at ${\mathrm{\ensuremath{\omega}}}_{0}$, whose amplitude oscillates with \ensuremath{\Omega}. For \ensuremath{\Delta}\ensuremath{\ne}0 and/or ${\mathrm{\ensuremath{\Omega}}}_{1}$\ensuremath{\ne}${\mathrm{\ensuremath{\Omega}}}_{2}$, the odd sidebands remain dispersionlike, while the central peak and the even sidebands split into absorption-emission doublets. A simple physical interpretation of the spectral features is given in terms of the dressed-atom model.