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Journal of Modern Optics

Intensity correlation and anti-correlations in coherently driven atomic vapor

Gombojav O. Ariunbold, Yuri V. Rostovtsev, Vladimir A. Sautenkov, Marlan O. Scully

Published Apr 15, 2010• 27 citations
Publisher

Abstract

Motivated by the recent experiment [Sautenkov, V.A.; Rostovtsev, Yu.V.; Scully, M.O. Phys. Rev. A 2005, 72, 065801], we study the field intensity fluctuations due to interaction between a laser with a finite bandwidth and a dense atomic medium. The intensity–intensity cross-correlation of two orthogonal, circular polarized beams can be controlled by the applied external magnetic field. A smooth transition from perfect correlations to anti-correlations (at zero delay time) of the outgoing beams is observed.

DOI
10.1080/09500341003777905

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Motivated by the recent experiment [Sautenkov, V.A.; Rostovtsev, Yu.V.; Scully, M.O. Phys. Rev. A 2005, 72, 065801], we study the field intensity fluctuations due to interaction between a laser with a finite bandwidth and a dense atomic medium. The intensity–intensity cross-correlation of two orthogonal, circular polarized beams can be controlled by the applied external magnetic field. A smooth transition from perfect correlations to anti-correlations (at zero delay time) of the outgoing beams is observed.
Motivated by the recent experiment [V.A. Sautenkov, Yu.V. Rostovtsev, and M.O. Scully, Phys. Rev. A 72, 065801 (2005)], we develop a theoretical model in which the field intensity fluctuations resulted from resonant interaction of a dense atomic medium with laser field having finite bandwidth. The intensity-intensity cross correlation between two circular polarized beams can be controlled by the applied external magnetic field. A smooth transition from perfect correlations to anti-correlations (at zero delay time) of the outgoing beams as a function of the magnetic field strength is observed. It provides us with the desired information about decoherence rate in, for example, 87^{87}87Rb atomic vapor.
We present measurements of the intensity fluctuations of electromagnetically induced absorption (EIA) in the 5S₁/₂ (F = 2)-5P₃/₂(F' = 3) transition of ⁸⁷Rb atoms. Using a linearly polarized laser, the intensity fluctuations between two circularly polarized light components was generated by the spontaneously transferred atomic coherence of EIA medium. The intensity fluctuations due to spontaneous transfer of coherence were changed from correlation of EIA at on-resonance to anti-correlation of EIA at off-resonance. We also investigated the dependence of the values of second-order correlation function g(²)(0) at zero delay time on the temperature of the atomic vapor cell and the incident laser power.
Cross correlation refers to the situation in which the fluctuations in the fields of two or more lasers are correlated in some way. Recently, Thomas et al. [ Opt. Lett.6, 298 ( 1981); Phys. Rev. Lett.48, 867 ( 1982)] proposed the generation of cross correlation between two laser fields interacting with a three-level system as a means of reducing noise and went on to exploit this property in the observation of narrow Ramsay fringes. Dalton and Knight [ J. Phy. B15, 3997 ( 1982)] discussed the theoretical aspects of cross correlation and showed that it produced interesting effects in population trapping for example. We have demonstrated that it has significant effects on the optical double-resonance (ODR) spectra [ J. Phys. B17, L389 ( 1984)]. On the other hand, the effects of non-Lorentzian laser line shapes have been shown by various workers to have significant effects on a wide range of phenomena, such as multiphoton ionization, resonance fluorescence, and ODR. In this paper we present a theory of the interactions of lasers whose fluctuations are governed by the phase-diffusion process with atomic systems that includes the effects of cross correlation and non-Lorentzian line shapes. We derive the basic equations (which in general have to be solved numerically) and obtain analytic results in the case in which the line shape is approximately Lorentzian near line center but falls off faster than a Lorentzian in the wings. We believe that this analytic model shows all the essential features of the interplay between cross correlation and non-Lorentzian line shapes. The theory is applied to the ODR experiment. In particular, we find that the asymmetry of the spectra is strongly affected by these two features, and so is the ODR spectral line shape when the saturating laser intensity is close to the threshold for producing two peaks.
Coherent signals produced by time delayed, fluctuating optical pulses interacting with atoms in the vapor phase have attracted much interest recently, due to their potential as a source of sub-picosecond time resolution. The theoretical description of such experiments brings into play many profound questions connected with stochastic Bloch equations. For example, even though the noise properties of a single laser beam may be Markovian in nature, in these experiments the atoms are subjected to at least two time-delayed fields which may be correlated. Because the atoms retain some memory of the first field at the time when the second field acts, the entire process becomes non-Markovian. In principle, the variation of such parameters as the homogeneous and inhomogeneous widths, allows the experimenter some degree of control over this memory time associated with the atomic medium.\n&more...
We report a detailed investigation on the properties of intensity correlation spectra for laser beams interacting with cold atoms under the condition of electromagnetically induced transparency (EIT). We describe the transition of their intensity fluctuations from correlation to anticorrelation as the mean intensity of the fields increases. Such a transition occurs for laser frequencies around the EIT resonance, which is characterized by a correlation peak. The transition point between correlation and anticorrelation is independent of power broadening and provides directly the ground-state coherence time. We introduce a method to extract in real time the correlation spectra of the system. The experiments were done in two distinct magneto-optical traps, one for cesium and the other for rubidium atoms, employing different detection schemes. A simplified theory is introduced assuming three-level atoms in $\ensuremath{\Lambda}$ configuration interacting with a laser with stochastic phase fluctuations, providing a good agreement with the experimental observations.