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Europhysics Letters (EPL)

Four-Wave Mixing in a 3D Optical Lattice

Andreas Hemmerich, Matthias Weidemüller, Theodor W. Hänsch

Published Aug 20, 1994• 40 citations
Publisher

Abstract

We have observed the reflection of a probe laser beam by a three-dimensional optical lattice of rubidium atoms. The reflection spectrum shows different kinds of narrow resonances which we attribute to degenerate (phase conjugation) and non-degenerate multiwave mixing processes. In order to explain the extremely narrow linewidth (300 Hz) of the degenerate four-wave mixing resonance and its dependence on the angle of incidence of the probe, we propose a novel physical mechanism which includes the formation of a long-range atomic-density grating acting as a hologram.

DOI
10.1209/0295-5075/27/6/003

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Russian Journal of Physical Chemistry B•Jul 1, 2015•0 citations
We have observed the reflection of a probe laser beam by a three-dimensional optical lattice of rubidium atoms. The reflection spectrum shows different kinds of narrow resonances which we attribute to degenerate (phase conjugation) and non-degenerate multiwave mixing processes. In order to explain the extremely narrow linewidth (300 Hz) of the degenerate four-wave mixing resonance and its dependence on the angle of incidence of the probe, we propose a novel physical mechanism which includes the formation of a long-range atomic-density grating acting as a hologram.
We present in this paper a theoretical study of the angular dependence of phase-conjugate emission via resonant degenerate four-wave mixing (FWM) in Doppler-broadened gas media. The nonlinear optical polarization is calculated through an expansion of the atomic density matrix up to the third order in the incident fields. One finds that, when the incident frequency is resonant for a single-photon transition, both strength and lineshape of the phase-conjugate emission strongly depend on the angle 0 between standing pump wave and probe wave. The emission intensity, maximum at grazing incidences, decreases rapidly by several orders of magnitude when 0 increases. Simultaneously the emission linewidth increases from homogeneous to Doppler width. Similar effects are predicted for nearly-degenerate FWM (different pump and probe frequencies). In particular, one shows that the bandwidth of the equivalent optical reflection filter undergoes a Doppler-broadening linearly increasing with sin θ. On the opposite, none of the above effects is predicted in two-photon-resonant FWM which does not exhibit any angular dependence.
Summary form only given. Previously, we have used four-wave mixing via coherent population trapping to achieve optical phase conjugation (OPC) with high gain, using two dye lasers and a sodium vapor cell. The /spl Lambda/ transition used involved the two hyperfine ground states and one excited state, so that two different optical frequencies were needed to satisfy the two-photon resonant condition between the probe and one of the pump beams. Later, we demonstrated in rubidium that a single hyperfine transition with Zeeman sublevels is enough to achieve OPC with equally high gain, thus eliminating the need for high-frequency sideband generation. However, in order to guarantee that the diffraction from the grating is primarily dispersive, the backward pump beam had to be detuned by about 60 MHz from the probe and the forward pump. One of the key disadvantages of such a nondegenerate scheme is that applications such as phase-conjugate mirrors are hard to implement. Here, we report the observation of optical phase conjugation in rubidium with equally high gain, but all the frequencies are degenerate.
Phase conjugation is an nonlinear effect that results from the four-wave-mixing process. This peculiar effect, in analogy to a mirror, reflects an incident beam in a way that the reflection constitutes the time-reversal of the original beam. By combining the phase conjugate mirror with ordinary mirrors, a special resonator, called phase conjugate resonator (PCR), is constructed. The phase conjugate resonator has been used in a wide range of applications, including phase aberration correction, image transmission, holography, and phase sensing using interferometers. Here, we explore theoretically the properties of phase conjugate mirror by investigating its action upon a variety of quantum states. In addition, we analyze the input-output relations of a phase conjugate resonator. Experimental results are reported that faithfully verify PCR's enhanced stability as compared to normal resonators. Furthermore, we observe a linewidth narrowing effect that is only present in the phase conjugate resonator.
We present experimental observations of phase-conjugate degenerate four-wave mixing in a two-level atomic system (the ${3s}^{2}{S}_{1/2}, F=2, {m}_{F}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2}, F=3, {m}_{F}=3$ transition in a diffuse, collision-free, thermal beam of atomic sodium) driven by cw, narrow-band $(\ensuremath{\sim}250 \mathrm{kHz}),$ stabilized pump and probe fields. The primary measurements that we report are of the peak signal strength of the four-wave-mixing interaction and the bandwidth of the four-wave-mixing spectrum (as the laser frequency is tuned through the resonant frequency) as a function of the intensity of the pump field. We compare these measurements with the predictions of a theoretical analysis in which extension to include the effect of the small transverse velocity $(\ensuremath{\sim}3 \mathrm{m}/\mathrm{s}\mathrm{e}\mathrm{c})$ of the atomic beam is critical. These measurements provide a direct verification of the theory of this important nonlinear interaction.
In this paper, we investigated the coherent degenerate and nondegenerate four-wave interaction in the propagation of a femtosecond laser pulse in atomic rubidium vapor. In the case of degenerate four-wave interaction, the mechanism for optical switching in an optically dense resonant medium is considered. The third-order nonlinear interaction of the laser beams intersecting in the cell at a small angle leads to a nonlinear response in the form of a fourth beam, which occurs as a result of the interaction between the two pump beams and the third signal laser beam.