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Physical Review A

Observation of correlated anti-Stokes emissions by multiwave mixing in sodium vapor

Koji Motomura, Mayumi Tsukamoto, A. Wakiyama, Ken-ichi Harada, Masaharu Mitsunaga

Published Apr 21, 2005• 22 citations
Publisher

Abstract

We study experimentally nonlinear optical processes in which Stokes and anti-Stokes fields build up under strong, resonant, counterpropagating pump laser excitation in atomic sodium vapor. We find that, at some pump frequency, two off-axis anti-Stokes emissions propagating along reflection-symmetric directions are strongly temporally correlated, with a correlation time of $0.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ and a correlation range of $1\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}$. It is shown by the numerical analysis based on six-wave mixing process involving pump, Stokes, and anti-Stokes waves in the forward and the backward directions that such correlated anti-Stokes emissions are possible when the medium is opaque for the Stokes field and transparent for the anti-Stokes field. Possibilities of quantum correlation for entangled photon generation using this system are discussed.

DOI
10.1103/physreva.71.043817

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Conference on Lasers and Electro-Optics•Jan 1, 2005•0 citations
We study experimentally nonlinear optical processes in which Stokes and anti-Stokes fields build up under strong, resonant, counterpropagating pump laser excitation in atomic sodium vapor. We find that, at some pump frequency, two off-axis anti-Stokes emissions propagating along reflection-symmetric directions are strongly temporally correlated, with a correlation time of 0.5\ensuremathμs0.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}0.5\ensuremathμs and a correlation range of 1mrad1\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}1mrad. It is shown by the numerical analysis based on six-wave mixing process involving pump, Stokes, and anti-Stokes waves in the forward and the backward directions that such correlated anti-Stokes emissions are possible when the medium is opaque for the Stokes field and transparent for the anti-Stokes field. Possibilities of quantum correlation for entangled photon generation using this system are discussed.
We present theoretically and experimentally a novel type of parametric fluorescence and oscillation in which four optical waves in off-axis, diagonal directions simultaneously build up under resonant counterpropagating pump-laser excitation in atomic sodium vapor. Two of the four are anti-Stokes shifted and the other two are Stokes shifted, and they are strongly coupled owing to electromagnetically induced diffraction. Theoretically, the Liouville-Maxwell equations are solved to derive four-wave propagation equations. Experimentally, we have observed four-wave parametric oscillation when a weak off-axis seed beam is introduced into otherwise axially symmetric parametric fluorescence patterns. Temporal waveforms are also analyzed, and strong correlations between any pairs of the four emissions are identified.
We have studied the space-time entangled Stokes-anti-Stokes photons generated from a three-level system. In the presence of counterpropagating pump and control lasers, paired Stokes and anti-Stokes fields are spontaneously emitted into opposite directions. The two-photon wave packet is generally a convolution of the phase matching and the third-order nonlinear susceptibility and the feature of the joint temporal correlation is determined by either of them. When the phase matching plays a major role in determining the spectral width of biphotons, the two-photon interference exhibits as conventional type-II spontaneous parametric down-conversion (SPDC). However, if the spectral width of paired photons is determined by the third-order nonlinear susceptibility, two types of four-wave mixings (FWMs) destructively interfere and contribute to the two-photon coincidences. In such a case, the coincidence counting rate appears as a damped Rabi oscillation and exhibits the photon antibunching. The oscillation frequency is equal to the effective Rabi frequency. We have also discussed polarization-entanglement generation in a three-state case. It is found that if the phase matching is crucial in determining the properties of paired Stokes and anti-Stokes photons, the generated state is the same as the degenerate type-II SPDC. However, if the spectral width is mainly controlled by the resonant linewidths in the third-order nonlinearity, one can select one FWM to produce polarization-entangled biphotons, but paired photons from the other FWM process is nonpolarization entangled.
We report second-order intensity correlations g ( 2 ) ( τ ) of directional midinfrared emissions from sodium vapor under bichromatic continuous-wave excitation. Directional emission at 2.34 µ m in the forward direction and at 2.21 µ m in both forward and backward directions exhibits g ( 2 ) ( 0 ) values that exceed unity yet remain well below the thermal limit of 2, indicating subthermal photon bunching characteristics of a multimode collectively driven process rather than purely independent amplified spontaneous emission. Cross-correlation measurements reveal that the counterpropagating 2.21 − µ m beams are positively correlated, demonstrating dynamic coupling between the two emission channels. Persistent oscillations in g ( 2 ) ( τ ) , observed across a broad range of pump powers, shift systematically to higher frequencies with increasing excitation power, consistent with ac Stark shifts of hyperfine sublevels. Together, these observations establish that the emission arises from a phase-matched, continuous-wave collective process combining features of mirrorless lasing and amplified spontaneous emission, with long-range dipole coherence and velocity-selective coupling governing the photon statistics and the forward-backward emission symmetry. The experiment uses a 10-cm buffer-gas-free sodium vapor cell under bichromatic excitation at 589.2 and 569.0 nm; the emitted midinfrared light is detected in a Hanbury Brown–Twiss configuration. The demonstrated backward emission is of particular interest for applications in laser guide star generation and mesospheric remote sensing, where understanding the statistical properties of the emitted light is essential for optimizing sodium-based light sources.
We study the cooperative effects between Raman and hyper-Raman processes in which two quanta from a pumping field are absorbed and another two entangled photons are generated. The symmetries of the involved operators can be reduced to SU(2)-algebra in which the Casimir vector of quasi-momentum of the two fields is conserved. Quantum correlations between the pump and the generated field states are investigated. Cooperative stabilization of two-mode coherent states between Stokes and anti-Stokes photons is shown using both semiclassical and quantum approaches. We show that the relaxation of the system is described by coherent states of the two-mode field. The possibilities of observing cross-correlations between the pump field and the generated field are analyzed.