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Self-homodyne technique for observing intensity squeezing in four-wave mixing in a pure two-level system

J. W. R. Tabosa, J. C. de Aquino Carvalho, Raoni S. N. Moreira

Published Jul 15, 2025• 0 citations
Publisher

Abstract

We report on a new technique to observe intensity squeezing based on four-wave mixing (FWM) in a pure two-level system. We employ a two-mode probe beam, where the two probe modes play a double role, either for generating the forward-FWM beams as well as local oscillators. The technique relies on the phase conjugation property associated with the generated forward-FWM. Using a cold ensemble of cesium atoms and a pump beam red-detuned by 30 MHz from resonance of the closed transition6S1/2, F = 4, mF = 4 → 6P3/2, F ′ = 5, mF ′ = 5, we have demonstrated directly the production of −0.35 dB of light intensity squeezing. Possible extension of the present technique is also discussed for FWM processes involving more complex atomic-level schemes.

DOI
10.1364/opticaopen.29565008.v1

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We report on a new technique to observe intensity squeezing based on four-wave mixing (FWM) in a pure two-level system. We employ a two-mode probe beam, where the two probe modes play a double role, either for generating the forward-FWM beams as well as local oscillators. The technique relies on the phase conjugation property associated with the generated forward-FWM. Using a cold ensemble of cesium atoms and a pump beam red-detuned by 30 MHz from resonance of the closed transition6S1/2, F = 4, mF = 4 → 6P3/2, F ′ = 5, mF ′ = 5, we have demonstrated directly the production of −0.35 dB of light intensity squeezing. Possible extension of the present technique is also discussed for FWM processes involving more complex atomic-level schemes.
We report on a new technique to observe intensity squeezing based on four-wave mixing (FWM) in a pure two-level system. We employ a two-mode probe beam, where the two probe modes play a double role, either for generating the forward-FWM beams as well as local oscillators. The technique relies on the phase conjugation property associated with the generated forward-FWM. Using a cold ensemble of cesium atoms and a pump beam red-detuned by 30 MHz from resonance of the closed transition6S1/2, F = 4, mF = 4 → 6P3/2, F ′ = 5, mF ′ = 5, we have demonstrated directly the production of −0.35 dB of light intensity squeezing. Possible extension of the present technique is also discussed for FWM processes involving more complex atomic-level schemes.
We have measured -3.5 dB (-8.1 dB corrected for losses) relative intensity squeezing between probe and conjugate beams generated by stimulated, nondegenerate four-wave mixing in hot rubidium vapor. Unlike early observations of squeezing in atomic vapors based on saturation of a two-level system, our scheme uses a resonant nonlinearity based on ground-state coherences in a three-level system. Since this scheme produces narrowband, squeezed light near an atomic resonance, it is of interest for experiments involving cold atoms or atomic ensembles.
We have generated squeezed states of light with a single pump beam propagating through Doppler broadened sodium vapor via forward four-wave mixing (FWM) with spatially degenerate pump and probe modes. The two probe-mode inputs are vacuum states at nondegenerate frequencies, which are transformed to squeezed vacuum by the FWM interaction. Compared with previous FWM configurations,1 this single-pass single-pump-beam configuration ensures maximal overlap of the four interacting beams, thus maximizing the squeezing nonlinearity and improving the overall efficiency. The transmitted pump has the wrong phase to act as the local oscillator for detecting the squeezed spectrum.1 Therefore, a cavity is used to filter out most of the transmitted pump intensity, and the squeezed vacuum is detected with another local oscillator using the standard dual-detector scheme. The residual pump beam provides a reference to monitor the phase between the pump and squeezed vacuum. The observed 0.8-dB reduction in the shot noise corresponds to an inferred 50% squeezing of the light at the exit of the vapor medium, which is in reasonable agreement with the theory given by Ho et al. 2 A linearly polarized pump is found to give less squeezing than a circularly polarized pump, possibly due to optical pumping.
We present a detailed characterization of the entanglement in a stimulated Fourwave mixing process.This process is widely studied by the homodyne detection, a technique insensitive to the details of the sideband modes of the involved beams.The emission profile of the FWM process in atomic media shows an imbalance in the amplification of the sidebands, which suggest an asymmetry in the entanglement of the generated states, that can not be observed by the homodyne detection.The stimulated FWM consists on a single frequency pump and a seed beam interacting with the hot rubidium atoms, generating a pair of entangled states, the probe and the conjugated.By the implementation of the resonantor detection, we revealed the hidden entanglement structure of the generated beams.We found that the usual characterization of the state through the homodyne detection is incomplete.On the contrary, the reconstruction of the covariance matrix from the resonant detection allows the full characterization of the quantum correlations and a more complete entanglement structure between the sideband frequency modes.Therefore, with the measurement using resonant detection over a Four-wave mixing process, we can demonstrate the advantage of the detection to reveal entanglement that would be hidden if the usual two-mode description is used.
We describe our efforts to observe squeezing, and related nonclassical effects, in three forward four-wave mixing experiments using sodium vapor as a nonlinear medium. In a single-beam experiment with homodyne detection, we found optically phase-sensitive noise, which was radio-frequency phase insensitive, in a cw dye-laser beam that had propagated through sodium vapor. The minima of the phase-sensitive noise were always at or above the coherent-state value. In our forward four-wave mixing experiment with probe–conjugate-beam direct detection and correlation, we found that the sodium-vapor interaction produced positive noise correlation between the probe and conjugate beams. The correlation, however, did not exceed the excess noises on these beams, so that a nonclassical behavior was not demonstrated. Finally, our forward four-wave mixing experiment with probe–conjugate-beam combination and homodyne detection did demonstrate the generation of squeezed-state light in our setup. Optically phase-sensitive noise with a minimum falling 4% below the coherent-state level was observed.