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arXiv:2511.12228 · Physical Review A

Second-order correlations in directed emissions in sodium atoms

A. Tonoyan, Sushree Subhadarshinee Sahoo, Anahit L. Gogyan, Oleg Tretiak, Razmik Aramyan, A. M. Akulshin, Dmitry Budker

Published May 19, 2026• 0 citations

Abstract

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.

DOI: 10.1103/q1s4-njnb

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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 demonstrate backward-directed continuous-wave (cw) emission at 2.21 {\mu}m generated on the 4P3/2-4S1/2 population-inverted transition in Na vapors two-photon excited with resonant laser light at 589 and 569 nm. Our study of power and atom-number-density threshold characteristics shows that lasing occurs at sub-10 mW total power of the applied laser light. The observed 6 mrad divergence is defined mainly by the aspect ratio of the gain region. We find that mirrorless lasing at 2.21 {\mu}m is magnetic field and polarization dependent that may be useful for remote magnetometry. The presented results could help determine the requirements for obtaining directional return from sodium atoms in the mesosphere

The mechanisms responsible for ultraviolet to mid-infrared light generation in sodium vapours two-photon excited with continuous-wave sub-100 mW power resonant laser radiation are elucidated from orbital angular momentum transfer of the applied light to the generated fields. The measured 9.5 MHz-wide spectral linewidth of the light at 819.7 nm generated by four-wave mixing, sets an upper limit to the linewidth of two fields resulting from amplified spontaneous emission at 2338 nm and 9093 nm on population inverted transitions. Understanding details of this new-field generation is central to applications such as stand-off detection and directional laser guide stars.

We study backward cooperative emissions from a dense sodium atomic vapor. Ultrashort pulses produced from a conventional amplified femtosecond laser system with an optical parametric amplifier are used to excite sodium atoms resonantly on the two-photon 3S –4S transition. Backward superfluorescent emissions (BSFEs), both on the 4S –3P and 4S –3P transitions, are observed. The picosecond temporal characteristics of the BSFE are observed using an ultrafast streak camera. The power laws for the dependencies of the average time delay and the intensity of the BSFEs on input power are analyzed in the sense of cooperative emission from nonidentical atomic species. As a result, an absolute (rather than relative) time delay and its fluctuations (free of any possible external noise) are determined experimentally. The possibility of a backward swept-gain superfluorescence as an artificial laser guide star in the sodium layer in the mesosphere is also discussed.

The parametric and nonparametric nonlinear processes responsible for generation of directional infrared radiation in sodium vapors, excited to the 4D 5/2 energy level by resonant laser radiation, are identified by the transfer of orbital angular momentum from the pump radiation to the generated fields. We show that the optical fields generated by amplified spontaneous emission (ASE) simultaneously participate in several loops of four-wave mixing (FWM) generating new directional emission. The measured spectral linewidth of the FWM emission at 819.7 nm sets an upper limit to the linewidth of two fields resulting from ASE at 2338.6 and 9093.0 nm, assuming their spectra are uncorrelated. Understanding details of the new-field generation is central to applications such as directional laser guide stars, stand-off magnetometry, and entangled field generation.

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.

population-inverted transition in Na vapors that are two-photon excited with resonant laser light at 589 and 569 nm. Our study of power and atom-number-density threshold characteristics shows that lasing occurs at sub-10 mW total power of the applied laser light. The observed 6 mrad divergence is defined mainly by the aspect ratio of the gain region. We find that mirrorless lasing at 2.21 μm is magnetic field and polarization dependent and this may be useful for remote magnetometry. The presented results could help determine the requirements for obtaining directional return from sodium atoms in the mesosphere.