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arXiv:2503.14705 · Physical Review A

Degenerate mirrorless lasing in thermal vapors

Aneesh Ramaswamy, Dmitry Budker, Simon Rochester, A. Papoyan, Svetlana Shmavonyan, Himadri Parashar, Vladimir V. Malinovsky, Svetlana Malinovskaya

Published Feb 24, 2026• 3 citations
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Abstract

Theoretical predictions were made for the steady-state gain of an orthogonally polarized probe field in a degenerate two-level alkali atom system driven by a linearly polarized continuous-wave pump field in [Opt. Mem. Neural Networks 32 (Suppl 3), S443-S446 (2023)]. Employing linear response theory, we computed the probe absorption spectrum under conditions where the pump was detuned from resonance. The results revealed a sub-natural linewidth dispersive feature near the pump resonance, characterized by both gain and absorption. Furthermore, a distinct pure gain peak emerged at a sideband associated with a dressed-state transition. These phenomena are generally absent outside the ultracold regime due to inhomogeneous broadening, primarily from Doppler effects, which obscure the fine spectral structure. In this paper, it is demonstrated that the sideband gain peak is sustained in the warm vapor regime when both the pump Rabi frequency and detuning exceed the Doppler width, $Ω_P > Δ_P \gg Δ_{Dop}$. Our results can enable degenerate mirrorless lasing in thermal alkali atom vapors, offering a significant enhancement in the signal-to-noise ratio for fluoroscopic remote magnetic sensing applications. The theoretical model studied in this paper is also a complete description of atomic vapors with isolated $J = 2 \to J' = 3$ transitions, such as atomic samarium.

DOI
10.1103/q121-sm9j

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Theoretical predictions were made for the steady-state gain of an orthogonally polarized probe field in a degenerate two-level alkali atom system driven by a linearly polarized continuous-wave pump field in [Opt. Mem. Neural Networks 32 (Suppl 3), S443-S446 (2023)]. Employing linear response theory, we computed the probe absorption spectrum under conditions where the pump was detuned from resonance. The results revealed a sub-natural linewidth dispersive feature near the pump resonance, characterized by both gain and absorption. Furthermore, a distinct pure gain peak emerged at a sideband associated with a dressed-state transition. These phenomena are generally absent outside the ultracold regime due to inhomogeneous broadening, primarily from Doppler effects, which obscure the fine spectral structure. In this paper, it is demonstrated that the sideband gain peak is sustained in the warm vapor regime when both the pump Rabi frequency and detuning exceed the Doppler width, ΩP>ΔP≫ΔDopΩ_P > Δ_P \gg Δ_{Dop}ΩP​>ΔP​≫ΔDop​. Our results can enable degenerate mirrorless lasing in thermal alkali atom vapors, offering a significant enhancement in the signal-to-noise ratio for fluoroscopic remote magnetic sensing applications. The theoretical model studied in this paper is also a complete description of atomic vapors with isolated J=2→J′=3J = 2 \to J' = 3J=2→J′=3 transitions, such as atomic samarium.
Abstract We report experimental evidence of degenerate mirrorless lasing in the forward direction under excitation of a dilute atomic Rb vapor with a single linearly polarized cw laser light resonant with cycling F e > F g atomic D 2 transitions. Light polarized orthogonally to the laser light is generated for the input light intensity exceeding a threshold value of ∼3 mW cm −2 . Application of a transverse magnetic field directed along the input light polarization reveals a sharp ∼20 mG wide magnetic resonance centered at B = 0. Increasing the incident light intensity from 3 to 300 mW cm −2 , the generated light undergoes rapid amplitude increase followed by a decline and resonance broadening. Such nonlinear behavior of the observed magnetic resonance is attributed to the population inversion on optical transitions between magnetic sublevels established under linearly polarized excitation. We present observations that indicate that a combination of nonlinear-optical effects occurs in this system, including degenerate mirrorless lasing and four-wave mixing.
Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.
The results of an experimental and theoretical study of the gain (or absorption) experienced by a weak probe beam propagating through a sodium vapor in the presence of an intense pump field that is nearly resonant with the 3s→3p atomic transition are presented. In general, the probe transmission spectrum is found to be comprised of three distinct features, two of which can lead to amplification of the probe wave. The origin of these features can be traced to the modification of the atomic level structure by the ac Stark effect. The experimentally measured spectra are in good agreement with the predictions of a theoretical model based on the solution of the density-matrix equations of motion for a two-level atom and including the effects of Doppler broadening. The dependence of the induced gain on the pressure of a helium buffer gas has been measured and is found to be in good agreement with the predictions of theory. The maximum gain observed in these experiments occurs at one of the Rabi sidebands and leads to a 38-fold increase in the intensity of the probe wave.
The effect of an intense pump beam on the intensity of the phase-conjugated emission is studied in the case of a three-level atom. We first extend to the case of cross-polarized pump beams the dressed-atom model that we have presented previously [Phys. Rev. A 34, 4008 (1986)] for the case of two-level atoms. The range of validity of our theory is \ensuremath{\Gamma} (natural width) ${\ensuremath{\Omega}}_{1}$ (Rabi frequency of the intense pump) ku (Doppler width). We have studied the line shape in degenerate four-wave mixing, the influence of a static magnetic field, and the resonances that appear in nondegenerate four-wave mixing. Experiments are done in a neon discharge using cw dye lasers. The experimental results are in good agreement with the theoretical predictions. In degenerate four-wave mixing, we have shown that the saturating dip disappears when the weak beams have orthogonal polarizations. In the presence of a static magnetic field and in the nearly degenerate case, narrow resonances corresponding to transitions between energy levels of the dressed atom are observed. The intensity and the width of these resonances are in very good agreement with the predictions of the theoretical model.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations
Theoretical calculations are presented for the probe absorption spectra of atoms having magnetically degenerate ground states which are subjected to weak pump fields that produce spatial polarization gradients. Apart from the Raman resonance contribution to the spectrum which has been observed experimentally, we predict that additional resonant structures should appear as a result of the atomic recoil that occurs during the absorption or emission of radiation by the atoms. The width of the atomic recoil resonances is directly related to the Doppler width associated with the driven transition. For sub-Doppler cooled atoms, the width can be much narrower than the optical pumping rate that determines the width of the Raman signal.