Amplification without inversion (AWI) and lasing without inversion (LWI) have been demonstrated only in three-level alkali schemes in which the lasing wavelength is comparable to the drive wavelengths; extending inversionless gain to the ultraviolet has remained open. Rein et al. (Phys. Rev. A 105, 023722, 2022) observed the Doppler-free three-photon coherence underlying a four-level double-dark-state scheme in thermal mercury vapor — levels 61S06^1S_0, 63P16^3P_1, 73S17^3S_1, 63P26^3P_2 driven at 253.7, 435.8, and 546.1 nm — and predicted by simulation that AWI on the 253.7 nm intercombination line is feasible, but the available incoherent pump (40 mW, about 0.5 MHz spectral width) fell short of the predicted threshold (above 80 mW at about 70 MHz) and no net gain or oscillation was observed. This problem asks for the completion of that program: experimental AWI at 253.7 nm with a noise-broadened, high-power incoherent pump while controlling coupling-laser frequency noise, Gaussian beam-overlap inhomogeneity, and parasitic incoherent two-/three-step excitation, followed by continuous-wave lasing without inversion in a ring cavity around the mercury cell — the first LWI at a wavelength far shorter than its drive lasers. A follow-up by the same group (Preissler et al., J. Phys. B 55, 244001, 2022) built the required acousto-optic driver (39.3 MHz noise band) and raised the pump to 420 mW, but the AWI measurement and the cavity demonstration remain unpublished.

Background

Continuous-wave coherent light in the ultraviolet (UV) is difficult to generate: reaching population inversion on a short-wavelength transition costs pump power that grows at least as the fourth power of the laser frequency, and nonlinear frequency-conversion crystals degrade under the required intensities. Lasing without inversion (LWI), proposed in the late 1980s by Kocharovskaya and Khanin, by Harris, by Scully, and by Imamoğlu, circumvents this by preparing quantum coherences that cancel absorption on the lasing transition while stimulated emission remains — typically through electromagnetically induced transparency (EIT), the destructive interference of absorption pathways in a coherently driven atom. Amplification without inversion (AWI) is the corresponding gain regime, measured as probe-beam transmission exceeding unity. LWI has been demonstrated experimentally in three-level schemes in rubidium (Zibrov et al., 1995) and sodium (Fry et al., 1993; Padmabandu et al., 1996), but in all demonstrations the lasing wavelength was comparable to the wavelengths of the drive lasers. In a thermal vapor, when the lasing transition has a much shorter wavelength than the coupling lasers, the first-order Doppler shifts of the fields differ strongly and wash out the narrow gain resonance except for a small velocity class.

Fry, Lukin, Walther, and Welch (Opt. Commun. 179, 499 (2000)) proposed a four-level scheme in neutral mercury that cancels this Doppler penalty: the ground state 61S06^1S_0 (level ∣1⟩|1\rangle) is linked to 63P16^3P_1 (∣2⟩|2\rangle) by the UV intercombination transition at 253.7 nm (an intercombination line is a weak, spin-forbidden transition between states of different spin multiplicity), ∣2⟩|2\rangle is coupled to 73S17^3S_1 (∣3⟩|3\rangle) by a strong drive at 435.8 nm, and ∣3⟩|3\rangle is coupled to 63P26^3P_2 (∣4⟩|4\rangle) by a weak drive at 546.1 nm, with a repumper at 404.7 nm emptying the metastable 63P06^3P_0 state. The two drives create a double dark state (also called interacting dark resonances) — a splitting of the EIT dark state induced by the fourth level. By arranging the three wavevectors non-collinearly with matched projections, the first-order Doppler shift of the three-photon resonance cancels for all velocity classes, so no atomic beam is needed. Sturm, Rein, Walther, and Walser (J. Opt. Soc. Am. B 31, 1964 (2014)) established the feasibility in detail by solving the radiation-damped optical Bloch equations (the standard density-matrix equations of motion for coherently driven atoms, here including spontaneous-emission decay) of the full 13-level system (the mercury Zeeman sublevels), modeling the incoherent pump as a laser beam with a broad noisy spectrum, and predicting UV LWI at 253.7 nm.

Rein, Schmitt, Sturm, Walser, and Walther (Phys. Rev. A 105, 023722 (2022)) reported the first experimental observation of this Doppler-free three-photon coherence in thermal mercury vapor and compared measured absorption spectra with the model. Several gaps remained. The measured three-photon resonance (full width at half maximum, FWHM, of 1.41 MHz) is about twice the model width (704 kHz), attributed to residual frequency fluctuations of the two coherent coupling lasers. The simulation assumes uniform (top-hat) transverse beam intensities while the experiment has Gaussian profiles, giving a complex spatial distribution of the coupling intensities in the overlap region and quantitative model–experiment differences. Parasitic incoherent two-step excitation (TSE, driven by the 253.7 nm probe and 435.8 nm drive) and incoherent three-step excitation (THSE, initiated by the 546.1 nm beam) raise the absorption baseline, and their scaling with beam powers and detunings was not mapped. Finally, the available incoherent pump at 253.7 nm — 40 mW with about 0.5 MHz spectral width, limited because the commercial acousto-optic modulator (AOM) driver could not transfer the white-noise modulation onto the AOM carrier (an AOM deflects and frequency-shifts a beam via a radio-frequency sound wave in a crystal) — fell short of the model threshold for AWI, which is a pump power above 80 mW at a spectral width of roughly 70 MHz. Their simulations show AWI feasible in the setup; converting it into sustained cw laser oscillation in a cavity would be the first LWI at a wavelength far shorter than the drive lasers.

Problem Statement

Demonstrate amplification without inversion (AWI) and then continuous-wave lasing without inversion (LWI) at 253.7 nm in thermal mercury vapor using the Doppler-free four-level double-dark-state scheme, converting the simulated AWI of the 61S0↔63P16^1S_0\leftrightarrow 6^3P_1 intercombination transition into observed gain and sustained laser oscillation.

(1) AWI: with the 435.8 nm strong drive and the 546.1 nm weak drive (plus the 404.7 nm repumper) establishing the Doppler-free three-photon coherence, incoherently pump the 61S0↔63P16^1S_0\leftrightarrow 6^3P_1 transition at 253.7 nm with an effective spectral width and power in the regime identified by the source's model — above 80 mW at roughly 70 MHz FWHM in the original analysis; the 2022 follow-up's parameter scan finds, for example, 50 MHz at 200 mW sufficient when the strong drive is raised to about 340 mW — and observe probe-beam transmission exceeding unity, that is, net gain, with control measurements showing that the gain requires both coupling lasers.

(2) LWI: place the mercury cell in a ring cavity (ring because the Doppler-free geometry produces unidirectional gain) whose round-trip losses are below the available gain, and demonstrate sustained continuous-wave laser oscillation at 253.7 nm.

Achieving this requires controlling the obstacles identified in the source: residual frequency fluctuations of the two coupling lasers (which currently roughly double the three-photon resonance width relative to the model), the Gaussian rather than uniform transverse intensity profiles of the overlapping beams, and the parasitic incoherent TSE/THSE excitation channels whose scaling with beam powers and detunings remains to be mapped.

References

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