Lasing without population inversion in a closed lifetime-broadened atomic system: experimental realization and quantitative feasibility of the İmamoğlu–Field–Harris (1991) scheme

İmamoğlu, Field, and Harris proposed in 1991 that a closed Λ-type three-level atom, whose level widths are set only by spontaneous emission and which is pumped by incoherent radiation on the very transition on which it lases, can exhibit steady-state small-signal gain with no population inversion in any atomic basis, provided the spontaneous-emission branching satisfies $\Gamma_{32}>\Gamma_{31}$ and the pump radiation satisfies an inversion of the radiation field, $\bar{n}_{13}>\bar{n}_{23}$. The paper treated collisions, laser phase noise, and Doppler broadening only qualitatively and proposed a schematic realization in neutral tin without spectroscopic data. The surviving open problem is to convert this proof-of-principle model into a quantitatively validated, experimentally demonstrated (or definitively ruled out) closed-system inversionless laser.

Background

Conventional lasers require population inversion — more atoms in the upper than the lower state of the lasing transition — because for a two-level medium in thermal equilibrium stimulated absorption exactly balances stimulated emission. Around 1989–1991 several proposals showed that atomic coherence can break this balance: when two absorption pathways reaching the same excited state interfere destructively, absorption is suppressed while the corresponding emission pathways are not, so a medium without population inversion can amplify. This is the principle of lasing without inversion (LWI), closely related to electromagnetically induced transparency (EIT), the coherent cancellation of absorption in a medium driven by a resonant coupling field.

İmamoğlu, Field, and Harris [Phys. Rev. Lett. 66, 1154 (1991)] analyzed the cleanest idealization of this idea: a closed Λ-type three-level atom, with states $|1\rangle$ and $|2\rangle$ forming the lower doublet and $|3\rangle$ excited. 'Closed' means no population leaves the three-state manifold: all pumping and decay are radiative and internal to it, so the level widths are purely lifetime-broadened, i.e. set by the spontaneous-emission rates $\Gamma_{31}$ and $\Gamma_{32}$ from $|3\rangle$ to $|1\rangle$ and $|2\rangle$. A coherent coupling field of Rabi frequency $\Omega_{23}$ (the measure of drive strength) acts on the $|2\rangle$–$|3\rangle$ transition, a weak probe/lasing field acts on $|1\rangle$–$|3\rangle$, and incoherent broadband radiation pumps both transitions at rates $R_{13}=\Gamma_{31}\bar{n}_{13}$ and $R_{23}=\Gamma_{32}\bar{n}_{23}$, where $\bar{n}_{ij}$ is the mean photon occupation number per mode of the pump radiation at the $|i\rangle$–$|j\rangle$ transition frequency. From the steady-state density-matrix equations they showed that small-signal gain on the probe coexists with the absence of population inversion in any atomic basis ($\rho_{11}>\rho_{22}+\rho_{33}$) provided the spontaneous-emission branching favors the $|3\rangle\to|2\rangle$ channel ($\Gamma_{32}>\Gamma_{31}$) and the pump radiation satisfies $\bar{n}_{13}>\bar{n}_{23}$. The latter is an inversion of the radiation field rather than of the atoms: because the $|1\rangle$–$|3\rangle$ transition frequency is higher than the $|2\rangle$–$|3\rangle$ one, equilibrium thermal radiation would give $\bar{n}_{13}<\bar{n}_{23}$, so the scheme requires nonthermal pump sources whose brightness (effective temperature) is higher at the higher frequency. The paper treated collisions and the coupling-laser linewidth (modeled as Wiener–Lévy phase diffusion, the standard model of laser phase noise) only qualitatively, as dephasing rates that must remain below $\Gamma_{32}$; it noted that Doppler broadening (the thermal spread of atomic velocities in a vapor) forces $\Omega_{23}$ to be comparable to the Doppler width and thereby reduces the gain cross section; and it offered a schematic realization in neutral tin (levels $5s^2 5p^2\,{}^3P_0$, $5s^2 5p^2\,{}^1S_0$, and $5s^2 5p 5d\,{}^1P_1$) without spectroscopic numbers.

The subsequent LWI literature clarified the concept considerably. Gain without bare-state population inversion is real, but in driven schemes there is generally a 'hidden' inversion in the dressed-state basis (the eigenstates of the atom plus the strong drive) or, as in the 1991 scheme, in the radiation field; thermodynamic analyses treat this field inversion as the laser's actual resource. Inversionless amplification and laser oscillation have been demonstrated in coherently driven and Zeeman-coherence schemes, engineered semiconductor manifolds — quantum-well intersubband systems, in which the three levels are discrete confinement states of electrons in a semiconductor heterostructure, so that decay rates and couplings can be chosen by design — have been proposed, and the radiation-field-inversion idea re-emerged in modern EIT quantum-heat-engine experiments, devices in which a coherently driven EIT medium converts photons absorbed from a hot thermal reservoir plus a coherent drive into bright, directional emission. What has not been done is to realize or quantitatively vet the original closed, incoherently pumped, purely lifetime-broadened scheme against realistic collisions, finite pump bandwidth, Doppler broadening, non-Wiener–Lévy laser phase statistics, and laboratory control of the field inversion.

Problem Statement

Can the closed, purely lifetime-broadened Λ-system lasing-without-inversion scheme of İmamoğlu, Field, and Harris (1991) — gain on the $|1\rangle$–$|3\rangle$ transition of a three-level atom pumped incoherently on the lasing transition itself, with coherent coupling $\Omega_{23}$ on $|2\rangle$–$|3\rangle$, no population inversion in any atomic basis ($\rho_{11}>\rho_{22}+\rho_{33}$), and a radiation-field inversion $\bar{n}_{13}>\bar{n}_{23}$ — be realized and quantitatively established in a real physical system? The common objective is to convert the 1991 proof-of-principle model into a quantitatively validated and experimentally demonstrated (or definitively ruled out) closed-system inversionless laser, which requires jointly:

(1) identifying real atomic manifolds (the proposed neutral-tin scheme $5s^2 5p^2\,{}^3P_0$ / $5s^2 5p^2\,{}^1S_0$ / $5s^2 5p 5d\,{}^1P_1$, or alternatives, including engineered level manifolds such as quantum-well intersubband systems) that simultaneously satisfy the spontaneous-emission branching $\Gamma_{32}>\Gamma_{31}$ with $\Gamma_{32}$ exceeding collisional and laser-linewidth-induced dephasing, an accessible transition for implementing $\Omega_{23}$, an adequately metastable $|2\rangle$ level, and pump radiation whose mode occupancies realize $\bar{n}_{13}>\bar{n}_{23}$;

(2) extending the model quantitatively to the effects the paper treated only qualitatively or neglected: population-transfer (excitation/deexcitation) collisions beyond pure dephasing; incoherent pumps of realistic finite spectral bandwidth, including the back-action of the atoms on the pump fields; Doppler broadening in vapors, including an assessment of mitigation strategies such as velocity-selective addressing, buffer gases, or cold atoms; and laser phase statistics beyond Wiener–Lévy phase diffusion together with multimode coupling, so that lasing thresholds in realistic systems can be predicted rather than bounded; and

(3) demonstrating experimentally steady-state inversionless gain or laser oscillation in this closed system while maintaining and controlling the radiation-field inversion $\bar{n}_{13}>\bar{n}_{23}$ across the relevant modes, and excluding conventional gain channels — population inversion in any basis, Raman-type two-photon gain, or dressed-state (hidden) inversion — as the operative mechanism.

A quantitatively supported finding that no real or engineered manifold can satisfy the joint constraints of parts (1) and (2), so that the scheme is definitively ruled out, also answers the question.

References

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