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arXiv:2408.09486

Numerical analysis of a superradiance-sideband-assisted laser with a zero frequency pulling and a narrow linewidth

Jeon, Mingyu, Jinuk Kim, Kyungwon An

Published Aug 18, 2024• 0 citations
arXivHTMLPDF

Abstract

Numerical simulations based on the quantum Langevin equations have been performed for a large number of two-level atoms in a beam interacting with a low-Q cavity with the atomic initial superposition states close to the north pole of the Bloch sphere. When the pump Rabi frequency was modulated at $Δ_{pa}$ with zero pump-atom detuning for various cavity-atom detunings, we obtained a lasing peak at the atomic resonance and superradiant lasing peaks at $\pmΔ_{pa}$ simultaneously while the central peak exhibiting a zero frequency pulling coefficient. The linewidth of the central peak was reduced beyond the gain narrowing as the mean number of atoms was increased, resulting in a minimum linewidth as small as a millionth of the atomic or cavity linewdith. A pump carrier detuning caused asymmetric heights for the side superradiant peaks, the height difference of which can be used to lock the pump laser to the atom within the linewidth of the central lasing peak. Our results may lead to development of a new type of ultra-stable active optical clocks for future frequency standards when applied to proper atomic systems.

DOI
10.48550/arxiv.2408.09486

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Numerical simulations based on the quantum Langevin equations have been performed for a large number of two-level atoms in a beam interacting with a low-Q cavity with the atomic initial superposition states close to the north pole of the Bloch sphere. When the pump Rabi frequency was modulated at ΔpaΔ_{pa}Δpa​ with zero pump-atom detuning for various cavity-atom detunings, we obtained a lasing peak at the atomic resonance and superradiant lasing peaks at ±Δpa\pmΔ_{pa}±Δpa​ simultaneously while the central peak exhibiting a zero frequency pulling coefficient. The linewidth of the central peak was reduced beyond the gain narrowing as the mean number of atoms was increased, resulting in a minimum linewidth as small as a millionth of the atomic or cavity linewdith. A pump carrier detuning caused asymmetric heights for the side superradiant peaks, the height difference of which can be used to lock the pump laser to the atom within the linewidth of the central lasing peak. Our results may lead to development of a new type of ultra-stable active optical clocks for future frequency standards when applied to proper atomic systems.
Active optical clocks based on collective atomic emission promise narrow lasing linewidths as well as reduced sensitivity to cavity fluctuations, yet residual frequency pulling limits their ultimate precision. Here, we propose a laser scheme that simultaneously achieves vanishing frequency pulling and ultranarrow linewidths by exploiting symmetry in collective superradiant emission. Atoms in a dense beam traversing a bad cavity are prepared in controlled superposition states using a pump laser with a sinusoidally modulated Rabi frequency Ω m . The resulting emission spectrum consists of a central lasing peak at the atomic resonance and two superradiant sidebands at symmetric detunings ± Ω m . Owing to their symmetric interaction, the central peak is protected against cavity-induced frequency shifts over detunings comparable to the cavity linewidth. As the atom number increases, its linewidth narrows far beyond the conventional gain-narrowing limit, reaching values as small as one millionth of the cavity linewidth. Small pump detunings break the symmetry of the sideband intensities, providing a robust error signal to stabilize the pump frequency without an external reference cavity. These results establish a symmetry-driven route toward ultrastable active optical clocks and collective-radiation sources with exceptional frequency stability.
Background: Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Methods: Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a superradiant laser as a function of the inhomogeneous width of the ensemble including variations of the spatial atom-field coupling within the resonator. Results: We present conditions on the atom numbers, the pump and coupling strengths required to reach the buildup of collective atomic coherence as well as scaling and limitations for the achievable laser linewidth. Conclusions: We show how sufficiently large numbers of atoms subject to strong optical pumping can induce synchronization of the atomic dipoles over a large bandwidth. This generates collective stimulated emission of light into the cavity mode leading to narrow-band laser emission at the average of the atomic frequency distribution. The linewidth is orders of magnitudes smaller than that of the cavity as well as the inhomogeneous gain broadening and exhibits reduced sensitivity to cavity frequency noise.
Abstract The implementation of a superradiant laser as an active frequency standard is predicted to provide better short-term stability and robustness to thermal and mechanical fluctuations when compared to standard passive optical clocks. However, despite significant recent progress, the experimental realization of continuous wave superradiant lasing still remains an open challenge as it requires continuous loading, cooling, and pumping of active atoms within an optical resonator. Here we propose a new scenario for creating continuous gain by using optical forces acting on the states of a two-level atom via bichromatic coherent pumping of a cold atomic gas trapped inside a single-mode cavity. Analogous to atomic maser setups, tailored state-dependent forces are used to gather and concentrate excited-state atoms in regions of strong atom-cavity coupling while ground-state atoms are repelled. To facilitate numerical simulations of a sufficiently large atomic ensemble, we rely on a second-order cumulant expansion and describe the atomic motion in a semi-classical point-particle approximation subject to position-dependent light shifts which induce optical gradient forces along the cavity axis. We study minimal conditions on pump laser intensities and detunings required for collective superradiant emission. Balancing Doppler cooling and gain-induced heating we identify a parameter regime of a continuous narrow-band laser operation close to the bare atomic frequency.
Abstract A new approach for analytically solving quantum nonlinear Langevin equations is proposed and applied to calculations of spectra of superradiant lasers where collective effects play an important role. We calculate lasing spectra for arbitrary pump rates and recover well-known results such as the pump dependence of the laser linewidth across the threshold region. We predict new sideband peaks in the spectrum of superradiant lasers with large relaxation oscillations as well as new nonlinear structures in the lasing spectra for weak pump rates. Our approach sheds new light on the importance of population fluctuations in the narrowing of the laser linewidth, in the structure of the lasing spectrum, and in the transition to coherent operation.
We study the collective emission of a beam of atomic dipoles into an optical cavity. Our focus lies on the effect of a finite detuning between the atomic transition frequency and the cavity resonance frequency. By developing a theoretical description of the coupled atom-cavity dynamics we analyze the stationary atomic configurations including a superradiant phase where the atoms undergo continuous monochromatic collective emission. In addition, we derive an analytical formula for the cavity pulling coefficient which characterizes the displacement of the emission frequency towards the cavity frequency. We find that the pulling is small if the cavity linewidth is much larger than the collective linewidth of the atomic beam. This regime is desired for building stable lasers because the emission frequency is robust against cavity length fluctuations. Furthermore, we investigate the stability of the atomic phases and compare our theoretical predictions with numerical results. Remarkably, we also find polychromatic emission regimes, where the spectrum has several frequency components while the light output is still superradiant.
Abstract Simultaneous strong coherent pumping of the two transitions of a V-level atom with very different decay rates has been predicted to create almost perfect inversion on the narrower transition. Using the example of the blue and red transitions in Strontium we show that for suitable operating conditions the corresponding resonant gain can be used to continuously operate a laser on the narrow transition. In particular, for a strong detuning of the pump field with respect to the narrow transition, coherent laser emission occurs close to the bare atomic transition frequency exhibiting only a negligible contribution from coherent pump light scattered into the lasing mode. Calculations of the cavity output spectrum show that the resulting laser linewidth can get much smaller than the bandwidth of the pump light and even the natural linewidth of the narrow atomic transition. Its frequency is closely tied to the atomic transition frequency for properly chosen atom numbers. Simulations including atomic motion show Doppler cooling on the strong transition with minor motion heating on the lasing transition, so that continuous laser operation in the presence of a magneto-optical trap should be possible with current experimental technology.