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arXiv:2501.13808 · Physical Review Letters

Nonreciprocal Interactions Induce Frequency Shifts in Superradiant Lasers

Tobias Nadolny, Matteo Brunelli, Christoph Bruder

Published May 14, 2025• 9 citations
arXivHTMLPDF

Abstract

Superradiant lasers, which consist of incoherently driven atoms coupled to a lossy cavity, are a promising source of coherent light due to their stable frequency and superior narrow linewidth. We show that when a fraction of the atoms is not driven, a shift in the lasing frequency and a broadening of the linewidth occur, limiting the performance of a superradiant laser. We explain this behavior by identifying nonreciprocal interactions between driven and undriven atoms, i.e., competing alignment and antialignment of their dipoles. Our results have implications for the realization of superradiant lasers, establishing the relevance of nonreciprocal phenomena for quantum technologies.

DOI
10.1103/physrevlett.134.193603

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Superradiant lasers, which consist of incoherently driven atoms coupled to a lossy cavity, are a promising source of coherent light due to their stable frequency and superior narrow linewidth. We show that when a fraction of the atoms is not driven, a shift in the lasing frequency and a broadening of the linewidth occur, limiting the performance of a superradiant laser. We explain this behavior by identifying nonreciprocal interactions between driven and undriven atoms, i.e., competing alignment and antialignment of their dipoles. Our results have implications for the realization of superradiant lasers, establishing the relevance of nonreciprocal phenomena for quantum technologies.
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.
The generation of very narrow linewidth light sources is of great importance in modern science. One such source is the superradiant laser, which relies on collectively interacting ultra long lived dipoles driven by incoherent light. Here we discuss a different way of generating spectrally pure light by coherently driving such dipoles inside an optical QED cavity. The light exiting cavity carries information about the detuning between the driving light and the atomic transition, but is also affected by the noise originating from all the decoherence processes that act on the combined atom-cavity system. We calculate these effects to obtain fundamental limits for frequency estimation and stabilization across a range of values of input light intensities and atom-light interaction strengths, estimate these limits in state-of-the-art cavity experiments with alkaline-earth atoms and identify favorable operating conditions. We find that the achievable linewidths are comparable to those of the superradiant laser.
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.
An ideal superradiant laser on an optical clock transition of noninteracting cold atoms is predicted to exhibit an extreme frequency stability and accuracy far below mHz-linewidth. In any concrete setup sufficiently many atoms have to be confined and pumped within a finite cavity mode volume. Using a magic wavelength lattice minimizes light shifts and allows for almost uniform coupling to the cavity mode. Nevertheless, the atoms are subject to dipole-dipole interaction and collective spontaneous decay which compromises the ultimate frequency stability. In the high density limit the Dicke superradiant linewidth enhancement will broaden the laser line and nearest neighbor couplings will induce shifts and fluctuations of the laser frequency. We estimate the magnitude and scaling of these effects by direct numerical simulations of few atom systems for different geometries and densities. For Strontium in a regularly filled magic wavelength configuration atomic interactions induce small laser frequency shifts only and collective spontaneous emission weakly broadens the laser. These interactions generally enhance the laser sensitivity to cavity length fluctuations but for optimally chosen operating conditions can lead to an improved synchronization of the atomic dipoles.
A new class of laser, which harnesses coherence in both light and atoms, is possible with ultracold alkaline-earth-metal atoms trapped in an optical lattice inside an optical cavity. Different lasing regimes, including superradiance, superradiant, and conventional lasing, are distinguished by the relative coherence stored in the atoms and in the cavity mode. We analyze the physics in two different experimentally achievable regions of the superradiant lasing regime. Our calculations confirm the narrow linewidth of superradiant lasing for the doubly forbidden clock transition ${}^{3}{P}_{0}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ of 87Sr^{87}\mathrm{Sr}87Sr atoms. Under strong driving of the dipole-forbidden transition ${}^{3}{P}_{1}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ of 88Sr^{88}\mathrm{Sr}88Sr atoms, the superradiant linewidth narrows further due to the coherent excitation of the cavity field.
Superradiant lasers may soon achieve state-of-the-art frequency purity, with linewidths of 1 mHz or less. In a superradiant (or bad-cavity) laser, coherence is primarily stored in the atomic gain medium instead of the optical field. This phase storage is characterized by spontaneous quantum synchronization of the optical dipole moments of each atom. To observe this synchronization, we create two independent superradiant atomic ensembles lasing in a single optical cavity and observe the dynamics of phase realignment, collective power enhancement, and steady-state frequency locking. This work introduces superradiant ensembles as a testbed for fundamental study of quantum synchronization as well and informs research on narrow linewidth superradiant lasers.