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arXiv:2409.06575 · Physical Review Research

Modeling of a continuous superradiant laser on the sub-mHz 1 S 0 → 3 P 0 transition in neutral strontium-88

Swadheen Dubey, Georgy A. Kazakov, Benedikt Heizenreder, Sheng Zhou, Shayne Bennetts, Stefan Alaric Schäffer, Ananya Sitaram, Florian Schreck

Published Mar 19, 2025• 9 citations
arXivHTMLPDF

Abstract

Continuous superradiance using a narrow optical transition has the potential to improve the short-term stability of state-of-the-art optical clocks. Even though pulsed superradiant emission on a mHz linewidth clock transition has been shown, true continuous operation, without Fourier limitation, has turned out to be extremely challenging. The trade-off between maintaining a high atomic flux while minimizing decoherence effects presents a significant obstacle. Here, we discuss the design of a machine that could overcome this problem by combining a high-flux continuous beam of ultracold strontium atoms with a bowtie cavity for the generation of superradiant lasing. To evaluate the feasibility of our design, we present simulation results for continuous high-efficiency cooling, loading, and pumping to the upper lasing state inside the bowtie cavity. We then present two different models for simulating the generated superradiant field by taking into account position-dependent shifts, collisional decoherence, light shifts, and atom loss. Finally, we estimate a laser linewidth of less than 100 mHz , limited by atom number fluctuations, resulting in an output power of hundreds of fW .

DOI
10.1103/physrevresearch.7.013292

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Continuous superradiance using a narrow optical transition has the potential to improve the short-term stability of state-of-the-art optical clocks. Even though pulsed superradiant emission on a mHz linewidth clock transition has been shown, true continuous operation, without Fourier limitation, has turned out to be extremely challenging. The trade-off between maintaining a high atomic flux while minimizing decoherence effects presents a significant obstacle. Here, we discuss the design of a machine that could overcome this problem by combining a high-flux continuous beam of ultracold strontium atoms with a bowtie cavity for the generation of superradiant lasing. To evaluate the feasibility of our design, we present simulation results for continuous high-efficiency cooling, loading, and pumping to the upper lasing state inside the bowtie cavity. We then present two different models for simulating the generated superradiant field by taking into account position-dependent shifts, collisional decoherence, light shifts, and atom loss. Finally, we estimate a laser linewidth of less than 100 mHz , limited by atom number fluctuations, resulting in an output power of hundreds of fW .
The prospects of superradiant lasing on the 7.5-kHz-wide $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{1}$ transition in 88Sr^{88}\mathrm{Sr}88Sr is explored by using numerical simulations of two systems based on realistic experimental numbers. One system uses the idea of demonstrating continuous superradiance in a simple, hot atom beam with high flux, and the other system is based on using ultracold atoms in a dipole guide. For the hot-beam system we consider a range of atom beam parameters as well as the impact of a scheme to discard fast atoms along the cavity axis. We find that the system achieves lasing above a flux of $2.5\ifmmode\times\else\texttimes\fi{}{10}^{12}$ atoms/s and that it is capable of outputting hundreds of nanowatts and suppressing cavity noise by a factor of 20--30. The relativistic transverse Doppler shifts cause a shift in the lasing frequency on the order of 500 Hz. For the cold-atom beam we account for decoherence and thermal effects when using a repumping scheme for atoms confined in a dipole guide. This is done by treating recoils and state-dependent forces acting on atoms in the dipole guide within the framework of the stochastic master equation. We find that the output power is on the order of hundreds of picowatts; however, transverse Doppler shifts can be neglected, and cavity noise can be suppressed on the order of a factor of 50--100. Additionally, we show that both systems exhibit local insensitivity to fluctuations in atomic flux.
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.
Today's narrowest linewidth lasers are limited by mirror motion in the reference optical resonator used to stabilize the laser's frequency.Recent proposals suggest that superradiant lasers based on narrow dipoleforbidden transitions in cold alkaline earth atoms could offer a way around this limitation.Such lasers operating on transitions with linewidth of order mHz are predicted to achieve output spectra orders of magnitude narrower than any currently existing laser.As a step towards this goal, we demonstrate and study a laser based on the 7.5-kHz linewidth dipole-forbidden 3 P 1 to 1 S 0 transition in laser-cooled and tightly confined 88 Sr.We can operate this laser in the bad-cavity or superradiant regime, where coherence is primarily stored in the atoms, or continuously tune to the more conventional good-cavity regime, where coherence is primarily stored in the light field.We show that the cold-atom gain medium can be repumped to achieve quasi-steady-state lasing.We also demonstrate up to an order of magnitude suppression in the sensitivity of laser frequency to changes in cavity length, verifying a key feature of the proposed narrow linewidth lasers.
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 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.
We will describe a next-generation active atomic frequency reference based on super-radiant pulses of laser light from the ultra-narrow, 1 mHz linewidth, optical clock transition in an ensemble of cold 87Sr atoms. Light is stimulated from the millihertz linewidth transition by confining an ensemble of laser cooled atoms inside of a high finesse optical cavity. Such a light source has been proposed as a next-generation active atomic frequency reference, with the potential to enable high-precision optical frequency references to be used outside laboratory environments. We achieve a remarkable short term fractional frequency stability, 6.7 × 1016 at 1 s of averaging, absolute accuracy, 2 Hz (4 × 1015 fractional frequency), and high insensitivity to changes in the cavity length that limits the performance of todays more stable lasers. We will also discuss current work on cavity-enhanced dispersive measurements to perform high resolution spectroscopy and atom counting.