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arXiv:2112.15420 · Physical Review A

Prospects of a superradiant laser based on a thermal or guided beam of Sr 88

Mikkel Tang, Stefan Alaric Schäffer, Jörg Helge Müller

Published Dec 9, 2022• 11 citations
arXivHTMLPDF

Abstract

The prospects of superradiant lasing on the 7.5-kHz-wide $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{1}$ transition in $^{88}\mathrm{Sr}$ 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.

DOI
10.1103/physreva.106.063704

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The prospects of superradiant lasing on the 7.5-kHz-wide 1S0\ensuremath-3P1^{1}S_{0}\text{\ensuremath{-}}^{3}P_{1}1S0​\ensuremath-3P1​ 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×\else\texttimes\fi10122.5\ifmmode\times\else\texttimes\fi{}{10}^{12}2.5\ifmmode×\else\texttimes\fi1012 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.
Sub-Natural Linewidth Superradiant Lasing with Cold 88^{88}88Sr Atoms
Superradiant lasers operate in the bad-cavity regime, where the phase coherence is stored in the spin state of an atomic medium rather than in the intracavity electric field. Such lasers use collective effects to sustain lasing and could potentially reach considerably lower linewidths than a conventional laser. Here, we investigate the properties of superradiant lasing in an ensemble of ultracold 88^{88}88Sr atoms inside an optical cavity. We extend the superradiant emission on the 7.5 kHz wide 3P1^3P_13P1​ →\rightarrow→ 1S0^1S_01S0​ intercombination line to several milliseconds, and observe steady parameters suitable for emulating the performance of a continuous superradiant laser by fine tuning the repumping rates. We reach a lasing linewidth of 820 Hz for 1.1 ms of lasing, nearly an order of magnitude lower than the natural linewidth
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 .
Superradiant lasers operate in the bad-cavity regime, where the phase coherence is stored in the spin state of an atomic medium rather than in the intracavity electric field. Such lasers use collective effects to sustain lasing and could potentially reach considerably lower linewidths than a conventional laser. Here, we investigate the properties of superradiant lasing in an ensemble of ultracold ^{88}Sr atoms inside an optical cavity. We extend the superradiant emission on the 7.5 kHz wide ^{3}P_{1}→^{1}S_{0} intercombination line to several milliseconds, and observe steady parameters suitable for emulating the performance of a continuous superradiant laser by fine tuning the repumping rates. We reach a lasing linewidth of 820 Hz for 1.1 ms of lasing, nearly an order of magnitude lower than the natural linewidth.
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.
Motivated by the outstanding short time stability and reliable continuous operation properties of microwave clock masers, intense worldwide efforts target the first implementation of their optical analogues based on narrow optical clock transitions and using laser cooled dilute atomic gases. While as a central line of research large efforts are devoted to create a suitably dense continuous ultracold and optically inverted atom beam source, recent theoretical predictions hint at an alternative implementation using a filtered thermal beam at much higher density. Corresponding numerical studies give encouraging results but the required very high densities are sensitive to beam collimation errors and inhomogeneous shifts. Here we present extensive numerical studies of threshold conditions and the predicted output power of such a superradiant laser involving realistic particle numbers and velocities along the cavity axis. Detailed studies target the threshold scaling as a function of temperature as well as the influence of eliminating the hottest part of the atomic distribution via velocity filtering and the benefits of additional atomic beam guiding. Using a cumulant expansion approach allows us to quantify the significance of atom-atom and atom-field correlations in such configurations. We predict necessary conditions to achieve a certain threshold photon number depending on the atomic temperature and density. In particular, we show that the temperature threshold can be significantly increased by using more atoms. Interestingly, a velocity filter removing very fast atoms has only almost negligible influence despite their phase perturbing properties. On the positive side an additional conservative optical guiding towards cavity mode antinodes leads to significantly lower threshold and higher average photon number. Interestingly we see that higher order atom-field and direct atom-atom quantum correlations play only a minor role in the laser dynamics, which is a bit surprising in the superradiant regime.
Highly stable laser sources based on narrow atomic transitions provide a promising platform for direct generation of stable and accurate optical frequencies. Here we investigate a simple system operating in the high-temperature regime of cold atoms. The interaction between a thermal ensemble of 88Sr^{88}\mathrm{Sr}88Sr at mK temperatures and a medium-finesse cavity produces strong collective coupling and facilitates high atomic coherence, which causes lasing on the dipole forbidden $^{1}S_{0}\ensuremath{\leftrightarrow}^{3}P_{1}$ transition. We experimentally and theoretically characterize the lasing threshold and evolution of such a system and investigate decoherence effects in an unconfined ensemble. We model the system using a Tavis-Cummings model and characterize the velocity-dependent dynamics of the atoms as well as the dependency on the cavity detuning.