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arXiv:1903.10196 · Physical Review Letters

Pulse Delay Time Statistics in a Superradiant Laser with Calcium Atoms

Torben Laske, Hannes Winter, Andreas Hemmerich

Published Sep 3, 2019• 84 citations
arXivHTMLPDF

Abstract

Cold samples of calcium atoms are prepared in the metastable ^{3}P_{1} state inside an optical cavity resonant with the narrow band (375 Hz) ^{1}S_{0}→^{3}P_{1} intercombination line at 657 nm. We observe a superradiant emission of hyperbolic secant shaped pulses into the cavity with an intensity proportional to the square of the atom number, a duration much shorter than the natural lifetime of the ^{3}P_{1} state, and a delay time fluctuating from shot to shot in excellent agreement with theoretical predictions. Our incoherent pumping scheme to produce inversion on the ^{1}S_{0}→^{3}P_{1} transition should be extendable to allow for continuous wave laser operation.

DOI
10.1103/physrevlett.123.103601

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Sub-Natural Linewidth Superradiant Lasing with Cold 88^{88}88Sr Atoms
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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.
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 .
An experiment is described in which large numbers ( approximately 10 16 ) of calcium atoms are placed in the 4s4p 3 P metastable level by optical pumping with a tunable dye laser and then studied spectroscopically. Equations governing the degree of excitation by the laser are derived. Predictions of the theory are shown to be in good agreement with experimental results. In particular, at low optical depths produced by 10 15 ground state atoms cm -2 the dye laser raises approximately 50% of the calcium atoms into the metastable state. At higher optical depths associated with 10 17 ground state atoms cm -2 the number of excited states is limited only by the laser energy and line width. For the dye laser used the largest number of metastables produced was approximately 10 16 . The absorption spectra of the 4s4p 2 P level is seen out to 4s4p 3 P to 4s22d 3 D. The relaxation rate between the excited state fine structure is studied directly with an optically delayed dye laser continuum. Other applications of this technique of producing large numbers of excited states are briefly discussed.
A superfluid atomic gas is prepared inside an optical resonator with an ultranarrow bandwidth on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerated or decelerated by multiples of two recoil momenta. The instability boundary for the onset of matter wave superradiance is recorded and its main features are explained by a mean field model.
Numerical simulations of an extended sample of three-level atoms with slow dipole dephasing exhibit a superfluorescent pulse shortly after incoherent pumping begins. The operator Maxwell-Bloch equations are simulated by classical Langevin equations. The counterpropagating fields are solved for in the (one-dimensional) limit of the Fresnel number near unity, with open-end boundary conditions. An initial, ``quiet'' buildup of the inversion is followed by superfluorescence. Oscillation of the populations, coherences, and fields is observed. The superfluorescence delay time is compared with analytical predictions made in the linear regime. A transition to amplified spontaneous emission is found as the pump rate is decreased.