Relaxation Oscillations, Stability, and Cavity Feedback in a Superradiant Raman Laser

Justin G. Bohnet, Zilong Chen, Joshua M. Weiner, Kevin C. Cox, and James K. Thompson

Phys. Rev. Lett. 109, 253602 – Published 18 December 2012

Abstract

We experimentally study the relaxation oscillations and amplitude stability properties of an optical laser operating deep into the bad-cavity regime using a laser-cooled ${}^{87}{Rb}$ Raman laser. By combining measurements of the laser light field with nondemolition measurements of the atomic populations, we infer the response of the gain medium represented by a collective atomic Bloch vector. The results are qualitatively explained with a simple model. Measurements and theory are extended to include the effect of intermediate repumping states on the closed-loop stability of the oscillator and the role of cavity feedback on stabilizing or enhancing relaxation oscillations. This experimental study of the stability of an optical laser operating deep into the bad-cavity regime will guide future development of superradiant lasers with ultranarrow linewidths.

Received 30 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.253602

Authors & Affiliations

Justin G. Bohnet^*, Zilong Chen, Joshua M. Weiner, Kevin C. Cox, and James K. Thompson

JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA

^*To whom all correspondence should be addressed. bohnet@jilau1.colorado.edu

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Vol. 109, Iss. 25 — 21 December 2012

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Figure 1
(a), (b) Physical setup and energy level diagram. The trapping light and Raman dressing laser (power $\propto Ω_{d}^{2}$ ) are injected along the cavity axis. The repumping light is applied perpendicular to the cavity axis. The emitted optical laser light is nearly resonant with the cavity mode (dashed lines) detuned from $ω_{cav}$ by $δ$ . The repumping is accomplished through a pair of two-photon transitions through intermediate optically excited states $| II ⟩$ and $| III ⟩$ with incoherent decay rates $Γ$ . We individually control the two-photon rates $W$ and $Γ_{3}$ with the repumping laser powers $\propto Ω_{1, 2}^{2}$ . $| 3 ⟩$ represents other metastable ground states besides the laser levels. (c) Example emitted laser photon flux $| A (t) |^{2}$ versus time showing spiking and relaxation oscillations at turn-on.Reuse & Permissions
Figure 2
(a) Parametric plots of the Bloch vector components $J_{z} (t)$ and $J_{⊥} (t)$ over a single cycle of modulation of the repumping rate for modulation frequencies below, near, and above resonance or $ω / 2 π = 0.11$ , 2.2, 8 kHz, from left to right. The points are the measured small-signal deviations about the measured steady-state Bloch vector (arrow). The solid curve is the predicted deviation from steady-state given the experimental parameters $N = 1.3 \times 10^{6}$ , $r = 0.71$ , $\bar{δ} = 1$ , $\bar{W} = 0.35 N C γ$ , and $N C γ = 125 \times 10^{3} s^{- 1}$ . The modulation depth $ϵ$ for data below and above resonance was doubled to make the response more visible. (b) The amplitude (upper) and phase (lower) response transfer functions $T_{A} (ω)$ , $T_{ϕ} (ω)$ of the light field for three values of the repumping rate $W$ . The points are measured data, and the lines are zero free-parameter predictions of the response. (Inset) $ω_{res}$ versus $W$ (points) and a fit to $ω_{0}$ (line) showing the expected frequency dependence of the relaxation oscillations on repumping rate.Reuse & Permissions
Figure 3
Effects of finite ratio of repumping rate $r$ (a) Comparison at two values of $r$ of $T_{A} (ω)$ versus modulation frequency. The points are measured data in good agreement with the zero-free parameter fit (lines). (b) Plot of the resonance frequency $ω_{res}$ (circle) and the peak value $T_{A} (ω_{res})$ (square) versus $r$ .Reuse & Permissions
Figure 4
Evidence of negative and positive cavity feedback. (a) Amplitude transfer functions of the emitted electric field for three detunings from cavity resonance. The data points are the average of 4 experimental trials. The lines are fitted transfer functions with N as a free parameter. (b) Cavity damping of collective atomic degrees of freedom. The response going from $\bar{δ} = 0.2$ (left) where the $γ_{0}$ is small to $\bar{δ} = 0.9$ (right) where the system is expected to be critically damped. The solid curves are sinusoidal fits to the data (circles). The dashed lines highlight the damping in both $J_{⊥}$ and $J_{z}$ .Reuse & Permissions

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