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Physical Review A

Four-level superradiant laser with full atomic cooperativity

Deshui Yu, Jingbiao Chen

Published May 7, 2010• 18 citations
Publisher

Abstract

We investigate a four-level superradiant laser whose intensity is proportional to ${N}^{2}$ and whose linewidth scales as $1/{N}^{2}$. In the absence of spontaneous emissions, we derive the stationary solutions of the atomic full cooperativity, analyze their stabilities, and find the corresponding irreducible representation based on group $U(4)$. We also investigate the spectra of the phase and amplitude fluctuations of the fields inside and outside the cavity and find that the amplitude fluctuations of the output fields cannot be squeezed in the low-frequency limit, which is completely different from the three-level superradiant laser system. Finally, we consider the stationary solutions corresponding to the partial cooperativity due to the symmetry breaking of $U(4)$ induced by the atomic spontaneous emissions.

DOI
10.1103/physreva.81.053809

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We investigate a four-level superradiant laser whose intensity is proportional to N2{N}^{2}N2 and whose linewidth scales as 1/N21/{N}^{2}1/N2. In the absence of spontaneous emissions, we derive the stationary solutions of the atomic full cooperativity, analyze their stabilities, and find the corresponding irreducible representation based on group U(4)U(4)U(4). We also investigate the spectra of the phase and amplitude fluctuations of the fields inside and outside the cavity and find that the amplitude fluctuations of the output fields cannot be squeezed in the low-frequency limit, which is completely different from the three-level superradiant laser system. Finally, we consider the stationary solutions corresponding to the partial cooperativity due to the symmetry breaking of U(4)U(4)U(4) induced by the atomic spontaneous emissions.
We discuss a laser with N three-level atoms resonantly and cooperatively interacting with two cavity modes. Its intensity is proportional to N2{\mathit{N}}^{2}N2, the linewidth scales as 1/N2{\mathit{N}}^{2}N2, and the output intensity fluctuations display up to 100% squeezing at low frequencies. We show that quantum fluctuations of the pump do not deteriorate the squeezing significantly. We also find that the fluctuation properties of the ``passive'' cavity mode which serves to collectively relax the atoms to the ground state are similar to those of the active mode. Finally we take into account spontaneous emission. Within a certain range of frequencies good squeezing can still be found. \textcopyright{} 1996 The American Physical Society.
We further develop the theory of the superradiant laser by allowing for submaximal atomic collectivity and spontaneous emission. In the absence of spontaneous emission we obtain a set of stationary solutions for different degrees of atomic cooperativity and investigate their fluctuation properties and interrelations with respect to the underlying U(3) symmetry. We use this set of solutions to discuss the breaking of U(3) by spontaneous emission. \textcopyright{} 1996 The American Physical Society.
We theoretically study a superradiant laser, deriving both the steady-state behaviors and small-amplitude responses of the laser's atomic inversion, atomic polarization, and light field amplitude. Our minimum model for a three-level laser includes atomic population accumulating outside of the lasing transition and dynamics of the atomic population distribution causing cavity frequency tuning, as can occur in realistic experimental systems. We show that the population dynamics can act as real-time feedback to stabilize or destabilize the laser's output power, and we derive the cavity frequency tuning for a Raman laser. We extend the minimal model to describe a cold-atom Raman laser using 87{}^{87}87Rb, showing that the minimal model qualitatively captures the essential features of the more complex system [Bohnet et al., Phys. Rev. Lett. 109, 253602 (2012)]. This work informs our understanding of the stability of proposed millihertz linewidth lasers based on ultranarrow optical atomic transitions and will guide the design and development of these next-generation optical frequency references.
We propose a minimalistic model to account for the main properties of a continuous superradiant laser, in which a beam of atoms crosses the mode of a high-finesse Fabry-Perot cavity, and collectively emits light into the cavity mode. We focus on the case of weak single atom - cavity cooperativity, and highlight the relevant regime where decoherence due to the finite transit time dominates over spontaneous emission. We propose an original approach where the dynamics of atoms entering and leaving the cavity is described by a Hamiltonian process. This allows deriving the main dynamical equations for the superradiant laser, without the need for a stochastic approach. We derive analytical conditions for a sustained emission and show that the ultimate linewidth is set by the fundamental quantum fluctuations of the collective atomic dipole. We calculate steady-state values of the two-body correlators and show that the continuous superradiant regime is tied to the growth of atom-atom correlations, although these correlations only have a small impact on the laser linewidth.
We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to 10310^3103 emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.
We investigate the intensity stability of the superradiant laser. Our study focuses on the architecture where a continuous beam of atoms in an electronically excited state crosses the mode of a high-finesse Fabry-Perot cavity, which has been proposed as a new architecture of an active optical clock. We show that such superradiant laser can become unstable and develop chaotic behavior. We derive an analytical criterion for this instability and find that it may only occur when the lifetime of photons in the cavity is significantly shorter than the lifetime of atoms. This criterion allows for refining the necessary parameters to run a superradiant laser as a frequency reference in the optical domain. In particular, we point-out the consequences of the instability on intensity fluctuations and laser linewidth. On the other hand, we also point out that the superradiant laser, when in the unstable regime, can become an interesting playground for studying chaos. At the mean-field level, there is a direct mapping to the Bénard instability associated with fluid turbulence; however quantum fluctuations associated with photon out-coupling and atom re-filling substantially modify the expected behaviors. Finally, we point-out the existence of a regular self-pulsing regime at large atom numbers.