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Оптика и спектроскопия

Steady-state cooperative effects in a continuously generating superradiant Raman laser

K. S. Tikhonov, Alexander Roth

Published Jan 1, 2022• 0 citations
Publisher

Abstract

A generalized model of the continuously generating superradiant Raman laser is considered. The model includes competing individual and cooperative atomic processes arising from the interaction of atoms with external light fields. We show that proper selection of the model parameters leads to cooperative effects in the atomic active laser medium. We calculate the steady state values of the atomic polarization and two-atom correlations. Using the quantum regression theorem, we determine the spectral characteristics of the collectively emitted light. We use cumulant expansion to estimate the higher-order correlations between atoms. Keywords: superradiant laser, correlated states of atoms, cooperative effects, cumulant expansion.

DOI
10.21883/eos.2022.08.54770.3656-22

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A generalized model of the continuously generating superradiant Raman laser is considered. The model includes competing individual and cooperative atomic processes arising from the interaction of atoms with external light fields. We show that proper selection of the model parameters leads to cooperative effects in the atomic active laser medium. We calculate the steady state values of the atomic polarization and two-atom correlations. Using the quantum regression theorem, we determine the spectral characteristics of the collectively emitted light. We use cumulant expansion to estimate the higher-order correlations between atoms. Keywords: superradiant laser, correlated states of atoms, cooperative effects, cumulant expansion.
A generalized model of the continuously generating superradiant Raman laser is considered. The model includes competing individual and cooperative atomic processes arising from the interaction of atoms with external light fields. We show that proper selection of the model parameters leads to cooperative effects in the atomic active laser medium. We calculate the steady state values ​​of the atomic polarization and two-atoms correlations. Using the quantum regression theorem, we determine the spectral characteristics of the collectively emitted light. We use cumulant expansion to estimate the higher-order correlations between atoms.
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.
Spin-polarised atomic ensembles probed by light based on the Faraday interaction are a versatile platform for numerous applications in quantum metrology and quantum information processing. Here we consider an ensemble of Alkali atoms that are continuously optically pumped and probed. Due to the collective scattering of photons at large optical depth, the steady state of atoms does not correspond to an uncorrelated tensor-product state, as is usually assumed. We introduce a self-consistent method to approximate the steady state including the pair correlations, taking into account the multilevel structure of atoms. We find and characterize regimes of Raman lasing, akin to the model of a superradiant laser. We determine the spectrum of the collectively scattered photons, which also characterises the coherence time of the collective spin excitations on top of the stationary correlated mean-field state, as relevant for applications in metrology and quantum information.
This thesis contributes to the field of collective effects in atomic ensembles. We explore synchronization of superradiant lasers in different coupling configurations and study superradiance in off-resonantly probed atomic ensembles, where we take into account the complete level structure of alkali metal atoms. In the first part we introduce the superradiant laser and extend the discussion of synchronization of symmetrically coupled superradiant lasers to unidirectional coupled superradiant lasers. We show that synchronization is also present when we replace the superradi- ant laser couplings with classical channels, meaning the synchronization can be considered a classical effect. In the second part we generalize a widely used approximation method taking into account lower order atom-atom correlations — the cumulant expansion method — to a basis independent formalism. We implement this formalism in a Python program allowing us to numerically calculate the n-atom reduced density matrix and two-time correlation functions for ensembles of multi-level atoms. This method allows us to study the stationary state of an ensemble of off-resonantly probed alkali metal atoms with a ground-state manifold consisting of many hyperfine levels. We show that collective effects in light-matter interaction depends on the tensor-polarizability of atoms and therefore cannot be explained on the basis of two-level-approximations.
Steady-state collective emission from ensembles of laser cooled atoms has been proposed as a method for generating sub-millihertz linewidth optical lasers, with potential for broad impacts across science and technology. We have built a model system that tests key predictions for such active oscillators using a Raman laser with laser cooled atoms as the gain medium. The laser operates deep in the bad-cavity, or superradiant, regime of laser physics, where the cavity decay rate is much greater than the atomic coherence decay rate. Specifically, we demonstrate that a system of 106 87Rb atoms trapped in a 1D standing wave optical lattice can spontaneously synchronize and collectively emit a quasi-continuous coherent optical output, even when the intracavity field contains on average < 1 photon.
The interaction of light with an atomic sample containing a large number of particles gives rise to many collective (or cooperative) effects, such as multiple scattering, superradiance, and subradiance, even if the atomic density is low and the incident optical intensity weak (linear optics regime). Tracing over the degrees of freedom of the light field, the system can be well described by an effective atomic Hamiltonian, which contains the light-mediated dipole-dipole interaction between atoms. This long-range interaction is at the origin of the various collective effects, or of collective excitation modes of the system. Even though an analysis of the eigenvalues and eigenfunctions of these collective modes does allow distinguishing superradiant modes, for instance, from other collective modes, this is not sufficient to understand the dynamics of a driven system, as not all collective modes are significantly populated. Here, we study how the excitation parameters, i.e., the driving field, determines the population of the collective modes. We investigate in particular the role of the laser detuning from the atomic transition, and demonstrate a simple relation between the detuning and the steady-state population of the modes. This relation allows understanding several properties of cooperative scattering, such as why superradiance and subradiance become independent of the detuning at large enough detuning without vanishing, and why superradiance, but not subradiance, is suppressed near resonance. We also show that the spatial properties of the collective modes allow distinguishing diffusive modes, responsible for radiation trapping, from subradiant modes.