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arXiv:2205.04698

Correlated steady states and Raman lasing in continuously pumped and probed atomic ensembles

Alexander Roth, Klemens Hammerer, K. S. Tikhonov

Published May 10, 2022• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2205.04698

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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.
Abstract Spin-polarized 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 characterizes 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.
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.
By allowing a large ensemble of laser cooled and trapped 87Rb atoms to interact collectively with an optical cavity, I have explored two phenomena that may prove useful for enhancing precision measurements: superradiant lasing and spin squeezing.\nSuperradiant lasers have been proposed as future ultrastable optical frequency references, with predicted linewidths < 1 millihertz. These lasers operate in an unusual regime of laser physics where collective emission from an atomic ensemble maps the quantum phase stored in the atoms onto the optical cavity field. I will give an overview of my experimental work using a cold-atom, superradiant Raman laser as a model system to confirm a number of the key predictions concerning superradiant lasing, including the possibility of coherent emission with < 1 intracavity photon on average and greatly reduced sensitivity to cavity frequency noise.\nI also present work using cavity-aided, coherence-preserving measurements of the atomic state population to create entanglement between atoms. The entanglement enables more precise estimation of the quantum phase at the heart of nearly all precision measurements and sensors utilizing quantum objects. By utilizing a cycling transition for the quantum non-demolition probe, we have reduced by several orders of magnitude the measurement induced back-action caused by spontaneous Raman transitions. We directly observe, with no background subtraction, a spin squeezed state with sensitivity to measuring a quantum phase enhanced 10.5 times in variance (i.e. 10.2 dB) beyond the standard quantum limit for an unentangled state. This experimental breakthrough demonstrates that quantum-aided sensing techniques can realize large enough enhancements to have a substantial impact on precision measurements and may aid advances in technology as well as searches for new physics.
Optimally extracting information from measurements performed on a physical system requires an accurate model of the measurement interaction. Continuously probing the collective spin of an alkali-metal atom cloud via its interaction with an off-resonant optical probe is an important example of such a measurement where realistic modeling at the quantum level is possible using standard techniques from atomic physics. Typically, however, tutorial descriptions of this technique have neglected the multilevel structure of realistic atoms for the sake of simplification. We account for the full multilevel structure of alkali-metal atoms and derive the irreducible form of the polarizability Hamiltonian describing a typical dispersive quantum measurement. For a specific set of parameters, we then show that semiclassical predictions of the theory are consistent with our experimental observations of polarization scattering by a polarized cloud of laser-cooled cesium atoms. We also derive the signal-to-noise ratio under a single-measurement trial and use this to predict the rate of spin squeezing with multilevel alkali-metal atoms for arbitrary detuning of the probe beam.
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.
We describe the mechanism of squeezing and entanglement in the ground-state spin subsystems of macroscopic atomic ensembles via the process of stimulated cooperative Raman-type scattering of correlated photon pairs. This mechanism is analogous to common optical pumping techniques normally used for depopulation of Zeeman sublevels in macroscopic atomic ensembles. We show that, by the excitation of atoms, oriented in their angular momenta, with nonclassical light consisting of a rare flux of strongly correlated photon pairs, essential correlations in the macroscopic spin fluctuations can be transferred and accumulated. In turn this leads to squeezing or entanglement in the quasispin (alignment) subsystems of macroscopic ensembles. We discuss in particular a scheme for an interferometer that would be available for the control or teleportation of quantum states created in quasispin subsystems. Such squeezed and entangled states can be stored in long-lived spin subsystems and can be further used in quantum information protocols based on the continuous variable technique.