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arXiv:2401.00785

Theoretical Study on Superradiant Raman Scattering with Rubidium Atoms in An Optical Cavity

Yu, Huihui, Yuan Zhang, Gang Chen, Chongxin Shan

Published Jan 1, 2024• 0 citations
arXivHTMLPDF

Abstract

Superradiant Raman scattering of Rubidium atoms has been explored in the experiment [Nature 484, 78 (2012)] to prove the concept of the superradiant laser, which attracts significant attentions in quantum metrology due to the expected ultra-narrow linewidth down to millihertz. To better understand the physics involved in this experiment, we have developed a quantum master equation theory by treating the Rubidium atoms as three-level systems, and coupling them with a dressed laser and an optical cavity. Our simulations show different superradiant Raman scattering pulses for the systems within the crossover and strong coupling regime, and the shifted and broader spectrum of the steady-state Raman scattering. Thus, our studies provide a unified view on the superradiant Raman scattering pulses, and an alternative explanation to the broad spectrum of the steady-state Raman scattering, as observed in the experiment. In future, our theory can be readily applied to study other interesting phenomena relying on the superradiant Raman scattering, such as magnetic field sensing, real-time tracking of quantum phase, Dicke phase transition of non-equilibrium dynamics and so on.

DOI
10.48550/arxiv.2401.00785

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Superradiant Raman scattering of Rubidium atoms has been explored in the experiment [Nature 484, 78 (2012)] to prove the concept of the superradiant laser, which attracts significant attentions in quantum metrology due to the expected ultra-narrow linewidth down to millihertz. To better understand the physics involved in this experiment, we have developed a quantum master equation theory by treating the Rubidium atoms as three-level systems, and coupling them with a dressed laser and an optical cavity. Our simulations show different superradiant Raman scattering pulses for the systems within the crossover and strong coupling regime, and the shifted and broader spectrum of the steady-state Raman scattering. Thus, our studies provide a unified view on the superradiant Raman scattering pulses, and an alternative explanation to the broad spectrum of the steady-state Raman scattering, as observed in the experiment. In future, our theory can be readily applied to study other interesting phenomena relying on the superradiant Raman scattering, such as magnetic field sensing, real-time tracking of quantum phase, Dicke phase transition of non-equilibrium dynamics and so on.
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.
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.
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In this thesis, I describe the theoretical development of the superradiant laser, or laser in the extreme bad-cavity regime. In this regime, the cavity decay rate is much greater than the atomic dynamics. The atoms emit photons into the cavity mode superradiantly in steady state. We develop group-theoretic methods that enable us to exactly solve mesoscopic systems with hundreds of atoms. We demonstrate the synchronization of atomic dipoles in steady-state superradiance. With this synchronized system, we propose conditional Ramsey spectroscopy which allows us to observe Ramsey fringes indefinitely, even in the presence of atomic decoherence. Furthermore, we explore manifestations of synchronization in the quantum realm with two superradiant atomic ensembles. We show that two such ensembles exhibit a dynamical phase transition from two disparate oscillators to quantum phase-locked dynamics. Finally, we study the mechanical eect of the light-atom interaction in the steady-state superradiance. We find efficient many-body cooling of atoms. The work described in this thesis lays the theoretical foundation for the superradiant laser and for a potential future of active optical frequency standards.
A new class of laser, which harnesses coherence in both light and atoms, is possible with ultracold alkaline-earth-metal atoms trapped in an optical lattice inside an optical cavity. Different lasing regimes, including superradiance, superradiant, and conventional lasing, are distinguished by the relative coherence stored in the atoms and in the cavity mode. We analyze the physics in two different experimentally achievable regions of the superradiant lasing regime. Our calculations confirm the narrow linewidth of superradiant lasing for the doubly forbidden clock transition ${}^{3}{P}_{0}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ of 87Sr^{87}\mathrm{Sr}87Sr atoms. Under strong driving of the dipole-forbidden transition ${}^{3}{P}_{1}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ of 88Sr^{88}\mathrm{Sr}88Sr atoms, the superradiant linewidth narrows further due to the coherent excitation of the cavity field.
In order to study quantum effects such as state superposition and entanglement, one would like to construct simple systems for which the damping rates are slow relative to the rate of coherent evolution. One such system is strong-coupling cavity quantum electrodynamics (QED), in which a single atom is coupled to a single mode of a high finesse optical cavity. In recent years, optical trapping techniques have been applied to the cavity QED system, allowing an individual atom to remain coupled to the cavity for long periods of time. For the purpose of future cavity QED experiments, one would like to gain as much control over the trapped atom as possible; in particular, one would like to cool the center of mass motion of the atom, to measure the magnetic field at the location of the atom, and to be able to prepare the atom in a given internal state. In the first part of this thesis, I present a scheme for driving Raman transitions inside the cavity that can be used to achieve these goals. After giving a detailed theoretical treatment of the Raman scheme, I describe how it can be implemented in the lab and discuss some preliminary experimental results. In the second part of this thesis, I present a number of simple field theory models. These models were developed in an attempt to understand some of the central ideas of theoretical physics by looking at how the ideas work in a highly simplified context. The hope is that by reducing the mathematical complexity of an actual theory, the underlying physical concepts can be more easily understood.