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arXiv:2503.11580

Complementary Collective Spin Descriptions of Superradiant Ramsey Spectroscopy

Gao, Ke-Xin, Yuan Zhang, Shi‐Lei Su, Gang Chen, Chongxin Shan, Klaus Mølmer

Published Mar 14, 2025• 0 citations
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Abstract

A recent experiment demonstrated delayed superradiance from strontium-88 atoms, which are coupled to a longitudinal mode of a cavity while being excited by laser pulses propagating along a transversal direction [Nat. Commun. 15, 1084 (2024)]. A coherent picture of the atomic ensemble dynamics in this experiment requires complementary representations of the external driving dynamics and the superradiant dynamics. To complement previous analyses, we introduce these representations by considering in-phase and out-of-phase superpositions of transverse collective spin components of two atomic sub-ensembles, and analyze the dynamics with the corresponding collective Dicke states and Bloch vectors. This approach also explains Ramsey spectroscopy experiments with the ensemble, and it may be employed to explore other phenomena, such as weak-to-strong coupling phase transitions and triggered superradiance.

DOI
10.48550/arxiv.2503.11580

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A recent experiment demonstrated delayed superradiance from strontium-88 atoms, which are coupled to a longitudinal mode of a cavity while being excited by laser pulses propagating along a transversal direction [Nat. Commun. 15, 1084 (2024)]. A coherent picture of the atomic ensemble dynamics in this experiment requires complementary representations of the external driving dynamics and the superradiant dynamics. To complement previous analyses, we introduce these representations by considering in-phase and out-of-phase superpositions of transverse collective spin components of two atomic sub-ensembles, and analyze the dynamics with the corresponding collective Dicke states and Bloch vectors. This approach also explains Ramsey spectroscopy experiments with the ensemble, and it may be employed to explore other phenomena, such as weak-to-strong coupling phase transitions and triggered superradiance.
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When an inverted ensemble of atoms is tightly packed on the scale of its emission wavelength or when the atoms are collectively strongly coupled to a single cavity mode, their dipoles will align and decay rapidly via a superradiant burst. However, a spread-out dipole phase distribution theory predicts a required minimum threshold of atomic excitation for superradiance to occur. Here we experimentally confirm this predicted threshold for superradiant emission on a narrow optical transition when exciting the atoms transversely and show how to take advantage of the resulting sub- to superradiant transition. A π/2-pulse places the atoms in a subradiant state, protected from collective cavity decay, which we exploit during the free evolution period in a corresponding Ramsey pulse sequence. The final excited state population is read out via superradiant emission from the inverted atomic ensemble after a second π/2-pulse, and with minimal heating this allows for multiple Ramsey sequences within one experimental cycle. Our scheme is an innovative approach to atomic state readout characterized by its speed, simplicity, and highly directional emission of signal photons. It demonstrates the potential of sensors using collective effects in cavity-coupled quantum emitters.
The collective behavior of ensembles of atoms has been studied in-depth since the seminal paper of Dicke [R. H. Dicke, Phys. Rev. 93, 99 (1954)], where he demonstrated that a group of emitters in collective states is able to radiate with increased intensity and modified decay rates in particular directions, a phenomenon which he called superradiance. Here, we show that the fundamental setup of two atoms coupled to a single-mode cavity can be distinctly exceeding the free-space superradiant behavior, a phenomenon which we call hyperradiance. The effect is accompanied by strong quantum fluctuations and surprisingly arises for atoms radiating out-of-phase, an alleged non-ideal condition, where one expects subradiance. We are able to explain the onset of hyperradiance in a transparent way by a photon cascade taking place among manifolds of Dicke states with different photon numbers under particular out-of-phase coupling conditions. The theoretical results can be realized with current technology and thus should stimulate future experiments.
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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.
We simulate the superradiant dynamics of ensembles of atoms in the presence of collective and individual atomic decay processes. We apply the Monte-Carlo wave-function method and identify quantum jumps in a reduced Dicke state basis, which reflects the permutation symmetry of the system. While the number of density matrix elements in the Dicke representation increases polynomially with atom number, the quantum jump dynamics populates only a single Dicke state at the time and thus efficient simulations can be carried out for tens of thousands of atoms. The superradiant pulses from initially excited atoms agree quantitatively with recent experimental results of strontium atoms but rapid atom loss in these experiments does not permit steady-state superradiance. By introducing an incident flux of new atoms to maintain a large average atom number, our theoretical calculations predict lasing with a millihertz linewidth despite rapid atom number fluctuations.