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arXiv:2306.12544 · Nature Communications

Collectively enhanced Ramsey readout by cavity sub- to superradiant transition

Eliot A. Bohr, Sofus L. Kristensen, Christoph Hotter, Stefan Alaric Schäffer, Julian Robinson-Tait, Jan W. Thomsen, Tanya Zelevinsky, Helmut Ritsch, Jörg Helge Müller

Published Feb 5, 2024• 22 citations

Abstract

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.

DOI: 10.1038/s41467-024-45420-x

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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.

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π/2

-excitation of the atoms to prepare a macroscopic collective spin protected from cavity superradiance. This requires that the two halves of the atomic ensemble are coupled to the cavity mode with opposite phase, which is naturally realized for a homogeneously filled volume covering odd and even sites of the cavity mode along the cavity axis. The origin of the superior precision can be traced back to destructive interference among sub-ensembles in the complex nonlinear collective atom field dynamics. In the same configuration we find surprising regular self-pulsing of the cavity output for suitable continuous illumination. Our simulations for large atom numbers employing a cumulant expansion are qualitatively confirmed by a full quantum treatment of smaller ensembles.

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.

Superradiant lasers promise continuous, narrow-linewidth coherent emission at the bare atomic transition frequency, enabling frequency references of exceptional precision. Recent experiments have advanced the field, but achieving truly continuous operation remains technically challenging. Here we propose an alternative route to an active optical frequency reference with fewer emitters using all-to-all dipole-dipole interactions mediated by a nanophotonic waveguide. We show that selectively pumping only a sub-ensemble of emitters, rather than the full ensemble, substantially improves emission characteristics. The collective interactions with unpumped emitters provide narrowband frequency selection and establish an effective feedback mechanism analogous to the role of a macroscopic cavity. We find directional superradiant emission with strongly phase-synchronized emitter correlations and a narrow output spectrum close to the bare emitter resonance. Our results demonstrate a strong metrological gain from selective partial pumping of quantum emitters with the second-order intensity correlation

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