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arXiv:2609.24800

Collective cavity quantum electrodynamics in solid-state optical clocks

Karen Mamian, Georgy A. Kazakov, Thorsten Schumm, Charles Roques-Carmes

physics.opticsnucl-thquant-phSubmitted Sep 21, 2026• Announced Sep 22, 2026• 0 citations
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Abstract

Solid-state frequency standards are generally limited by strong decoherence, rendering conventional interrogation schemes inefficient. The $^{229}$Th nuclear clock provides a unique and timely platform for solid-state optical metrology and nuclear cavity quantum electrodynamics (QED), featuring a coherence time many orders of magnitude shorter than the radiative lifetime in current experiments. Here, we propose and analyze three cavity QED-enhanced clock interrogation schemes that turn this timescale mismatch into an advantage, leveraging collective coupling of thorium nuclei to nanophotonic modes to enable fast interrogation and detection despite the long population lifetime. We reveal the central role of collective cooperativity in determining the clock frequency instability, and derive the optimal conditions (power, working-point detuning, thorium density) for clock operation.

Related papers

Toward nanophotonic platforms for solid-state $^{229}$Th nuclear clocks

Sandro Kraemer, Karen Mamian, Toby Bi +18 more

While the $^{229}$Th nuclear isomer has recently been observed and laser-excited, converting optical nuclear manipulation into a chip-scale solid-state frequency standard remains an open challenge. Here, we present a nanophotonic platform to realize an all-solid-state nuclear clock based on the low-energy isomeric transition of $^{229}$Th embedded in high-$Q$ fluoride photonic resonators. By coupling ensembles of thorium nuclei to confined optical modes, we show that resonant field build-up in the cavity can substantially enhance the nuclear excitation rate, enabling optical interrogation at practical laser intensities. We model the nuclei-photon interaction dynamics and outline a technological roadmap toward addressing this challenge, including resonator fabrication in fluoride crystals, thorium implantation, nuclear excitation with integrated lasers, and on-chip detection of vacuum-ultraviolet photons. As an initial proof of concept, we implant a crystalline fluoride whispering-gallery-mode resonator with $^{229}$Th and assess the impact of implantation-induced damage on resonator performance. Our platform leverages recent advances in materials integration and nanophotonics to chart a realistic route toward compact and scalable nuclear frequency standards.

physics.opticsCross-listedarXiv:2604.20687•Apr 23, 2026•0 citations

A thorium-229 optical nuclear clock with feedback loop

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The laser-accessible nuclear transition in the thorium-229 isotope has been identified as a promising candidate for the realization of an optical nuclear clock. Such a nuclear clock might rival or outperform current optical clocks based on electron-shell transitions in atoms or ions, is expected to be more robust against external perturbations, and provides enhanced sensitivity in clock-based tests of fundamental principles of physics. Here, we implement a thorium-229 nuclear clock by stabilizing a continuous-wave laser to the 148 nm nuclear transition with rapid feedback based on continuous absorption spectroscopy. The thorium-229 nuclei are embedded into a millimeter-sized, room temperature calcium fluoride crystal. A subharmonic of the 148 nm radiation is continuously compared to a Yb+ single-ion clock. The nuclear clock shows a simple shot-noise limited scaling of the fractional frequency instability of $3\cdot 10^{-12} \sqrt{τ/\text{s}}$ where $τ$ is the averaging time, approaching $10^{-15}$ instabilities over 1 day of continuous operation. Improvements of the instability by several orders of magnitude can be projected for future solid-state nuclear clocks. We use the nuclear clock to constrain models of ultralight dark matter by searching for periodic fluctuations and slow drifts in the nuclear transition energy, on time scales between 20 s and 1 day. Drawing benefit from the enhanced sensitivity of the thorium-229 transition, these constraints compete with the best atomic clocks concerning dark matter coupling to photons and go beyond previous measurements regarding coupling to the strong force and quarks.

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In this paper we derive the nonlocal Time-Energy uncertainty principle and then apply the published $^{229}$Th nuclear clock data as a first probe of the nonlocality scale \(E_M\). By using the direct clock-energy channel, we find conservative lower bounds on \(E_M\) at the tens of MeV scale, with optimistic present-data estimates reaching the hundred MeV scale. Including the known nuclear sensitivity enhancement of the $^{229}$Th transition gives us stronger model dependent bounds in the GeV range, while nuclear-scale reference-energy scenarios can reach the TeV range. The conclusion we draw from this is that nuclear clocks already provide an experimental route from nonlocal time--energy uncertainty to measurable laboratory bounds on non-Planckian nonlocality. We explore the idea of using a squeezed-state experiment with the $^{229}\mathrm{Th}$ nuclear clock to test the time--energy structure of nonlocal quantum field theory. The idea is reasonably obtainable within the near future of nuclear clock experiments. One would prepare an ensemble of thorium nuclei in a coherent superposition of the nuclear ground state and the low-lying isomeric clock state, entangle the participating nuclei through a collective interaction, and generate a family of spin-squeezed states with a tunable squeezing parameter $r$. Then a phase-controlled analysis pulse will rotate the selected collective nuclear quadrature into a measurable ground-isomer population difference. Near a strongly polarized collective state the normalized operators $J_y/\sqrt{S}$ and $J_z/\sqrt{S}$ obey the same approximate canonical algebra as the phase and amplitude quadratures of a squeezed optical mode. We use this experiment to either probe or bound the nonlocal energy scale $E_M$.

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Quantum-enhanced metrology relies on entanglement to achieve sensitivities beyond the standard quantum limit. While remarkable progress has been made in generating highly entangled many-body states, extracting their metrological advantage remains a central challenge because the encoded information is often inaccessible to realistic measurements. A key development of the past decade has been the realization that many-body interactions can play a dual role: they can be used not only to generate entanglement, but also to decode it. This idea underlies interaction-based readout and time-reversal protocols, in which controlled non-linear dynamics transform weakly encoded signals into experimentally accessible observables. Cavity quantum electrodynamics (QED) provides a particularly powerful setting for these approaches because it combines collective enhancement, tunable interactions, and controllable reversibility within a single platform. In this review, we discuss the emergence of time-reversal protocols in cavity QED, from their conceptual roots in Loschmidt echoes to modern implementations of signal amplification through a time-reversed interaction (SATIN), scrambling-enhanced metrology, and more general interaction-based readout schemes. We examine the physical mechanisms that enable reversible many-body dynamics, review key experimental demonstrations, and discuss future directions involving complex entangled states, nonlinear decoding, and emerging quantum platforms. Together, these developments suggest that the ability to decode quantum information may become as important as the ability to generate it, establishing reversible many-body dynamics as a central resource for quantum-enhanced sensing.

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Robert J. Lewis-Swan, Diego Barberena, Juan A. Muniz +4 more

In the context of quantum metrology, optical cavity-QED platforms have primarily been focused on the generation of entangled atomic spin states useful for next-generation frequency and time standards. Here, we report a complementary application: the use of optical cavities to generate nonclassical states of light for electric field sensing below the standard quantum limit. We show that cooperative atom-light interactions in the strong collective coupling regime can be used to engineer generalized atom-light cat states which enable quantum enhanced sensing of small displacements of the cavity field even in the presence of photon loss. We demonstrate that metrological gains of 10-20 dB below the standard quantum limit are within reach for current cavity-QED systems operating with long-lived alkaline-earth atoms.

arXiv:1909.07524•Physical Review Letters•May 12, 2020•22 citations
Solid-state frequency standards are generally limited by strong decoherence, rendering conventional interrogation schemes inefficient. The 229^{229}229Th nuclear clock provides a unique and timely platform for solid-state optical metrology and nuclear cavity quantum electrodynamics (QED), featuring a coherence time many orders of magnitude shorter than the radiative lifetime in current experiments. Here, we propose and analyze three cavity QED-enhanced clock interrogation schemes that turn this timescale mismatch into an advantage, leveraging collective coupling of thorium nuclei to nanophotonic modes to enable fast interrogation and detection despite the long population lifetime. We reveal the central role of collective cooperativity in determining the clock frequency instability, and derive the optimal conditions (power, working-point detuning, thorium density) for clock operation.
Toward nanophotonic platforms for solid-state 229^{229}229Th nuclear clocks
While the 229^{229}229Th nuclear isomer has recently been observed and laser-excited, converting optical nuclear manipulation into a chip-scale solid-state frequency standard remains an open challenge. Here, we present a nanophotonic platform to realize an all-solid-state nuclear clock based on the low-energy isomeric transition of 229^{229}229Th embedded in high-QQQ fluoride photonic resonators. By coupling ensembles of thorium nuclei to confined optical modes, we show that resonant field build-up in the cavity can substantially enhance the nuclear excitation rate, enabling optical interrogation at practical laser intensities. We model the nuclei-photon interaction dynamics and outline a technological roadmap toward addressing this challenge, including resonator fabrication in fluoride crystals, thorium implantation, nuclear excitation with integrated lasers, and on-chip detection of vacuum-ultraviolet photons. As an initial proof of concept, we implant a crystalline fluoride whispering-gallery-mode resonator with 229^{229}229Th and assess the impact of implantation-induced damage on resonator performance. Our platform leverages recent advances in materials integration and nanophotonics to chart a realistic route toward compact and scalable nuclear frequency standards.
The laser-accessible nuclear transition in the thorium-229 isotope has been identified as a promising candidate for the realization of an optical nuclear clock. Such a nuclear clock might rival or outperform current optical clocks based on electron-shell transitions in atoms or ions, is expected to be more robust against external perturbations, and provides enhanced sensitivity in clock-based tests of fundamental principles of physics. Here, we implement a thorium-229 nuclear clock by stabilizing a continuous-wave laser to the 148 nm nuclear transition with rapid feedback based on continuous absorption spectroscopy. The thorium-229 nuclei are embedded into a millimeter-sized, room temperature calcium fluoride crystal. A subharmonic of the 148 nm radiation is continuously compared to a Yb+ single-ion clock. The nuclear clock shows a simple shot-noise limited scaling of the fractional frequency instability of 3⋅10−12τ/s3\cdot 10^{-12} \sqrt{τ/\text{s}}3⋅10−12τ/s​ where τττ is the averaging time, approaching 10−1510^{-15}10−15 instabilities over 1 day of continuous operation. Improvements of the instability by several orders of magnitude can be projected for future solid-state nuclear clocks. We use the nuclear clock to constrain models of ultralight dark matter by searching for periodic fluctuations and slow drifts in the nuclear transition energy, on time scales between 20 s and 1 day. Drawing benefit from the enhanced sensitivity of the thorium-229 transition, these constraints compete with the best atomic clocks concerning dark matter coupling to photons and go beyond previous measurements regarding coupling to the strong force and quarks.
In this paper we derive the nonlocal Time-Energy uncertainty principle and then apply the published 229^{229}229Th nuclear clock data as a first probe of the nonlocality scale EME_MEM​. By using the direct clock-energy channel, we find conservative lower bounds on EME_MEM​ at the tens of MeV scale, with optimistic present-data estimates reaching the hundred MeV scale. Including the known nuclear sensitivity enhancement of the 229^{229}229Th transition gives us stronger model dependent bounds in the GeV range, while nuclear-scale reference-energy scenarios can reach the TeV range. The conclusion we draw from this is that nuclear clocks already provide an experimental route from nonlocal time--energy uncertainty to measurable laboratory bounds on non-Planckian nonlocality. We explore the idea of using a squeezed-state experiment with the 229Th^{229}\mathrm{Th}229Th nuclear clock to test the time--energy structure of nonlocal quantum field theory. The idea is reasonably obtainable within the near future of nuclear clock experiments. One would prepare an ensemble of thorium nuclei in a coherent superposition of the nuclear ground state and the low-lying isomeric clock state, entangle the participating nuclei through a collective interaction, and generate a family of spin-squeezed states with a tunable squeezing parameter rrr. Then a phase-controlled analysis pulse will rotate the selected collective nuclear quadrature into a measurable ground-isomer population difference. Near a strongly polarized collective state the normalized operators Jy/SJ_y/\sqrt{S}Jy​/S​ and Jz/SJ_z/\sqrt{S}Jz​/S​ obey the same approximate canonical algebra as the phase and amplitude quadratures of a squeezed optical mode. We use this experiment to either probe or bound the nonlocal energy scale EME_MEM​.
We implement permanent spectral tuning to bring lifetime-limited emitters into collective resonance within an integrated photonic cavity. This addresses a fundamental challenge in solid-state cavity QED: combining multiple coherent quantum emitters with scalable nanophotonics. Our hybrid approach decouples emitter synthesis from nanophotonic fabrication using straightforward techniques that make cavity QED broadly accessible. High doping densities allow us to couple several coherent emitters to a single cavity mode, while optically-induced frequency shifting provides long-lived spectral control. By tuning two molecules into resonance, we demonstrate controlled formation of collective quantum states, establishing a scalable platform for many-body cavity QED. This opens pathways toward chemically-designed quantum systems where optical properties are engineered through synthetic chemistry.
Quantum-enhanced metrology relies on entanglement to achieve sensitivities beyond the standard quantum limit. While remarkable progress has been made in generating highly entangled many-body states, extracting their metrological advantage remains a central challenge because the encoded information is often inaccessible to realistic measurements. A key development of the past decade has been the realization that many-body interactions can play a dual role: they can be used not only to generate entanglement, but also to decode it. This idea underlies interaction-based readout and time-reversal protocols, in which controlled non-linear dynamics transform weakly encoded signals into experimentally accessible observables. Cavity quantum electrodynamics (QED) provides a particularly powerful setting for these approaches because it combines collective enhancement, tunable interactions, and controllable reversibility within a single platform. In this review, we discuss the emergence of time-reversal protocols in cavity QED, from their conceptual roots in Loschmidt echoes to modern implementations of signal amplification through a time-reversed interaction (SATIN), scrambling-enhanced metrology, and more general interaction-based readout schemes. We examine the physical mechanisms that enable reversible many-body dynamics, review key experimental demonstrations, and discuss future directions involving complex entangled states, nonlinear decoding, and emerging quantum platforms. Together, these developments suggest that the ability to decode quantum information may become as important as the ability to generate it, establishing reversible many-body dynamics as a central resource for quantum-enhanced sensing.
In the context of quantum metrology, optical cavity-QED platforms have primarily been focused on the generation of entangled atomic spin states useful for next-generation frequency and time standards. Here, we report a complementary application: the use of optical cavities to generate nonclassical states of light for electric field sensing below the standard quantum limit. We show that cooperative atom-light interactions in the strong collective coupling regime can be used to engineer generalized atom-light cat states which enable quantum enhanced sensing of small displacements of the cavity field even in the presence of photon loss. We demonstrate that metrological gains of 10-20 dB below the standard quantum limit are within reach for current cavity-QED systems operating with long-lived alkaline-earth atoms.