We explore an array of quantum emitters as non-equilibrium probes, coupled to a one-dimensional photonic waveguide, aiming to estimate its properties such as wave number which encodes the waveguide frequency and dispersive characteristics. By considering transient dynamics following initial excitation, we show that the quantum Fisher information (QFI) can be significantly enhanced through careful emitter positioning. For two-emitter probes, optimal spacing stabilizes populations and coherences in the single-excitation subspace, suppressing super radiant decay and extending both the magnitude and longevity of QFI. Randomized emitter configurations also reveal that vanishing waveguide-mediated cross decay maximizes both achievable sensitivity and the temporal duration over which information about the parameter remains accessible. Extending to multipartite probes, we demonstrate that the maximum QFI and its temporal integral scale with system size, exceeding the Heisenberg limit for all positioning strategies. Our results highlight the potential of waveguide-coupled emitter arrays as versatile quantum sensors, where collective radiative dynamics can be harnessed to achieve tunable, long-lived, and enhanced precision.We explore an array of quantum emitters as non-equilibrium probes, coupled to a one-dimensional photonic waveguide, aiming to estimate its properties such as wave number which encodes the waveguide frequency and dispersive characteristics. By considering transient dynamics following initial excitation, we show that the quantum Fisher information (QFI) can be significantly enhanced through careful emitter positioning. For two-emitter probes, optimal spacing stabilizes populations and coherences in the single-excitation subspace, suppressing super radiant decay and extending both the magnitude and longevity of QFI. Randomized emitter configurations also reveal that vanishing waveguide-mediated cross decay maximizes both achievable sensitivity and the temporal duration over which information about the parameter remains accessible. Extending to multipartite probes, we demonstrate that the maximum QFI and its temporal integral scale with system size, exceeding the Heisenberg limit for all positioning strategies. Our results highlight the potential of waveguide-coupled emitter arrays as versatile quantum sensors, where collective radiative dynamics can be harnessed to achieve tunable, long-lived, and enhanced precision.

quant-pharXiv:2606.11975Jun 11, 20260 citations

Super-Heisenberg-limited Sensing via Collective Subradiance in Waveguide Quantum Electrodynamics

Xin Wang, Zeyang Liao

We explore the quantum-metrological potential of subwavelength-spaced emitter arrays coupled to a one-dimensional nanophotonic waveguide. In this system, strong dipole--dipole interactions profoundly modify the collective optical response, leading to the emergence of ultranarrow subradiant resonances. Through an eigenmode analysis of the effective non-Hermitian Hamiltonian, we derive the decay rate of the most subradiant state, which, within the present model and geometry, exhibits an $N^{-3}$ scaling with even--odd oscillatory behavior in the deep-subwavelength regime. This scaling is directly observable in the single-photon scattering spectrum, enabling the detection of minute changes in atomic separation with a figure of merit that scales as $ N^3 $. The quantum Fisher information (QFI) scales as $N^6$ and can be closely approached by measuring spectral shifts near the steepest slope of the most subradiant resonance. These enhancements remain robust under realistic positional disorder, confirming that dipole--dipole-engineered subradiance provides a viable resource for quantum metrology. Our work bridges collective waveguide-QED physics and high-precision sensing, opening a route toward scalable quantum sensors on integrated nanophotonic platforms.We explore the quantum-metrological potential of subwavelength-spaced emitter arrays coupled to a one-dimensional nanophotonic waveguide. In this system, strong dipole--dipole interactions profoundly modify the collective optical response, leading to the emergence of ultranarrow subradiant resonances. Through an eigenmode analysis of the effective non-Hermitian Hamiltonian, we derive the decay rate of the most subradiant state, which, within the present model and geometry, exhibits an $N^{-3}$ scaling with even--odd oscillatory behavior in the deep-subwavelength regime. This scaling is directly observable in the single-photon scattering spectrum, enabling the detection of minute changes in atomic separation with a figure of merit that scales as $ N^3 $. The quantum Fisher information (QFI) scales as $N^6$ and can be closely approached by measuring spectral shifts near the steepest slope of the most subradiant resonance. These enhancements remain robust under realistic positional disorder, confirming that dipole--dipole-engineered subradiance provides a viable resource for quantum metrology. Our work bridges collective waveguide-QED physics and high-precision sensing, opening a route toward scalable quantum sensors on integrated nanophotonic platforms.

quant-pharXiv:2512.14463Physical Review AppliedDec 17, 20251 citation

Programmable Superradiance in an Interacting Qubit Array

Botao Du, Qihao Guo, Ruichao Ma

When multiple quantum emitters couple to a common electromagnetic environment, interference in their collective radiative dynamics gives rise to superradiance and subradiance. In regimes where coherent interactions and collective dissipation compete, the microscopic many-body dynamics and quantum correlations among the emitters that underlie superradiance and subradiance are theoretically challenging and remain experimentally elusive, even though collective emission has been observed in many physical systems. Here, we realize a superconducting qubit array coupled to a common microwave waveguide that mediates collective dissipation, with simultaneous access to coherent interactions and microscopic measurements of many-body dynamics. Engineered qubit-waveguide couplings with tunable amplitude and phase enable control of collective interference and the resulting super- and subradiant states. Leveraging site-resolved control and readout, we directly observe the microscopic decay dynamics of multi-qubit states across different excitation manifolds and track the evolution of populations and tunable quantum correlations. We reveal collective decay in regimes beyond the ideal Dicke model, where strong qubit-qubit interactions stabilize superradiance and subradiance against local dephasing and reshape decay pathways through spatially and spectrally structured many-body eigenstates. Our results establish a flexible platform for exploring collective phenomena in many-body quantum optics and driven-dissipative approaches to robust quantum information processing.When multiple quantum emitters couple to a common electromagnetic environment, interference in their collective radiative dynamics gives rise to superradiance and subradiance. In regimes where coherent interactions and collective dissipation compete, the microscopic many-body dynamics and quantum correlations among the emitters that underlie superradiance and subradiance are theoretically challenging and remain experimentally elusive, even though collective emission has been observed in many physical systems. Here, we realize a superconducting qubit array coupled to a common microwave waveguide that mediates collective dissipation, with simultaneous access to coherent interactions and microscopic measurements of many-body dynamics. Engineered qubit-waveguide couplings with tunable amplitude and phase enable control of collective interference and the resulting super- and subradiant states. Leveraging site-resolved control and readout, we directly observe the microscopic decay dynamics of multi-qubit states across different excitation manifolds and track the evolution of populations and tunable quantum correlations. We reveal collective decay in regimes beyond the ideal Dicke model, where strong qubit-qubit interactions stabilize superradiance and subradiance against local dephasing and reshape decay pathways through spatially and spectrally structured many-body eigenstates. Our results establish a flexible platform for exploring collective phenomena in many-body quantum optics and driven-dissipative approaches to robust quantum information processing.

cond-mat.quant-gasCross-listedarXiv:2605.12442May 13, 20260 citations

Subradiant states of quantum bits coupled to a one-dimensional waveguide

Andreas Albrecht, Loïc Henriet, Ana Asenjo-Garcı́a +3 more

The properties of coupled emitters can differ dramatically from those of their individual constituents. Canonical examples include sub- and super-radiance, wherein the decay rate of a collective excitation is reduced or enhanced due to correlated interactions with the environment. Here, we systematically study the properties of collective excitations for regularly spaced arrays of quantum emitters coupled to a one-dimensional waveguide. We find that, for low excitation numbers, the modal properties are well-characterized by spin waves with a definite wavevector. Moreover, the decay rate of the most subradiant modes obeys a universal scaling with a cubic suppression in the number of emitters. Multi-excitation subradiant eigenstates can be built from fermionic combinations of single excitation eigenstates; such 'fermionization' results in multiple excitations that spatially repel one another. We put forward a method to efficiently create and measure such subradiant states, which can be realized with superconducting qubits. These measurement protocols probe both real-space correlations (using on-site dispersive readout) and temporal correlations in the emitted field (using photon correlation techniques).The properties of coupled emitters can differ dramatically from those of their individual constituents. Canonical examples include sub- and super-radiance, wherein the decay rate of a collective excitation is reduced or enhanced due to correlated interactions with the environment. Here, we systematically study the properties of collective excitations for regularly spaced arrays of quantum emitters coupled to a one-dimensional waveguide. We find that, for low excitation numbers, the modal properties are well-characterized by spin waves with a definite wavevector. Moreover, the decay rate of the most subradiant modes obeys a universal scaling with a cubic suppression in the number of emitters. Multi-excitation subradiant eigenstates can be built from fermionic combinations of single excitation eigenstates; such 'fermionization' results in multiple excitations that spatially repel one another. We put forward a method to efficiently create and measure such subradiant states, which can be realized with superconducting qubits. These measurement protocols probe both real-space correlations (using on-site dispersive readout) and temporal correlations in the emitted field (using photon correlation techniques).

arXiv:1803.02115New Journal of PhysicsJan 23, 2019152 citations

Non-Markovian delay-assisted sensing with waveguide-coupled quantum emitters

Prajit Dhara, Isack Padilla, Saikat Guha +2 more

We show that in a minimal setup of two waveguide-coupled quantum emitters, separated by long distances and subject to an external field, time-delayed feedback can be a resource for sensing field gradients. While the field gradient induces a detuning between the emitters; the large interatomic separations render the system dynamics non-Markovian. We show that the quantum Fisher information (QFI) for estimating the detuning parameter, and thereby the field gradient, is enhanced in the presence of non-Markovian delay. Such an enhancement can be attributed to the formation of atom-photon quasi-bound states that enable the field to interact with the emitters for longer times, thereby gaining more information about their relative detunings. Additionally, in the presence of delay, the interaction between the emitters is mediated via multiple spectral modes of the field, further enhancing the sensing capabilities of the system. Our results establish non-Markovian time-delayed feedback and multimode reservoirs as a resource for distributed quantum sensing with waveguide-coupled quantum emitters.We show that in a minimal setup of two waveguide-coupled quantum emitters, separated by long distances and subject to an external field, time-delayed feedback can be a resource for sensing field gradients. While the field gradient induces a detuning between the emitters; the large interatomic separations render the system dynamics non-Markovian. We show that the quantum Fisher information (QFI) for estimating the detuning parameter, and thereby the field gradient, is enhanced in the presence of non-Markovian delay. Such an enhancement can be attributed to the formation of atom-photon quasi-bound states that enable the field to interact with the emitters for longer times, thereby gaining more information about their relative detunings. Additionally, in the presence of delay, the interaction between the emitters is mediated via multiple spectral modes of the field, further enhancing the sensing capabilities of the system. Our results establish non-Markovian time-delayed feedback and multimode reservoirs as a resource for distributed quantum sensing with waveguide-coupled quantum emitters.

quant-pharXiv:2605.05434Physical Review ResearchMay 8, 20260 citations

Quantum Enhanced Sensitivity through Many-Body Bloch Oscillations

Hassan Manshouri, Moslem Zarei, Mehdi Abdi +2 more

We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling behaviors in two different phases, namely localized and extended. Our results provide a quantitative ansatz for quantum Fisher information in terms of time, probe size, and the number of excitations. In the long-time regime, the quantum Fisher information is a quadratic function of time, touching the Heisenberg limit. The system size scaling drastically depends on the phase changing from quantum-enhanced scaling in the extended phase to size-independent behavior in the localized phase. Furthermore, increasing the number of excitations always enhances the precision of the probe, although, in the interacting systems the enhancement becomes less eminent than the non-interacting probes. This is due to the induced localization by increasing the interaction between the excitations. We show that a simple particle configuration measurement together with a maximum likelihood estimation can closely reach the ultimate precision limit in both single- and multi-particle probes.We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling behaviors in two different phases, namely localized and extended. Our results provide a quantitative ansatz for quantum Fisher information in terms of time, probe size, and the number of excitations. In the long-time regime, the quantum Fisher information is a quadratic function of time, touching the Heisenberg limit. The system size scaling drastically depends on the phase changing from quantum-enhanced scaling in the extended phase to size-independent behavior in the localized phase. Furthermore, increasing the number of excitations always enhances the precision of the probe, although, in the interacting systems the enhancement becomes less eminent than the non-interacting probes. This is due to the induced localization by increasing the interaction between the excitations. We show that a simple particle configuration measurement together with a maximum likelihood estimation can closely reach the ultimate precision limit in both single- and multi-particle probes.

arXiv:2406.13921QuantumJul 11, 20256 citations

N^{-3}

scaling with even--odd oscillatory behavior in the deep-subwavelength regime. This scaling is directly observable in the single-photon scattering spectrum, enabling the detection of minute changes in atomic separation with a figure of merit that scales as $ N^3 $. The quantum Fisher information (QFI) scales as

N^6

and can be closely approached by measuring spectral shifts near the steepest slope of the most subradiant resonance. These enhancements remain robust under realistic positional disorder, confirming that dipole--dipole-engineered subradiance provides a viable resource for quantum metrology. Our work bridges collective waveguide-QED physics and high-precision sensing, opening a route toward scalable quantum sensors on integrated nanophotonic platforms.