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arXiv:2603.13130 · PRX Quantum

Extracting information from a superradiant burst using simple measurements

Federico Belliardo, Anjun Chu, Martin Koppenhöfer, Aashish A. Clerk

quant-phSubmitted Mar 13, 2026• Announced Mar 16, 2026• 0 citations
v1 · Mar 13, 2026v2 · Mar 31, 2026
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Abstract

It is well known that superradiant decay of an ensemble of $N$ spins generates a complex non-classical state of light. Here, we consider the information content of a superradiant burst of photons: how is information encoded in the initial spin state distributed among the emitted photons, and can it be extracted using simple measurements? Despite the complexity of the photonic burst state, we show that a simple homodyne measurement combined with an optimized filter and linear estimator recovers the $N$-scaling of the quantum Fisher information of the initial spin state (including cases exhibiting $N^2$ Heisenberg scaling). Even more surprising, the temporal mode with optimal information content contains a vanishing fraction of the total emitted photons in the large-$N$ limit, suggesting an effective compressing of information. Our results and setup represent a new way to perform cavity based readout of solid-state spin ensembles that allows one to utilize resonant spin-photon interactions.

Comments
27 pages, 5 figures

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It is well known that superradiant decay of an ensemble of NNN spins generates a complex non-classical state of light. Here, we consider the information content of a superradiant burst of photons: how is information encoded in the initial spin state distributed among the emitted photons, and can it be extracted using simple measurements? Despite the complexity of the photonic burst state, we show that a simple homodyne measurement combined with an optimized filter and linear estimator recovers the NNN-scaling of the quantum Fisher information of the initial spin state (including cases exhibiting N2N^2N2 Heisenberg scaling). Even more surprising, the temporal mode with optimal information content contains a vanishing fraction of the total emitted photons in the large-NNN limit, suggesting an effective compressing of information. Our results and setup represent a new way to perform cavity based readout of solid-state spin ensembles that allows one to utilize resonant spin-photon interactions.
Photonic states with large and fixed photon numbers, such as Fock states, enable quantum-enhanced metrology but remain an experimentally elusive resource. A potentially simple, deterministic, and scalable way to generate these states consists of fully exciting NNN quantum emitters equally coupled to a common photonic reservoir, which leads to a collective decay known as Dicke superradiance. The emitted NNN-photon state turns out to be a highly entangled multimode state, and to characterize its metrological properties in this work we (i) develop theoretical tools to compute the quantum Fisher information of general multimode photonic states, (ii) use it to show that Dicke superradiant photons in one-dimensional waveguides achieve Heisenberg scaling, which can be saturated by a parity measurement, and (iii) study the robustness of these states to experimental limitations in state-of-the-art atom-waveguide QED setups.
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In this work, we consider a quantum memory formed by an ensemble of 3-level atoms to study the emission of light in a Fock state for one and two excitations, exhibiting the superradiant character in these processes. In this setup, a writing laser beam may induce quantum transitions between pairs of levels, leaving either one or two of these atoms excited in an appropriate coherently distributed state across the cloud, thus storing quantum information. After that, a reading laser beam extracts this information in the form of one or two photons, respectively, in a superradiant emission at a specific mode of the electromagnetic field that depends on the details of the stored state. Then, we can certify the quantum nature of light, making sure that a semi-classical approach is inadequate to describe this phenomenon. The central point is the development of an analytical theory for the interaction between atoms and light in this context. We find the beam’s spatio-temporal profile, showing that the modes in which the generated read and write photons are counterpropagating. Following the theory, the two-photon wavepacket is consistent with the profile obtained for two independent photons, each identical to the one achieved for a single superradiant emission. These conclusions match with experimental studies of quantum information storage by a cloud of cold atoms realized by the quantum optics group at UFPE, where we notice a good agreement between theory and experiment. These studies allowed the first characterizations of the superradiant emission of two photons by an atomic ensemble.
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.
We study the superradiant emission of an inverted spin ensemble strongly coupled to a superconducting cavity. After fast inversion, we detune the spins from the cavity and store the inversion for tens of milliseconds, during which the remaining transverse spin components disappear. Switching back on resonance enables us to study the onset of superradiance. A weak trigger pulse of a few hundred photons shifts the superradiant burst to earlier times and imprints its phase onto the emitted radiation. For long hold times, the inversion decreases below the threshold for spontaneous superradiance. There, the energy stored in the ensemble can be used to amplify microwave pulses passing through the cavity.
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.