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arXiv:2610.38690

Quantum Observables of Nonperturbative Superradiant Scattering

Asimina Arvanitaki, Savas Dimopoulos, Marios Galanis, Derek J. Li

hep-phhep-thquant-phSubmitted Oct 28, 2026• Announced Oct 30, 2026
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Abstract

Inelastic scattering from $N$ coherent spins, or any two-state system, scales as $N^2$, invalidating the Born approximation at large $N$ even at weak coupling. We develop a nonperturbative theory of this superradiant scattering and its backreaction on the spins. Since one particle can exchange many quanta, the target's energy-transfer and energy-variance rates keep their favorable $N^2$ scaling even after the cross section saturates, unless a conservation law limits each encounter to exchange of one quantum. We apply the theory to millicharged-particle searches, as well as neutron and charged-particle beams that can test quantum protocols for detecting cosmic relics.

AI Summary

Coherent inelastic scattering from $N$ identically prepared two-level systems has a Born rate proportional to $N^2$. This paper asks how scattering and target observables behave once the collective coupling invalidates the Born approximation. It treats the ensemble as a precessing classical dipole, computes nonperturbative scattering using time-dependent eikonal and Floquet methods, and retains Holstein–Primakoff fluctuations to calculate target backreaction. For projectile-spin-independent interactions, the energy-transfer channels have Bessel-function weights and permit multiquantum exchange. Although the total contact-scattering cross section saturates at $2\pi R^2$, the leading energy-variance growth retains its quadratic Born form through $\sum_n n^2\sigma_n=\tfrac12\int d^2b\,\bar\chi^2$. Mean energy transfer vanishes at leading eikonal order; its first nonzero, next-order contribution also remains quadratic in the potential. By contrast, spin exchange with a spin-$1/2$ projectile permits only one quantum per encounter: both response rates saturate, with the contact spin-flip cross section approaching $\pi R^2/2$. Applications include polarized thermal neutrons, charged-particle beams, and projected terrestrial millicharged-particle searches. The latter example maintains coherence up to approximately $15$ GeV for the specified target parameters; its variance-sensitivity projection assumes approximately $48$ dB squeezing. The treatment requires weak deflection, $|V|\ll E_{\rm kin}$, short projectile wavelength relative to interaction scales, populated channels satisfying $|n|\omega_0\ll E_{\rm kin}$, and weak target backreaction. Beam projections neglect absorption or capture, stopping, ionization, heating, and induced spin relaxation; experimental sensitivity additionally depends on readout noise and measurement statistics.

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Inelastic scattering from NNN coherent spins, or any two-state system, scales as N2N^2N2, invalidating the Born approximation at large NNN even at weak coupling. We develop a nonperturbative theory of this superradiant scattering and its backreaction on the spins. Since one particle can exchange many quanta, the target's energy-transfer and energy-variance rates keep their favorable N2N^2N2 scaling even after the cross section saturates, unless a conservation law limits each encounter to exchange of one quantum. We apply the theory to millicharged-particle searches, as well as neutron and charged-particle beams that can test quantum protocols for detecting cosmic relics.
Coherent inelastic scattering from NNN identically prepared two-level systems has a Born rate proportional to N2N^2N2. This paper asks how scattering and target observables behave once the collective coupling invalidates the Born approximation.
It treats the ensemble as a precessing classical dipole, computes nonperturbative scattering using time-dependent eikonal and Floquet methods, and retains Holstein–Primakoff fluctuations to calculate target backreaction. For projectile-spin-independent interactions, the energy-transfer channels have Bessel-function weights and permit multiquantum exchange. Although the total contact-scattering cross section saturates at 2πR22\pi R^22πR2, the leading energy-variance growth retains its quadratic Born form through ∑nn2σn=12∫d2b χˉ2\sum_n n^2\sigma_n=\tfrac12\int d^2b\,\bar\chi^2∑n​n2σn​=21​∫d2bχˉ​2. Mean energy transfer vanishes at leading eikonal order; its first nonzero, next-order contribution also remains quadratic in the potential. By contrast, spin exchange with a spin-1/21/21/2 projectile permits only one quantum per encounter: both response rates saturate, with the contact spin-flip cross section approaching πR2/2\pi R^2/2πR2/2.
Applications include polarized thermal neutrons, charged-particle beams, and projected terrestrial millicharged-particle searches. The latter example maintains coherence up to approximately 151515 GeV for the specified target parameters; its variance-sensitivity projection assumes approximately 484848 dB squeezing.
The treatment requires weak deflection, ∣V∣≪Ekin|V|\ll E_{\rm kin}∣V∣≪Ekin​, short projectile wavelength relative to interaction scales, populated channels satisfying ∣n∣ω0≪Ekin|n|\omega_0\ll E_{\rm kin}∣n∣ω0​≪Ekin​, and weak target backreaction. Beam projections neglect absorption or capture, stopping, ionization, heating, and induced spin relaxation; experimental sensitivity additionally depends on readout noise and measurement statistics.
I present a derivation of the many qualitative changes to basic scattering theory that result when a (partially) coherent matter beam inelastically interacts with a quantum target. The weak beam limit, where only one object in the beam interacts with the quantum target, is developed. Some of the basic changes to scattering theory are as follows. (1) The transition probability can increase as the square of the number of particles in the beam. (2) The transition probability is not proportional to the convolution of the total inelastic cross section with the momentum distribution of the beam. (3) The transition probability to different final states of the target does not depend on the population in the initial states but depends on the amplitudes for the initial states. (4) The total transition probability depends on the differential cross section integrated over all final angles and on the differential cross section only in the forward scattering direction. (5) The transition probability can be nonzero even when the beam misses the target. (6) In the perturbative limit, the transition probability can be related to classical, large scale properties of the beam (such as the average density).
We recently showed that macroscopic nuclear spin ensembles prepared in coherent spin states can dramatically enhance the interaction rates of weakly interacting cosmic relics-such as dark matter and the cosmic neutrino background-through collective quantum effects analogous to Dicke superradiance, where the de-excitation and excitation rates scale as the square of the number of spins, N2N^2N2. We thus coined these processes superradiant interactions. In this paper, we propose a protocol to realize this enhancement and boost the discovery potential for such relics. We show how concepts from quantum optics can be adapted to nuclear spins coupled to superconducting circuits, enabling high-sensitivity systems. The spins are first initialized into a coherent spin state via a π/2π/2π/2 Rabi pulse from the ground state. When the circuit is sufficiently detuned from resonance, the spin-circuit interaction implements a squeezing Hamiltonian. Because squeezing must outpace spin relaxation and dephasing, the protocol favors macroscopic ensembles and high-quality superconducting circuits. During this squeezing phase, the standard quantum variance is reduced by up to 4.8 orders of magnitude-equivalent to 48 dB of squeezing-for circuits with quality factors Q∼108Q \sim 10^8Q∼108-10910^9109. The signal imprinted on the spins during the squeezing protocol can be magnified by further utilizing the squeezing interactions, easing the requirement for shot-noise-limited readout. This protocol has the potential to significantly accelerate axion and dark photon dark matter searches and extend the reach of existing axion experiments to probe QCD axion-nuclear spin couplings. More broadly, it paves the way for detecting coherent inelastic interactions from other cosmic relics-most notably the cosmic neutrino background-and establishes nuclear-spin-based systems as a new class of quantum, ultra-low-threshold detectors.
Recently, a superradiant phase transition first predicted theoretically in the quantum Rabi model (QRM) has been verified experimentally. This further stimulates the interest in the study of the process of phase transition and the nature of the superradiant phase since the fundamental role of the QRM in describing the interaction of light and matter, and more importantly, the QRM contains rich physics deserving further exploration despite its simplicity. Here we propose a scheme consisting of two successive diagonalizations to accurately obtain the ground-state and excited states wavefunctions of the QRM in full parameter regime ranging from weak to deep-strong couplings. Thus, one is able to see how the phase transition occurs and how the photons populate in Fock space of the superradiant phase. We characterize the photon populations by borrowing the distribution concept in random matrix theory and find that the photon population follows a Poissonian-like distribution once the phase transition takes place and further exhibits the statistics of Gaussian unitary ensemble with increasing coupling strength. More interestingly, the photons in the excited states behave even like the statistics of Gaussian orthogonal ensemble. Our results not only deepen understanding on the superradiant phase transition but also provide an insight on the nature of the superradiant phase of the QRM and related models.
We discuss the theory of the nonzero temperature (T)(T)(T) spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with a gap $\ensuremath{\Delta}$. For $T\ensuremath{\ll}\ensuremath{\Delta}$, we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particle S\mathcal{S}S matrix which is shown to have a superuniversal form at low momenta. This is established by computations on the O(3)O(3)O(3) $\ensuremath{\sigma}$ model, and strong- and weak-coupling expansions (the latter using a Majorana fermion representation) for the two-leg S=1/2S=1/2S=1/2 Heisenberg antiferromagnetic ladder. As an aside, we note that the strong-coupling calculation reveals an S=1S=1S=1, two-particle bound state which leads to the presence of a second peak in the T=0T=0T=0 inelastic neutron-scattering (INS) cross section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasiparticle peak in the INS cross section, the spin diffusivity, and for the field dependence of the NMR relaxation rate 1/T1{1/T}_{1}1/T1​ of the effective semiclassical model; these are expected to be asymptotically exact for the quantum antiferromagnets in the limit $T\ensuremath{\ll}\ensuremath{\Delta}$. The results for 1/T1{1/T}_{1}1/T1​ are compared with the experimental findings of Takigawa et al. [Phys. Rev. Lett. 76, 2173 (1996)] and the agreement is quite good. In the regime $\ensuremath{\Delta}<T<$(a typical microscopic exchange) and we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.