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arXiv:2606.06621

Collective decay of interacting bosons

Bennet Windt, Lorenzo Rossi, Alexander V. Poshakinskiy, Daniel Malz, Dominik S. Wild

quant-phSubmitted Jun 4, 2026• Announced Jun 8, 2026• 0 citations
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Abstract

We study a bosonic analog of the paradigmatic Dicke model of superradiance, comprising interacting bosonic modes subject to fully symmetric collective decay. Depending on the interaction strength, we uncover qualitatively distinct regimes of emission. For strong interactions, the emission closely resembles Dicke superradiance, with perturbative corrections arising from the presence of additional levels. For weaker interactions, the bosonic statistics qualitatively changes the dynamics, leading to a crossover to subradiant emission. Remarkably, we show that the dynamics in this regime can be described by rate equations analogous to those of the Dicke model despite the large accessible bosonic Hilbert space. Our findings are based on a combination of analytical arguments and large-scale numerics enabled by the permutational symmetry of the problem and may be probed in circuit QED experiments.

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We study a bosonic analog of the paradigmatic Dicke model of superradiance, comprising interacting bosonic modes subject to fully symmetric collective decay. Depending on the interaction strength, we uncover qualitatively distinct regimes of emission. For strong interactions, the emission closely resembles Dicke superradiance, with perturbative corrections arising from the presence of additional levels. For weaker interactions, the bosonic statistics qualitatively changes the dynamics, leading to a crossover to subradiant emission. Remarkably, we show that the dynamics in this regime can be described by rate equations analogous to those of the Dicke model despite the large accessible bosonic Hilbert space. Our findings are based on a combination of analytical arguments and large-scale numerics enabled by the permutational symmetry of the problem and may be probed in circuit QED experiments.
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We study the dynamics of an ensemble of NNN two-level emitters undergoing collective decay at rate ΓΓΓ and collective incoherent pumping at rate RRR, confined to the fully symmetric Dicke ladder. Although the population dynamics are confined to a finite set of rate equations, their quantum-trajectory representation involves infinitely many pump-decay histories. We derive an exact finite continued fraction for the Laplace-transformed Dicke-state populations by resumming the infinitely many quantum trajectories generated by competing pump and decay processes. Our construction provides a physically transparent interpretation of the tridiagonal resolvent and extends to arbitrary permutationally symmetric initial states. In the strong- and weak-pumping regimes, we obtain perturbative transient solutions. We also identify exact relaxation eigenvalues and emission observables at balanced pump and decay strengths. Our solution provides a starting point for extending trajectory-based analytical methods to more general driven-dissipative collective systems.
Dicke superradiance describes an ensemble of N permutationally invariant two-level systems collectively emitting radiation with a peak radiated intensity scaling as N 2 . Individual Dicke states are typically entangled. However, the density matrix during superradiant decay is a mixture of such states, raising the subtle question of whether the total state is entangled or separable. We resolve this by showing analytically that for any N , starting from the fully excited state, the collective decay preserves separability for all times. This answers a longstanding question on the role of entanglement in Dicke superradiance and underscores that, despite collective dissipation, separable states remain separable under these dynamics.
Abstract The dynamics of the Dicke model, which describes the interaction of N two-level atoms with a resonant field mode, is studied in the presence of dissipation and in strong non-equilibrium for a moderate number of atoms. Starting from a highly excited state, it is investigated to what extent signatures of superradient phenomena known from the thermodynamic limit , namely, superradiant light emission and atom-field correlations characteristic for the superradiant phase, appear on transient time scales. Attention is also paid to subtleties of modeling dissipation in the weak coupling limit and to the dynamics in phase space. The latter allows phase space correlators to be defined as indicators for collective behavior on transient time scales. These findings may be of relevance for the realization of Dicke physics with superconducting circuits.
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.
We solve Dicke superradiance with two or more competing collective decay channels of tunable rates using a symbolic quantum-trajectory construction. The method yields closed time-domain populations and observables as finite combinations of exponential terms for arbitrary numbers of emitters and arbitrary decay rates. For two channels, the behavior of the stationary ground-state distribution resembles a first-order phase transition at the point where the channel-rate ratio is equal to unity. For balanced ddd-channel decay, we obtain scaling laws for the superradiant peak time and intensity. These results unify and extend single-channel Dicke dynamics to multilevel emitters and provide a compact tool for cavity and waveguide experiments, where permutation-symmetric reservoirs engineer multiple collective decay paths.