Spontaneous collective decay in driven atomic ensembles can generate coherence far from equilibrium, as illustrated by superradiant lasers where decay into a single-mode cavity synchronizes atomic phases into a macroscopic dipole and yields superradiant emission of light with an ultranarrow spectrum. Whether similar ordering persists in multimode reservoirs with propagation and competing collective decay channels remains an open question. We address this problem by analyzing atoms coupled to one-dimensional electromagnetic baths through two models. The first is a ring cavity supporting two bright collective decay channels, and the second is a bidirectional waveguide where, in addition to competition between channels, propagation induces coherent dipole-dipole interactions. For suitable incoherent pumping strengths, the dynamics enters a synchronization window in which collective decay overcomes disordering processes, leading to spontaneous steady-state phase ordering and superradiant emission. We extract the thresholds marking the onset of synchronization and show that the maximum intensity scales quadratically in both models. The resulting order is not described by a single macroscopic dipole: in the ring cavity spontaneous chirality emerges at the level of individual trajectories, while the waveguide develops a local chirality with different orders dominating opposite ends of the atomic array. The analysis of the emitted light spectrum reveals a linewidth that seems to narrow with increased system size in the ring cavity, while narrowing in the waveguide remains inconclusive within accessible numerics. These results clarify how competition and propagation shape emergent order in one-dimensional reservoirs and identify regimes where steady-state superradiance may arise beyond the Dicke limit.
Spontaneous collective decay in driven atomic ensembles can generate coherence far from equilibrium, as illustrated by superradiant lasers where decay into a single-mode cavity synchronizes atomic phases into a macroscopic dipole and yields superradiant emission of light with an ultranarrow spectrum. Whether similar ordering persists in multimode reservoirs with propagation and competing collective decay channels remains an open question. We address this problem by analyzing atoms coupled to one-dimensional electromagnetic baths through two models. The first is a ring cavity supporting two bright collective decay channels, and the second is a bidirectional waveguide where, in addition to competition between channels, propagation induces coherent dipole-dipole interactions. For suitable incoherent pumping strengths, the dynamics enters a synchronization window in which collective decay overcomes disordering processes, leading to spontaneous steady-state phase ordering and superradiant emission. We extract the thresholds marking the onset of synchronization and show that the maximum intensity scales quadratically in both models. The resulting order is not described by a single macroscopic dipole: in the ring cavity spontaneous chirality emerges at the level of individual trajectories, while the waveguide develops a local chirality with different orders dominating opposite ends of the atomic array. The analysis of the emitted light spectrum reveals a linewidth that seems to narrow with increased system size in the ring cavity, while narrowing in the waveguide remains inconclusive within accessible numerics. These results clarify how competition and propagation shape emergent order in one-dimensional reservoirs and identify regimes where steady-state superradiance may arise beyond the Dicke limit.
Recent advances in generating well controlled dense arrangements of individual atoms in free space have generated interest in understanding how the extended nature of these systems influences superradiance phenomena. Here, we provide an in-depth analysis on how space-dependent light shifts and decay rates induced by dipole-dipole interactions modify the steady-state properties of coherently driven arrays of quantum emitters. We characterize the steady-state phase diagram, with particular focus on the radiative properties in the steady state. Interestingly, we find that diverging from the well-established Dicke paradigm of equal all-to-all interactions significantly modifies the emission properties. In particular, the prominent quadratic scaling of the radiated light intensity with particle number in the steady state—a hallmark of steady-state Dicke superradiance—is entirely suppressed, resulting in only linear scaling with particle number. We show that this breakdown of steady-state superradiance occurs due to the emergence of additional dissipation channels that populate not only superradiant states but also subradiant ones. The additional contribution of subradiant dark states in the dynamics leads to a divergence in the time scales needed to achieve steady states. Building on this, we further show that measurements taken at finite times for extended atom ensembles reveal properties closely mirroring the idealized Dicke scenario. Published by the American Physical Society 2024
Dicke superradiance is an example of emergence of macroscopic quantum coherence via correlated dissipation. Starting from an initially incoherent state, a collection of excited atoms synchronizes as they decay, generating a macroscopic dipole moment and emitting a short and intense pulse of light. While well understood in cavities, superradiance remains an open problem in extended systems due to the exponential growth of complexity with atom number. Here we show that Dicke superradiance is a universal phenomenon in ordered arrays. We present a theoretical framework - which circumvents the exponential complexity of the problem - that allows us to predict the critical distance beyond which Dicke superradiance disappears. This critical distance is highly dependent on the dimensionality and atom number. Our predictions can be tested in state of the art experiments with arrays of neutral atoms, molecules, and solid-state emitters and pave the way towards understanding the role of many-body decay in quantum simulation, metrology, and lasing.
The driven Dicke model, with interesting quantum phases induced by parametrized driving, has been intensively studied in cavities, where permutation symmetry applies due to the atoms' equal coupling to the field and identical interaction. As a result, the system, with proper initialization, can remain in a highly symmetric subset of the state space, where the photon emission of each atom constructively interferes with the other, leading to superradiance at steady state. However, because of the degeneracy of steady states for the driven Dicke model, the steady state can be qualitatively altered by an infinitesimal perturbation. In this work, we simulate superconducting qubits coupled to a one-dimensional waveguide as the extended system and theoretically investigate four kinds of perturbations: local dephasing, individual driving phases, the separation between adjacent qubits, and individual detunings. Using an angular momentum basis, we predict the dimension of the degenerate subspace and study the transition within the subspace due to the perturbation.
The Dicke model describes the coherent interaction of a laser-driven ensemble of two-level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to, e.g., atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced collective decay of an excitation that is shared by N atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by nonthermal Markovian noise. The interplay between dissipative and coherent elements leads to a genuine nonequilibrium dynamics in the bistable regime, which is expressed via a nonconservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke model become exact in the large-N-limit. The absence of an effective free-energy functional, however, necessitates the inclusion of fluctuation corrections with O(1/N) for finite $N<\ensuremath{\infty}$ to locate the nonthermal first-order phase transition between the superradiant and the empty cavity.
Superradiance is an extensive cooperative spontaneous emission phenomenon, exhibited by some atomic collective-spin states. However, distinct initial states differ in their decay dynamics. Dicke states ∣j,m⟩ with distinct numbers of excitations n=m+j, driven by vacuum fluctuations, have their peak emission intensity shifted in time. Rotating Dicke states relative to the decay axis introduces an interesting parity structure that affects the pulse profile and photon correlations. Squeezed-bath prepared states undergo a squeezing-controlled crossover to the rotated Dicke states, making the emission character dependent on the amount of squeezing transferred from light to the atomic state. For semiclassical states with a macroscopic dipole moment, like the atomic coherent state, the emission intensity depends on their polarization. We present detailed results on the superradiant dynamics of a representative selection of states expanded in Dicke states to highlight the initial state as an independent dynamical control parameter. For large-N, we are able to predict fairly accurately the pulse profile in each case using the mean-field approximation, an approach based on the Fokker--Planck equation. We also present comparative results on the intensity correlation function, quantify the coherent and incoherent contributions of the emission, and contrast between small and large ensembles.
We experimentally investigate the collective radiative decay of a fully inverted ensemble of two-level atoms for a chiral, i.e., propagation direction-dependent light-matter coupling. Despite a fundamentally different interaction Hamiltonian which has a reduced symmetry compared to the standard Dicke case of superradiance, we do observe a superradiant burst of light. The burst occurs above a threshold number of atoms, and its peak power scales faster with the number of atoms than in the case of free-space Dicke superradiance. We measure the first-order coherence of the burst and experimentally distinguish two regimes, one dominated by the coherence induced during the excitation process and the other governed by vacuum fluctuations. Our results shed light on the collective radiative dynamics of cascaded quantum many-body systems, i.e., systems in which each quantum emitter is only driven by light radiated by emitters that are upstream in the cascade. Our findings may turn out useful for generating multiphoton Fock states as a resource for quantum technologies. Published by the American Physical Society 2024