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Physical Review A

Qualitatively altered driven Dicke superradiance in extended systems due to infinitesimal perturbations

Wenqi Tong, F. Robicheaux

Published Dec 2, 2024• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.110.063701

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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.
This work discusses the effects of infinitesimal perturbations on the steady-state behavior of the driven Dicke model and the open Dicke model. This work discovers highly degenerate steady states of the unperturbed system and uses degenerate perturbation theory to investigate the effects of different perturbations. This method can be applied to different systems with high degeneracy in steady states and can be combined with other numerical methods with high computational efficiency to facilitate calculations for a large number of atoms. Besides, this work also reveals the nonlinear quantum optics mediated by transmons chirally coupled to a one-dimensional waveguide. Full-quantum calculations reveal that the incoherent light emerging from a single chiral transmon under monochromatic, coherent, resonant driving originates predominantly from two-photon processes. We also show that one chiral transmon transforms two independent photons into an entangled photon pair with opposite shifts in momentum. We introduce a local drive with independent tunability and manipulate the Rabi frequencies of the driving through the waveguide and the local drive. The interplay between these two drives allows a significant modulation of the photon statistics of the transmitted light.
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
Spontaneous collective decay in incoherently driven atomic ensembles can generate macroscopic coherence in the steady state, as exemplified by steady-state superradiance in single-mode cavities. Whether spontaneous order persists beyond the Dicke limit, where competing collective decay channels and light propagation might preclude an ordered phase, remains an open question. We address it by analyzing incoherently pumped atoms coupled to one-dimensional electromagnetic baths through two models: a ring cavity with two bright decay channels, and a bidirectional waveguide where propagation additionally induces Hamiltonian dipole-dipole interactions. We find that both systems sustain steady-state phase order with intensity scaling as N2N^2N2, but that the order takes two qualitatively distinct forms, neither described by a single macroscopic dipole. In the ring cavity, individual trajectories spontaneously break mirror symmetry, locking the atomic phases and the emitted field to one of two chiral orders. In the waveguide, coherent interactions instead enforce a phase-separated steady state in which the two chiral orders coexist, each dominating one end of the array. Our results show how competition and propagation shape emergent order beyond the Dicke limit.
We study the steady-state behavior of the open Dicke model, which describes the collective interaction of NNN spin-1/21/21/2 particles with a lossy, quantized cavity mode and exhibits a superradiant phase transition above a critical light-matter coupling. While the standard model conserves total spin, Kirton and Keeling \cite{PhysRevLett.118.123602} demonstrated that even infinitesimal homogeneous local dephasing destroys this phase transition, and that local atomic decay can restore it. We analyze this interplay using degenerate perturbation theory across subspaces of fixed total spin, SSS. For coupling strengths above the threshold, there exists a critical spin value ScS_cSc​ such that the superradiant phase transition occurs only for S>ScS>S_cS>Sc​. The perturbative approach captures how weak dephasing and decay induce mixing between different SSS-subspaces, yielding a steady-state spin distribution whose width scales as 1/N1/\sqrt{N}1/N​. This framework requires only the first and second moments and can be implemented via different methods that can yield these two moments (for example, the 2nd-cumulant approach), circumventing the need for full density matrix calculations. These results bridge the quantum Rabi model and Dicke physics, elucidate the roles of dephasing and decay in collective quantum effects, and apply broadly to open quantum systems with degenerate steady states.
We study the steady-state behavior of the open Dicke model, which describes the collective interaction of NNN spin-1/21/21/2 particles with a lossy, quantized cavity mode and exhibits a superradiant phase transition above a critical light-matter coupling. While the standard model conserves total spin, Kirton and Keeling [Phys. Rev. Lett. 118, 123602 (2017)] demonstrated that even infinitesimal homogeneous local dephasing destroys this phase transition and that local atomic decay can restore it. We analyze this interplay using degenerate perturbation theory across subspaces of fixed total spin, SSS. For coupling strengths above the threshold, there exists a critical spin value Sc{S}_{c}Sc​ such that the superradiant phase transition occurs only for S>ScS>{S}_{c}S>Sc​. The perturbative approach captures how weak dephasing and decay induce mixing between different SSS subspaces, yielding a steady-state spin distribution whose width scales as 1/N1/\sqrt{N}1/N​. This framework requires only the first and second moments and can be implemented via different methods that can yield these two moments (for example, the second-cumulant approach), circumventing the need for full density matrix calculations. These results bridge the quantum Rabi model and Dicke physics, elucidate the roles of dephasing and decay in collective quantum effects, and apply broadly to open quantum systems with degenerate steady states.
Abstract We consider the superradiant transition of a generalized Tavis–Cummings model, where a number of two-level qubits are coupled to a dissipative cavity. The cavity is coherently driven through a parametric medium, and all-to-all interactions between the qubits are introduced. While the nonlinear gain from the parametric drive breaks the U (1) symmetry of the standard Tavis–Cummings model, thus giving rise to superradiance with squeezed cavity fields, we show that the interactions impact the collective excitations and significantly modify the superradiant transition. Insights into the superradiant phase transitions, as well as the interaction effects, are obtained through effective models involving only a handful of low-lying collective states, under which the steady-state phase diagram of the hybrid system is faithfully reproduced. Our study is relevant to Rydberg-atom arrays coupled to a parametrically driven cavity, where the long-range interactions derive from the dipole–dipole interatomic interactions.