We present an analytical approach for the study of driven Dicke superradiance based on a Heisenberg-Langevin formulation. We calculate the steady-state fluctuations of both the atomic-spin and light-field operators. While the atoms become entangled below a critical drive, exhibiting spin squeezing, we show that the radiated light is in a classical-like coherent state whose amplitude and spectrum are identical to those of the incident driving field. Therefore, the nonlinear atomic system scatters light as a linear classical scatterer. Our results are consistent with the recent theory of coherently radiating spin states. The presented Heisenberg-Langevin approach should be simple to generalize for treating superradiance beyond the permutation-symmetric Dicke model.
We present an analytical approach for the study of driven Dicke superradiance based on a Heisenberg-Langevin formulation. We calculate the steady-state fluctuations of both the atomic-spin and light-field operators. While the atoms become entangled below a critical drive, exhibiting spin squeezing, we show that the radiated light is in a classical-like coherent state whose amplitude and spectrum are identical to those of the incident driving field. Therefore, the nonlinear atomic system scatters light as a linear classical scatterer. Our results are consistent with the recent theory of coherently radiating spin states. The presented Heisenberg-Langevin approach should be simple to generalize for treating superradiance beyond the permutation-symmetric Dicke model.
We discuss the possibility of generating spin squeezed states by means of driven superradiance, analytically affirming and broadening the finding in [Phys. Rev. Lett. 110, 080502 (2013)]. In an earlier paper [Phys. Rev. Lett. 112, 140402 (2014)] the authors determined that spontaneous purely-dissipative Dicke model superradiance failed to generate any entanglement over the course of the system's time evolution. In this article we show that by adding a driving field, however, the Dicke model system can be tuned to evolve toward an entangled steady state. We discuss how to optimize the driving frequency to maximize the entanglement. We show that the resulting entanglement is fairly strong, in that it leads to spin squeezing.
Entanglement constitutes a main feature that distinguishes quantum from classical physics. Here, however, we show that entanglement may also serve as the essential ingredient for the emergence of classical behavior in a radiating spin system. We consider the relation between the state of a macroscopic spin, such as an atomic ensemble, and the radiation it emits. We introduce a new class of macroscopic spin states, the coherently radiating spin states (CRSSs), defined as the asymptotic eigenstates of the SU(2) lowering operator. We find that a spin emitter in a CRSS radiates classical coherent light, although the CRSS itself is a quantum entangled state exhibiting spin squeezing. We further show that the CRSS is naturally realized in Dicke superradiance and underlies the dissipative Dicke phase transition, hence predicting the optimal scaling of spin squeezing in superradiance. More generally, the CRSS emerges as the ground state of a collective spin Hamiltonian. The CRSS thus provides a promising concept for studying many-body spin systems in various platforms, with applications ranging from quantum metrology and lasing to phase transitions. Published by the American Physical Society 2024
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.
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.
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
We analyze the properties across steady-state phase transitions of two all-to-all driven-dissipative spin models that describe possible dynamics of N two-level systems inside an optical cavity: squeezed superradiance and driven superradiance. We show that the finite size behavior around the critical points can be captured correctly by carefully identifying the relevant nonlinearities in the Holstein-Primakoff representation of spin operators in terms of bosonic variables. With these tools, we calculate analytically various observables across the phase transitions and obtain their finite size scalings, including numerical prefactors. In particular, we look at the amount of spin squeezing carried by the steady states, of relevance for quantum metrology applications, and describe in analytical detail the mechanism by which the optimal spin squeezing acquires logarithmic corrections that depend on the system size. We also demonstrate that the logarithmic nature of these corrections is difficult to characterize through numerical procedures for any experimentally realistic and/or simulable values of particle number. We complement all of our analytical arguments with numerical benchmarks.