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.
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.
In recent years, chiral quantum optics has emerged as an active research area due to the promising applications in quantum information processing as well as nonlinear optics. We present results on the properties of the incoherent component of the transmitted light after transmons chirally coupled to a waveguide. The well-known resonance fluorescence of one chiral transmon resembles nonlinear quantum optics as it can convert the coherent light, with photons having spatially extensive coherence and Poisson distribution, into a field with spatially localized coherence and bunching photon statistics. However, another chiral transmon can undo the effect of the first transmon regardless of the Rabi frequency under the idealization involved in this work. A full wavefunction calculation shows that, in the weak driving limit, this incoherent light mainly comes from two-photon processes - one chiral transmon converts two independent photons into a photon pair with opposite momentum shift. In addition to the driving through the waveguide, a local driving with independently tunable amplitude and phase can address each transmon individually. The interplay between the waveguide driving and local driving modulates the contribution of the incoherent transmission and hence enables the engineering of the quantum statistics of the transmitted field, with tunable g(2)(0) spanning anti-bunched, coherent, and strongly bunched regimes.
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.
Abstract We theoretically investigate the influences of two coherent driving fields on the asymmetric transmission of single photon in the atom-waveguide system. The atom is considered as a Λ system. One transition of the atom chirally couples to the waveguide. The other transition is driven by two coherent driving fields. The transmission probabilities for the single photon incidents from the left ( T lr ) and right ( T rl ) are given respectively. The calculated results show that one can realize T lr = 0 ( T rl ≠ 0) or T rl = 0 ( T lr ≠ 0) by manipulating the phase difference between the two coherent driving fields. The influence of the decay rate of the metastable state on the asymmetric transmission is also discussed.
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 N2, 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 investigate a possibility to generate nonclassical states in light-matter coupled noisy quantum systems, namely, the anisotropic Rabi and Dicke models. In these hybrid quantum systems, a competing influence of coherent internal dynamics and environment-induced dissipation drives the system into nonequilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model, the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state displays light-matter entanglement, we also find that the full state is entangled. Furthermore, as a natural extension of the anisotropic Rabi model to an infinite spin subsystem, we next explored the NESS of the anisotropic Dicke model. The NESS of this linearized Dicke model is also an inseparable state of light and matter. With an aim to enrich the dynamics beyond the sustainable entanglement found for the NESS of these hybrid quantum systems, we also propose to combine an all-optical feedback strategy for quantum state protection and for establishing quantum control in these systems. Our present work further elucidates the relevance of such hybrid open quantum systems for potential applications in quantum architectures.
Waveguide Quantum Electrodynamics (WQED) offers a suitable stage for controlling the interaction of light with atoms, allowing for collective phenomena such as super- and subradiance. In a chiral waveguide setup, the quantum state evolves through all the Hilbert space, rendering an exact theoretical treatment exponentially hard and unobtained to date for more than ∼20 atoms. In this work, we use a computationally efficient higher order mean-field approximation to model the radiation dynamics in a chirally coupled array of atoms, showing good agreement with recent experimental results. Further, based on a perturbative approximation of the full dynamics, we develop an analytical solution that captures photon statistics for a moderate atom number, N, and a homogeneous atom-waveguide coupling, β. Finally, we show that capturing the onset of second-order coherence from a fully inverted state requires a fourth-order mean-field approximation, as lower-order treatments fail to account for the necessary four-body correlations. These results illustrate the complex behavior of a symmetry-lacking system, and the methods discussed here provide systematic analytical solutions to which semi-classical methods such as the cumulant expansion or the truncated Wigner approximation can be benchmarked.