We study the impact of destructive interference on the collective dynamics of two distant three-level V-type systems coupled to a waveguide in a strong-coupling regime in which the rotating-wave approximation (RWA) and Markovian approximation are inapplicable. By employing a polaronlike unitary transformation, we derive a transformed RWA Hamiltonian and combine it with the resolvent operator to study the non-Markovian dynamics and derive the condition under which the bound states exist due to the destructive interference, which can be realized by tuning the distance between the two V systems. We use a time-dependent variational approach with the multiple Davydov ansatz to numerically validate the analytical predictions and reveal the dynamical signature of bound states. We illustrate that the populations of symmetric and antisymmetric single-excitation states can be trapped in the long-time limit due to the bound states or possess a long lifetime due to subradiance. Moreover, the excitation probability can exhibit long-lived oscillation due to the coexistence of a bound state and a subradiant state. Our results offer insights into the destructive interference in distant multilevel emitters in a strong-coupling regime.
We study the impact of destructive interference on the collective dynamics of two distant three-level V-type systems coupled to a waveguide in a strong-coupling regime in which the rotating-wave approximation (RWA) and Markovian approximation are inapplicable. By employing a polaronlike unitary transformation, we derive a transformed RWA Hamiltonian and combine it with the resolvent operator to study the non-Markovian dynamics and derive the condition under which the bound states exist due to the destructive interference, which can be realized by tuning the distance between the two V systems. We use a time-dependent variational approach with the multiple Davydov ansatz to numerically validate the analytical predictions and reveal the dynamical signature of bound states. We illustrate that the populations of symmetric and antisymmetric single-excitation states can be trapped in the long-time limit due to the bound states or possess a long lifetime due to subradiance. Moreover, the excitation probability can exhibit long-lived oscillation due to the coexistence of a bound state and a subradiant state. Our results offer insights into the destructive interference in distant multilevel emitters in a strong-coupling regime.
Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation (RWA). Employing static and dynamical polaron ansatze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground state magnetization, and entanglement entropy of the two qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting new dynamical effects arising in ultrastrong waveguide-QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also on the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.
We analyze the dynamics of quantum beats in a system of two V-type three-level atoms coupled to a waveguide. We show that quantum beats can be collectively enhanced or suppressed, akin to Dicke super- and subradiance, depending on the interatomic separation and the initial correlations between the atoms. In particular, the interference properties of the collective beats are determined by the distance between the atoms modulo the beat wavelength. We study the collective atomic and field dynamics, illustrating a crossover from a Markovian to a non-Markovian regime as the atomic separation becomes sufficiently large to bring memory effects of the electromagnetic environment into consideration. In such a non-Markovian regime, collective quantum beats can be enhanced beyond the Markovian limit as a result of retardation effects. Our results demonstrate the rich interplay between multilevel and multiatom quantum interference effects arising in a system of distant quantum emitters.
Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ans\"atze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.
We employ a time-dependent variational approach with the multiple Davydov D2 ansatz and two approximate analytical methods to study the spontaneous emission of a V-type artificial atom in the strong-coupling regime, where the decay rate of the emitter becomes a considerable fraction of its transition frequencies, and focus on quantum-interference-induced effects. The variational approach is found to be accurate in certain strong-coupling regimes and is used as the benchmark to address the validity of the analytical methods: the rotating-wave approximation (RWA) and the transformed RWA (TRWA). It is found that the TRWA is fairly accurate in the strong-coupling regime where the RWA breaks down. By using the numerical and analytical methods, we illustrate that there are dark lines and line narrowing in the emission spectra in the strong-coupling regime and in a wide accessible range of the emitter parameters. We also illustrate how the emission spectrum is altered by the counter-rotating couplings. The present results offer insights into the experimental observation of the quantum-interference-induced effect in the strong-coupling regime and in the context of artificial atoms.
We study the emission spectrum of two distant qubits strongly coupled to a waveguide by using the numerical and analytical approaches, which are beyond the Markovian approximation and the rotating-wave approximation. The numerical approach combines the Dirac-Frenkel time-dependent variational principle with the multiple Davydov D1 ansatz. A transformed rotating-wave approximation (TRWA) treatment and a standard perturbation (SP) are used to analytically calculate the emission spectrum. It is found that the variational approach and the TRWA treatment yield accurate emission spectra of the two distant qubits in certain strong-coupling regimes while the SP breaks down. The emission spectrum is found to be asymmetric irrespective of the two-qubit distance and exhibits a single peak, double peaks, and multiple peaks depending on the two-qubit distance as well as the initial states. In sharp contrast with the single-qubit case, the excited-state populations of the two qubits can ultraslowly decay due to the subradiance even in the presence of a strong qubit-waveguide coupling, which in turn yields an ultranarrow emission line. Our results provide insights into the emission spectral features of the two distant qubits in the strong light-matter coupling regime.
Abstract We study the resonance and dynamics of a three-level V-type system strongly driven by a quasiperiodic bichromatic field by making use of a unitary-transformation (UT) method. The UT is used to construct a periodic effective Hamiltonian which incorporates the effects of counter-rotating couplings and takes a physically transparent form, and the Floquet theory is used to calculate transition probabilities. By comparing the UT results with those from the rotating-wave approximation (RWA) and generalized Floquet theory, we illustrate that the UT method captures not only accurate resonance structures but also dynamics of the driven V system in a strong-driving regime where the RWA breaks down. We show that there are two dynamical features, namely, peak-dip structures and beat behaviors, which are ascribed to a time-dependent coupling between the two upper levels due to the counter-rotating terms and cannot be described by a RWA Hamiltonian. Moreover, we show that the effective Hamiltonian can be used to calculate higher-order Bloch–Siegert shifts, which is another feature caused by the counter-rotating terms. Present work offers insights into the role of counter-rotating couplings in a bichromatically driven three-level system.