In this work we develop a semianalytical variational Ansatz to study the properties of few-photon excitations interacting with a collection of quantum emitters in regimes that go beyond the rotating-wave approximation. This method can be used to approximate both the static and dynamical properties of a superconducting qubit in an open transmission line, including the spontaneous emission spectrum and the resonances in scattering experiments. The approximations are quantitatively accurate for rather strong couplings, as shown by a direct comparison to matrix-product-state numerical methods, and provide also a good qualitative description for stronger couplings well beyond the Markovian regime.
In this work we develop a semianalytical variational Ansatz to study the properties of few-photon excitations interacting with a collection of quantum emitters in regimes that go beyond the rotating-wave approximation. This method can be used to approximate both the static and dynamical properties of a superconducting qubit in an open transmission line, including the spontaneous emission spectrum and the resonances in scattering experiments. The approximations are quantitatively accurate for rather strong couplings, as shown by a direct comparison to matrix-product-state numerical methods, and provide also a good qualitative description for stronger couplings well beyond the Markovian 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.
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.
The time and space resolved dynamics of a qubit with an Ohmic coupling to propagating 1D photons is studied, from weak coupling to the ultrastrong coupling regime. A nonperturbative study based on matrix product states shows the following results, (i) The ground state of the combined systems contains excitations of both the qubit and the surrounding bosonic field. (ii) An initially excited qubit equilibrates through spontaneous emission to a state, which under certain conditions is locally close to that ground state, both in the qubit and the field. (iii) The resonances of the combined qubit-photon system match those of the spontaneous emission process and also the predictions of the adiabatic renormalization [A. J. Leggett et al., Rev. Mod. Phys. 59, 1 (1987)]. Finally, nonperturbative ab initio calculations show that this physics can be studied using a flux qubit galvanically coupled to a superconducting transmission line.
We discuss both the spectrum and the dynamics of cavity QED in the presence of dissipation beyond the standard perturbative treatment of losses. Using the dynamical polaron ansatz and matrix-product state simulations, we discuss the case where both light-matter g coupling and system-bath interaction are in the ultra-strong-coupling regime. We provide a critical g for the onset of Rabi oscillations. Besides, we demonstrate that the qubit is dressed by the cavity and dissipation. Such a dressing governs the dynamics and, thus, it can be measured. Finally, we sketch an implementation for our theoretical ideas within circuit QED technology.
Quantum optics with giant emitters has shown a new route for the observation and manipulation of non-Markovian properties in waveguide QED. In this paper we extend the theory of giant atoms, hitherto restricted to the perturbative light-matter regime, to deal with the ultrastrong-coupling regime. Using static and dynamical polaron methods, we address the low-energy subspace of a giant atom coupled to an Ohmic waveguide beyond the standard rotating-wave approximation. We analyze the equilibrium properties of the system by computing the atomic frequency renormalization as a function of the coupling characterizing the localization-delocalization quantum phase transition for a giant atom. We show that virtual photons dressing the ground state are nonexponentially localized around the contact points but decay as a power law. The dynamics of an initially excited giant atom is studied, pointing out the effects of ultrastrong coupling on the Lamb shift and the spontaneous emission decay rate. Finally, we comment on the existence of the so-called oscillating bound states beyond the rotating-wave approximation.
Single-photon scattering in waveguide-QED systems plays a pivotal role in quantum information processing and communication. We introduce a time-dependent variational approach employing a modified multiple Davydov Ansatz to simulate single-photon dynamics in one-dimensional waveguide-QED systems within the strong-coupling regime. The method is benchmarked across three configurations: a single qubit, two distant qubits, and a ladder-type qutrit coupled to the waveguide. For the single- and two-qubit cases, the variational results exhibit excellent agreement with those derived from a transformed rotating-wave approximation (TRWA). The accuracy of our approach is further verified by an analysis of the local-in-time error, which remains small even under strong coupling, indicating its potential superiority over TRWA in specific regimes. In addition, by contrasting our results with the rotating-wave approximation, we elucidate the significant influence of counter-rotating couplings on scattering dynamics. Our findings establish this variational method as a reliable and versatile tool for investigating single-photon scattering in diverse waveguide-QED systems, particularly in regimes where traditional approximations falter.