We theoretically study the few-and many-body dynamics of photons in chiral waveguides.In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide.We show that the system supports correlated multiphoton bound states, which have a welldefined photon number n and propagate through the system with a group delay scaling as 1=n 2 .This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system.For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency.Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition.Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons.Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters.Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.
The emergence of multi-photon bound states in quantum nonlinear media is an intriguing phenomenon that has attracted significant theoretical and experimental interest. Such bound states can emerge in quite different settings, such as arrays of quantum emitters coupled to photonic waveguides and Rydberg nonlinear media. The theoretical tools to characterize the bound states are equally diverse, ranging from Bethe ansatz to effective field theories. Here, we propose and utilize a spin-model formulation of quantum atom-light interactions as a general, unified framework to study bound states, and apply this formalism to several distinct systems. We show how to obtain the bound-state dispersion relation within the two-excitation subspace, and also numerically investigate how the properties of higher multi-photon bound states manifest themselves in the propagation of large photon number pulses and spatio-temporal correlations at the output. Interestingly, for all the specific systems studied (chiral and bi-directional waveguides, and Rydberg media), we find that the large-photon number limit always coincides with the well-known semi-classical soliton phenomenon of self-induced transparency or immediate generalizations thereof.
Solitons are known to occur in the context of atom-light interaction via the well-known semiclassical phenomenon of self-induced transparency (SIT). Separately, in the regime where both light and atoms are fully treated quantum mechanically, quantum few-photon bound states are known to be a ubiquitous phenomenon that arises in different systems such as atoms coupled to chiral or bidirectional waveguides, and in Rydberg atomic media. In the specific case of two-level atoms coupled to a chiral waveguide, a recent analysis based on Bethe ansatz has established that SIT emerges from the quantum realm as a superposition of quantum many-photon bound states. Beyond this case, however, the nature of any connection between the full quantum many-body regime and semiclassical behavior has not been established. Here, we employ a general spin-model formulation of quantum atom-light interfaces to numerically investigate this problem, taking advantage of the fact that this approach readily allows for powerful many-body simulations based on matrix product states (MPS). We first analytically derive the two-photon bound state dispersion relation for a variety of atom-light interfaces and then proceed to numerically investigate the multiexcitation bound states dynamics. Interestingly, for all the specific systems studied, we find that the large-photon number limit always coincides with the soliton phenomenon of self-induced transparency or immediate generalizations thereof.
We present a quantum dynamical study of pulsed few-photon scattering from a single artificial atom, consisting of a two-level system (TLS) or qubit, in a waveguide QED system, directly comparing and contrasting two different quantum theoretical simulation methods: (i) an input-output scattering approach that uses frequency-dependent scattering matrices, and (ii) a matrix product states (MPS) approach, which uses quantum noise operators in time bins and a tensor network technique to solve the time-dependent waveguide function for the entire system. Beginning with pulsed excitation using one-photon and two-photon Fock state pulses, we first show how to compute time-dependent observables with the scattering matrix approach, in terms of frequency integrals that encode the pulse spectrum, including how to extract the population dynamics of the excited quantum emitter, as well as the linear and nonlinear contributions. We present solutions for both symmetric and chiral TLS coupling. We then show how to compute the qubit and field observables in a more direct way using MPS, and obtain the characteristic bird-like shape for the two-photon correlation function at two times, which has been observed in recent experiments. We compare and contrast both of these methods, for one and two-photon excitation pulses, and show excellent agreement. We also present a study of the linear and nonlinear contributions, which can easily be calculated using scattering theory, and show the important role of pulse duration. Finally, we demonstrate the clear advantages of MPS by easily going to higher N-photon excitations, and show selected example population dynamics of up to eight-photon Fock-state pulses, manifesting in clear nonlinear population oscillations during the pulse interaction, similar to classical Rabi oscillations, but with quantum input fields that have a vanishing electric field expectation value.
The study of waveguide-QED systems, where a continuum of quantum field modes is coupled to qubits or two-level systems, has improved our ability to manipulate quantum light-matter interactions on chip. In the typical theoretical approaches to waveguide QED, there are a few necessary approximations, e.g., considering the system in the weak excitation regime, or treating the waveguide as a bath. However, these inherent approximations can break down with short pulse excitation. Here, we investigate the few-photon quantum nonlinear response of chiral qubits, when excited with one and two-photon Fock states. Our theory uses a numerically exact approach, based on Matrix Product States, avoiding the limitations of the usual waveguide-QED approximations. Using a chiral-emitter waveguide system, we show explicitly the breakdown of the weak excitation approximation, and study the single and two-photon nonlinear responses. We demonstrate the impact on the qubit population, and discuss how the phase change can be examined from the photon quantum correlation functions, seeing a radical departure from scattering theory solutions.
We study the problem of two-photon routing in waveguide QED ladders where a few two-level quantum emitters (QEs) are simultaneously coupled with two chiral waveguides. We analyze the routing probability in two regimes, namely, under a purely plane wave approximation (scattering case) and in the presence of photon-photon bound state formation. Within the scattering case, we examine the two-photon routing in the presence of up to five QEs, considering two possibilities separately: ideal-symmetric coupling and the critical coupling scenario. We examine the photon routing up to the two QEs for the bound state situation and compare the photon redirection efficiency with the corresponding scattering case. Our findings show the potential of utilizing chiral light-matter interactions in multi-photon and multi-emitter-based quantum networking protocols where interlinking among spatially distant nodes is required.