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.
Single-photon detection plays important roles in implementing desired quantum information processing. In this work, we propose a single itinerant photon detector based on absorption by two interacting atoms coupling to a waveguide, which can work in the microwave regime. Both the cases of giant and small atoms are considered. Each atom is modeled as a three-level system, with only one transition coupling to the waveguide. Our analysis reveals that, for a single atom coupled to the waveguide, the maximum detection probability is intrinsically limited to 0.5. This limit, however, can be lifted under perfectly chiral coupling, where unit detection probability becomes achievable. For the non-chiral case, we show that when a giant molecule consisting of two giant atoms with direct interaction couples to the waveguide, the single-photon detection probability can reach the ideal value of 1. Furthermore, we extend the model to the regime of small atoms and show that perfect single-photon detection remains attainable by appropriately tuning the direct coupling strength and the interatomic separation. These results provide a feasible route toward high-efficiency microwave single-photon detection based on engineered atom-waveguide interactions.
Abstract In modern quantum optics chiral waveguide quantum-electrodynamical (wQED) systems are attracting a lot of attention from the perspective of fundamental science, and possible interesting applications. In our work we theoretically analyze the eigenstates in a two-excitation domain of an ensemble of two-level atoms that are periodically spaced, and asymmetrically coupled to a guided mode. We found that in a regime when all atoms emit photons in-phase, most eigenstates in such a system can be well-approximated and described through the eigenstates from a single excitation domain, while the rest present a superposition of bound states with two strongly attracting excitations, and states, for which the excitations strongly repel from each other occupying the opposite edges of the system.
We study the nonreciprocal properties of transmitted photons in a chiral waveguide quantum electrodynamics (QED) system, including single- and two-photon transmissions and second-order correlations. For the single-photon transmission, the nonreciprocity is induced by the effects of chiral coupling and atomic dissipation in the weak coupling region. It vanishes in the strong coupling regime when the effect of atomic dissipation becomes ignorable. In the case of two-photon transmission, there exist two ways of going through the emitter: independently as plane waves and formation of bound state. Besides the nonreciprocal behavior of plane waves, the bound state that differs in two directions also alters transmission probabilities. In addition, the second-order correlation of transmitted photons depends on the interference between plane wave and bound state. The destructive interference leads to the strong antibunching in the weak coupling region, while the effective formation of bound state leads to the strong bunching in the intermediate coupling region. However, the negligible interactions for left-propagating photons hardly change the statistics of the input coherent state.
We present a time-dependent quantum calculations of the first order and second order photon correlation functions for the scattering of a single-photon pulse on a two-level atom (qubit) embedded in a one-dimensional open waveguide. Within Markov approximation we find the analytic expression for the quantum operator of positive frequency electric field. We restricted Hilbert space of initial states by the states with one and two excitations and show that the photon probability amplitudes are given by the off-diagonal matrix elements of the electric field operator between these states. For two-excitation initial state where the atom is excited and there exists a single photon in a waveguide we calculate the second order correlation function which describes the measurements by two detectors at two different space-time points. The second order correlation function exhibits the interference term showing that the measurements of two detectors are correlated. This interference is similar to that found in the Hanbury Brown and Twiss correlation experiment with two indistinguishable photons.