Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.
Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.
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.
Waveguide quantum electrodynamics (WQED) offers a powerful framework for controlling light-matter interactions and realizing collective phenomena such as super- and subradiance. In general waveguide settings, the quantum dynamics spans the full Hilbert space, rendering exact theoretical treatments exponentially difficult and currently out of reach, and only a few models have exact, analytical solutions. Motivated by recent experiments, we treat the thermodynamic limit of the number of atoms,
N→∞, while the homogeneous atom-waveguide coupling
β→0 keeping the optical depth
4Nβ fixed. In this limit, a second order mean field method is exact, giving analytical solutions for the statistics of the photons emitted in the waveguide both for chiral and symmetric configurations starting from full inversion. As
N→∞, the emission in freespace approaches that of an independent ensemble. However, until a special time,
≈1.59× the lifetime of a single-atom, we show an exponentially enhanced superradiance in the waveguide as the optical depth increases. After the special time, the emission into the waveguide exhibits subradiance. We also show that the initial shot-to-shot fluctuations in the rate of emission into the waveguide diminish in a chiral system and vanish in a symmetric system as
N approaches
∞. Additionally, the equal-time second-order correlation becomes trivial, showing that finite-size effects are essential to observe the emergence of second-order coherence. Finally, going beyond the thermodynamic limit requires higher order mean field methods. Our results illustrate finite- and infinite-body collective effects in symmetric and symmetry-lacking systems.
In the study of optical properties of large atomic systems, a weak laser driving is often assumed to simplify the system dynamics by linearly coupled equations. Here we investigate the light-scattering properties of atomic ensembles beyond weak-field excitation through the cumulant expansion method. By progressively incorporating higher-order correlations into the steady-state equations, an enhanced accuracy can be achieved in comparison to the exact solutions obtained by solving a full density matrix. Our analysis reveals that, in the regime of weak dipole-dipole interaction, the first-order expansion yields satisfactory predictions for optical depth, while denser atomic configurations necessitate consideration of higher-order correlations. As the intensity of incident light increases, atom saturation effects become noticeable, giving rise to significant changes in light transparency, energy shift, and decay rate. This saturation phenomenon extends to subradiant atom arrays even under weak driving conditions, leading to substantial deviations from the linear model. Our findings demonstrate that the mean-field model is a good extension to linear models as it balances both accuracy and computational complexity. However, the crucial role of higher-order cumulants in large and dense atom systems remains unclear, since it is challenging theoretically owing to the exponentially increasing Hilbert space in such light-matter interacting systems.
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.
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.