Sorting quantum fields into different modes according to their Fock-space quantum numbers is a highly desirable quantum operation. In this Letter, we show that a pair of two-level emitters, chirally coupled to a waveguide, may scatter single- and two-photon components of an input pulse into orthogonal temporal modes with a fidelity ≳0.9997. We develop a general theory to characterize and optimize this process and reveal that such a high fidelity is enabled by an interesting two-photon scattering dynamics: while the first emitter gives rise to a complex multimode field, the second emitter recombines the field amplitudes, and the net two-photon scattering induces a self-time reversal of the input pulse mode. The presented scheme can be employed to construct logic elements for propagating photons, such as a deterministic nonlinear-sign gate with a fidelity ≳0.9995.
Sorting quantum fields into different modes according to their Fock-space quantum numbers is a highly desirable quantum operation. In this Letter, we show that a pair of two-level emitters, chirally coupled to a waveguide, may scatter single- and two-photon components of an input pulse into orthogonal temporal modes with a fidelity ≳0.9997. We develop a general theory to characterize and optimize this process and reveal that such a high fidelity is enabled by an interesting two-photon scattering dynamics: while the first emitter gives rise to a complex multimode field, the second emitter recombines the field amplitudes, and the net two-photon scattering induces a self-time reversal of the input pulse mode. The presented scheme can be employed to construct logic elements for propagating photons, such as a deterministic nonlinear-sign gate with a fidelity ≳0.9995.
We present a scheme for implementing a high-fidelity non-linear phase shift on a photonic state. The scheme is based on repeated scattering off a two-level quantum emitter embedded in a chiral or one-sided waveguide. The waveguide is equipped with elements inducing second-order dispersion and temporal phase shifts, which effectively form a harmonic trap and confine the photon pulses to a Gaussian shape. The same quantum emitter can be used for each scattering, and thus, only one quantum emitter is needed in this scheme. To illustrate the application of our scheme for photonic quantum computing and quantum communication, we analyze the implementation of a control-Z gate and a deterministic Bell-state analyzer for photonic qubits. Through numerical optimization, we show that we can reach a control-Z gate fidelity of F∼99.2% (F∼96%) and a success probability of Ps∼99.6% (Ps∼98%) for a Bell-state measurement with N=17 (N=5) scatterings.
Quantum nonlinearity is an essential ingredient for many quantum technologies, but often the nonlinearity is too weak to be exploited at the few-photon level. However, few photons interacting strongly with single quantum emitters in a waveguide environment can impact a significant nonlinear response, opening up a wide range of photon-photon correlations. Using a waveguide-QED system containing a single atom (treated as a two-level system) chirally coupled to a waveguide, we theoretically investigate two-photon nonlinearities with delay-controlled temporal correlations. We use both matrix product states (MPS) and a frequency-dependent scattering theory approach to analyze the exact population dynamics, as well as the first-order and second-order photon correlation functions in transmission of the system, when pumped by a two-photon Fock-state pulse with a bimodal temporal pulse envelope. The two-photon Fock-state pulses are considered to be either two single photons localized to each peak of the pulse, or both photons delocalized (but correlated) between the two peaks. We consider the regimes of a short, moderate, and (relatively) long distance between the two pulse peaks, comparing the important differences in the temporal correlations with the two types of two-photon pulses. We demonstrate the strikingly different nonlinear features and quantum correlations that occur for uncorrelated and correlated two-photon pairs in experimentally accessible regimes.
Engineering deterministic photonic gates with simple resources is one of the long-standing challenges in photonic quantum computing. Here, we design a passive conditional gate between copropagating photons using an array of only two-level emitters. The key resource is to harness the effective photon-photon interaction induced by the chiral coupling of the emitter array to two waveguide modes with different resonant momenta at the emitter’s transition frequency. By studying the system’s multiphoton scattering response, we demonstrate that, in certain limits, this configuration induces a nonlinear π -phase shift between the polariton eigenstates of the system without distorting spectrally the wave packets. Then, we show how to harness this nonlinear phase shift to engineer a conditional, deterministic photonic gate in different qubit encodings, with a fidelity arbitrarily close to 1 in the limit of large number of emitters and coupling efficiency. Our configuration can be implemented in topological photonic setups with multiple chiral-edge modes, opening their use for quantum information processing, or in other setups where such chiral light-matter couplings can be effectively obtained, such as optical fibers or photonic-crystal optical and microwave waveguides.
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 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.
We employ a cascaded system approach to numerically simulate the interaction of photon pulses with a two-level scatterer in a chiral waveguide QED setup and show that the scattering of a two-photon pulse may lead to the predominant population of only two output wave packet modes in an entangled state, $|2,0\ensuremath{\rangle}--|0,2\ensuremath{\rangle}$. In a complementary wave-packet basis, this is a product state of two orthogonal single-photon wave packets. Operating this process in reverse allows a perfect merging of distinguishable single-photon wave packets into a single-mode pulse carrying two identical photons.