Abstract The role of optical nonlinearity in light propagation through two different 1D open QED lattices is investigated, namely a chain of qubits with direct coupling between the nearest neighbors and a chain of connected resonators to each of which a qubit is side‐coupled. Using the more accurate truncated Heisenberg‐Langevin equations method, a reduction of light transmission with increasing intensity in these lattices is shown due to effective photon–photon interactions and related photon blockade mediated by nonlinearity in qubits. In contrast to the direct‐coupled qubits, a revival in the light transmission is found in the side‐coupled qubits at relatively higher intensities due to saturation of qubits by photons. In absence of bulk dissipation, it is found that the standard quasi‐classical analysis fails to capture the reduction in light transmission due to effective photon–photon interaction. A systemic method is devised to modify the quasi‐classical analysis to give much better results.
Abstract The role of optical nonlinearity in light propagation through two different 1D open QED lattices is investigated, namely a chain of qubits with direct coupling between the nearest neighbors and a chain of connected resonators to each of which a qubit is side‐coupled. Using the more accurate truncated Heisenberg‐Langevin equations method, a reduction of light transmission with increasing intensity in these lattices is shown due to effective photon–photon interactions and related photon blockade mediated by nonlinearity in qubits. In contrast to the direct‐coupled qubits, a revival in the light transmission is found in the side‐coupled qubits at relatively higher intensities due to saturation of qubits by photons. In absence of bulk dissipation, it is found that the standard quasi‐classical analysis fails to capture the reduction in light transmission due to effective photon–photon interaction. A systemic method is devised to modify the quasi‐classical analysis to give much better results.
We investigate the role of optical nonlinearity in light propagation through two different waveguide QED lattices, namely a chain of qubits with direct coupling between the nearest neighbors and a chain of connected resonators to each of which a qubit is side-coupled. We apply an efficient truncated Heisenberg-Langevin equations method to show loss of coherent light transmission with increasing intensity in these lattices due to effective photon-photon interactions and related photon blockade mediated by nonlinearity in qubits. In contrast to the direct-coupled qubits, we find a revival in the coherent light transmission in the side-coupled qubits at relatively higher intensities due to saturation of qubits by photons. We further study these lattices within the quasi-classical approximation, which fails for a broad set of parameters. We then devise a technique to modify the quasi-classical analysis to give much better results. Lastly, we examine light propagation in an inhomogeneous lattice of side-coupled qubits and observe non-monotonicity in light transmission with increasing light intensity.
We apply the quantum Langevin equations approach to study nonlinear light propagation through one-dimensional interacting open quantum lattice models. We write a large set of quantum Langevin equations of lattice operators obtained after integrating out the light fields and use them to derive nonequilibrium features of the lattice models. We first consider a Heisenberg-type interacting spin-21 chain with nearest-neighbor coupling. The transient and steady-state transport properties of an incoming monochromatic laser light are calculated for this model. We find how the local features of the spin chain and the chain length dependence of light transport coefficient evolve with an increasing power of the incident light. The steady-state light transmission coefficient at a higher power depends nonmonotonically on the interaction in a finite chain. While the nonlinear light transmission in our studied model seems to be ballistic in the absence of interaction and for a high interaction, it shows an apparent system-size dependence at intermediate interactions. Later, we extend this method to the long-range interaction between spins of the driven-dissipative lattice model and to incorporate various losses typical in many atomic and solid-state systems.
The propagation of N photons in one dimensional waveguides coupled to M qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of N, M, qubit inter distance and light-matter coupling. The quantum evolution is numerically solved via the matrix product states technique. The time evolutions for both the field and qubits are computed. The nonlinear character (as a function of N/M) depends on the computed observable. While perfect reflection is obtained for N/M≅1, photon-photon correlations are still resolved for ratios N/M=non-zero. Inter-qubit distance enhances the nonlinear response. Moving to the ultrastrong coupling regime, we observe that inelastic processes are robust against the number of qubits and that the qubit-qubit interaction mediated by the photons is qualitatively modified. The theory developed in this work models experiments in circuit QED, photonic crystals and dielectric waveguides.
Analogous to Coulomb blockade for electrons, photon blockade is a key quantum optical effect in which the presence of one photon prevents the transmission of subsequent ones through a nonlinear medium. Beyond its fundamental interest, photon and multi-photon blockade are actively studied as mechanisms for generating technologically-relevant quantum states of light. Although photon blockade typically requires achieving strong light-matter coupling, increasing the number of atoms fails to enhance antibunching. Here, we analyze the optical transmission properties of a quantum resonator that embeds a two-photon-coupled ensemble of emitters, combining an approximate analytical approach with full quantum numerical simulations. We show that when light and matter are coupled via a two-photon interaction, both single- and multi-photon blockade can benefit from a collective enhancement. We propose different driving schemes in which the second or third-order correlation functions are strongly suppressed with increasing atom number. Differently from established methods, this collective enhancement of non-classical properties occurs with unitary transmission and is ultimately constrained only by decoherence. This demonstrates that collective two-photon couplings are a powerful mechanism for realizing photon blockade even in platforms where individual strong coupling is not achievable.
Strong coupling between light and matter has been demonstrated both in classical cavity quantum electrodynamics (QED) systems and in more recent circuit-QED experiments. This enables the generation of strong nonlinear photon-photon interactions at the single-photon level, which is of great interest for the observation of quantum nonlinear optical phenomena, the control of light quanta in quantum information protocols such as quantum networking, as well as the study of strongly correlated quantum many-body systems using light. Recently, strong coupling has also been realized in a variety of one-dimensional (1D) waveguide- QED experimental systems, which in turn makes them promising candidates for quantum information processing. Compared to cavity-QED systems, there are two new features in waveguide-QED: the existence of a continuum of states and the restricted 1D phase space, which together bring in new physical effects, such as the bound-state effects. This thesis consists of two parts: 1) understanding the fundamental interaction between local quantum objects, such as two-level systems and four-level systems, and photons confined in the waveguide; 2) exploring its implications in quantum information processing, in particular photonic quantum computation and quantum key distribution. First, we demonstrate that by coupling a two-level system (TLS) or three/fourlevel system to a 1D continuum, strongly-correlated photons can be generated inside the waveguide. Photon-photon bound states, which decay exponentially as a function of the relative coordinates of photons, appear in multiphoton scattering processes. As a result, photon bunching and antibunching can be observed in the photon-photon correlation function, and nonclassical light source can be generated on demand. In the case of an N-type four-level system, we show that the effective photon-photon interaction mediated by the four-level system, gives rise to a variety of nonlinear optical phenomena, including photon blockade, photon-induced tunneling, and creation of single-photon states and photon pairs with a high degree of spectral entanglement, all in the absence of a cavity. However, to enable greater quantum networking potential using waveguide- QED, it is important to study systems having more than just one TLS/qubit. We develop a numerical Green function method to study cooperative effects in a system of two qubits coupled to a 1D waveguide. Quantum beats emerge in photon-photon correlations, and persist to much longer time scales because of non-Markovian processes. In addition, this system can be used to generate a high-degree of long-distance entanglement when one of the two qubits is driven by an on-resonance laser, further paving the way toward waveguide-QED-based quantum networks. Furthermore, based on our study of light-matter interactions in waveguide- QED, we investigate its implications in quantum information processing. First, we study quantum key distribution using the sub-Possonian single photon source obtained by scattering a coherent state off a two-level system. The rate for key generation is found to be twice as large as for other sources. Second, we propose a new scheme for scalable quantum computation using flying qubits--propagating photons in a one-dimensional waveguide--interacting with matter qubits. Photonphoton interactions are mediated by the coupling to a three- or four-level system, based on which photon-photon -phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
The idea of making photons effectively interact has attracted a lot of interest in recent years, for several reasons. Firstly, since photons do not naturally interact with each other, it is of fundamental physical interest to see what kind of medium can mediate interactions between these fundamental and non-interacting particles, and to what extent. Secondly, photonics is a major candidate for future quantum technology, due to the easy manipulation, readout, and transport of photons, which makes them ideal for quantum information processing. Finally, achieving strong and tunable interactions among photons would open up an avenue for exploring the many-body physics of a fluid of light. In this thesis, we will see how a cavity formed of subwavelength lattices of two-level atoms can confine photons to a nonlinear environment for a long time, such that emitted photons have accumulated strong correlations both among their momenta and in their temporal statistics. This speaks of a strong photon-photon interaction within the cavity. The nonlinearity originates in the saturability of individual atoms, and the lattice structure results in a strong and low-loss collective interaction with light. While a single atomic lattice has a largely linear nature, as the effect of individual atoms washes out in the collective response, the confining geometry of the cavity means the photons are exposed to the underlying saturability of the atoms for such a long time that the nonlinearity is revived. We will analyse this system both using a standard input-output formalism, where the nonlinear physics of the system is handled numerically, and a powerful Green's function-based approach that allows for exact analytical results with no additional approximations. This analytical description has the potential to lead to an exact study of the many-body physics of interacting photons in a two-dimensional setting.