When the energy of a quantum emitter aligns with the photonic bandgap of the waveguide, variety of distinct quantum optical phenomena emerges. The paradigmatic example of such nontrivial interaction results in the formation of a qubit-photon bound state (QPBS) where a single photon is exponentially localized around the qubit position. Superconducting quantum circuits has been extensively used for studying QPBS where the photonic band gaps are generated in two-dimensional periodic structures such as photonic crystals and metamaterials. Nonetheless, in all the experiments reported so far, the exponential nature of the bound state wave function is justified by making two assumptions (1) that the waveguide is infinite in length and (2) the coupling to the external ports are absent. These assumptions are difficult to achieve for a physical device and the transition from an experimentally realizable finite-size system to the theoretically assumed infinite device size has never been thoroughly understood. Here, we have realized an alternative platform based on a three-dimensional (3D) rectangular waveguide that has a naturally occurring low-frequency cutoff for generating QPBS as proposed in Shahmoon and Kurizki [Phys. Rev. A 87, 033831 (2013)]. In its theoretical description, we explicitly take into consideration the finite nature of the 3D waveguide arising due to its metallic boundaries and coupling to microwave ports and demonstrate how the infinite waveguide limit arises in such a finite system.
When the energy of a quantum emitter aligns with the photonic bandgap of the waveguide, variety of distinct quantum optical phenomena emerges. The paradigmatic example of such nontrivial interaction results in the formation of a qubit-photon bound state (QPBS) where a single photon is exponentially localized around the qubit position. Superconducting quantum circuits has been extensively used for studying QPBS where the photonic band gaps are generated in two-dimensional periodic structures such as photonic crystals and metamaterials. Nonetheless, in all the experiments reported so far, the exponential nature of the bound state wave function is justified by making two assumptions (1) that the waveguide is infinite in length and (2) the coupling to the external ports are absent. These assumptions are difficult to achieve for a physical device and the transition from an experimentally realizable finite-size system to the theoretically assumed infinite device size has never been thoroughly understood. Here, we have realized an alternative platform based on a three-dimensional (3D) rectangular waveguide that has a naturally occurring low-frequency cutoff for generating QPBS as proposed in Shahmoon and Kurizki [Phys. Rev. A 87, 033831 (2013)]. In its theoretical description, we explicitly take into consideration the finite nature of the 3D waveguide arising due to its metallic boundaries and coupling to microwave ports and demonstrate how the infinite waveguide limit arises in such a finite system.
Light-matter interaction at the single-quantum level is the heart of many regimes of high fundamental importance to modern quantum technologies. Strong interaction of a qubit with a single photon of an electromagnetic field mode is described by the cavity/circuit electrodynamics (QED) regime which is one of the most advanced platforms for quantum computing. The opposite regime of the waveguide QED, where qubits interact with a continuum of modes in an infinite one-dimensional space, is also at the focus of recent research revealing novel quantum phenomena. Despite the demonstration of several key features of waveguide QED, the transition from an experimentally realizable finite-size system to the theoretically assumed infinite device size is neither rigorously justified nor fully understood. In this paper, we formulate a unifying theory which under a minimal set of standard approximations accounts for physical boundaries of a system in all parameter domains. Considering two qubits in a rectangular waveguide which naturally exhibits a low frequency cutoff we are able to account for infinite number of modes and obtain an accurate description of the waveguide transmission, a life-time of a qubit-photon bound state and the exchange interaction between two qubit-photon bounds states. For verification, we compare our theory to experimental data obtained for two superconducting qubits in a rectangular waveguide demonstrating how the infinite size limit of waveguide QED emerges in a finite-size system. Our theory can be straightforwardly extended to other waveguides such as the photonic crystal and coupled cavity arrays.
Abstract Embedding tunable quantum emitters in a photonic bandgap structure enables control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite-range emitter–emitter interactions via bound photonic states. Here, we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant (λ/60). The metamaterial is formed by periodically loading a transmission line with compact, low-loss, low-disorder lumped-element microwave resonators. Tuning the qubit frequency in the vicinity of a band-edge with a group index of ng = 450, we observe an anomalous Lamb shift of −28 MHz accompanied by a 24-fold enhancement in the qubit lifetime. In addition, we demonstrate selective enhancement and inhibition of spontaneous emission of different transmon transitions, which provide simultaneous access to short-lived radiatively damped and long-lived metastable qubit states.
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.
Qubits strongly coupled to a photonic crystal give rise to qubit-photon dressed bound states.These bound states, comprising the qubits and spatially localized photonic modes induced around the qubits, are the basis for many exotic physical scenarios.The localization of these states changes with qubit detuning from the photonic crystal band edge, offering an avenue of in situ control of bound-state interaction.Here, we present experimental results from a device with two transmon qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and interbound state interactions.We observe a fourth-order two-photon virtual process between bound states indicating strong coupling between the photonic crystal and transmon qubits.Because of their localization-dependent interaction, these states offer the ability to realize one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits' spatial organization.The widely tunable, strong, and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems that use bound states to build and study quantum spin models.
Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincaré disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example, by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically frustrated hyperbolic quantum spin models with finite-range or exponentially decaying interaction.
We study quantum features of electromagnetic radiation propagating in a one-dimensional superconducting quantum metamaterial composed of an infinite chain of charge qubits placed within two stripe massive superconducting resonators. The quantum-mechanical model is derived assuming weak fields and that, at low temperatures, each qubit is either unoccupied or occupied by a single Cooper pair. We demonstrate the emergence of two bands of single-photon qubit bound states with the energies lying outside the photon continuum---one is above and the second slightly below the linear photon band. The higher energy band varies slowly with the qubit-photon center of mass quasimomentum. It becomes practically flat provided that the electromagnetic energy is far below the Josephson energy when the latter is small compared to the charging energy. The dispersion of the lower band is practically identical to that of free photons. The emergence of bound states may cause radiation trapping indicating possible applicability for the control of photon transport in superconducting qubit-based artificial media.