We propose a simple circuit quantum electrodynamics (QED) experiment to test the generation of entanglement between two superconducting qubits. Instead of the usual cavity QED picture, we study qubits which are coupled to an open transmission line and get entangled by the exchange of propagating photons. We compute their dynamics using a full quantum field theory beyond the rotating-wave approximation and explore a variety of regimes which go from a weak coupling to the recently introduced ultrastrong-coupling regime. Due to the existence of single photons traveling along the line with finite speed, our theory shows a light cone dividing the space time in two different regions. In one region, entanglement may only arise due to correlated vacuum fluctuations while in the other, the contribution from exchanged photons shows up.
We propose a simple circuit quantum electrodynamics (QED) experiment to test the generation of entanglement between two superconducting qubits. Instead of the usual cavity QED picture, we study qubits which are coupled to an open transmission line and get entangled by the exchange of propagating photons. We compute their dynamics using a full quantum field theory beyond the rotating-wave approximation and explore a variety of regimes which go from a weak coupling to the recently introduced ultrastrong-coupling regime. Due to the existence of single photons traveling along the line with finite speed, our theory shows a light cone dividing the space time in two different regions. In one region, entanglement may only arise due to correlated vacuum fluctuations while in the other, the contribution from exchanged photons shows up.
In the last decade, the field of Quantum Optics has been enriched with a completely new platform: superconducting quantum circuits, also known as circuit-QED. This platform builds on the original designs of superconducting qubits, that is few-level systems made of superconducting islands and Josephson junctions, but adds to it a new ingredient, microwave photons. In this talk I will review circuit-QED with a focus on two complementary lines of research: ultrastrong light-matter coupling and strongly correlated propagating photons. The first topic deals with novel designs of superconducting qubits, engineering their coupling to the microwave radiation field to reach Rabi frequencies that approach the qubit and photon frequencies. In this regime, known as ”ultrastrong coupling”, the rotating wave approximation from Quantum Optics is no longer valid, the vacuum may spontaneously polarize, producing photons that get bound to the qubit, and novel physics is expected to emerge. I will review recent experiments on this topic, together with various theoretical proposals to tame this ultrastrong coupling. The second topic revolves around the notion of ”propagating” photons in these circuits. Most experiments in circuit-QED so far adopted the typical configuration of artificial atoms (qubits) interacting with artificial cavities (LC resonators). This proved useful in order to reach the strong coupling regime, demonstrating Rabi oscillations and developing a variety of protocols for quantum information, tomograhy, entanglement, etc. However, recent experiments have shown that it is possible to also work with propagating photons, replacing the LC resonators with open transmission lines, and studying the scattering properties of those artificial atoms. In this context we have worked on developing new technology to detect and control these photons, engineering single-photon detectors, quantum metamaterials and photonic crystals, or even new nonlinear media based on coupled cavities.
Waveguide circuit quantum electrodynamics (waveguide circuit QED) studies light-matter interaction with superconducting circuits in one dimension. In circuit QED, natural atoms are replaced by superconducting qubits consisting of a non-linear Josephson junction, resulting in an anharmonic energy spectrum just like real atoms. With superconducting qubits, it is possible to study quantum optical phenomena and reach new regimes hard to achieve with real atoms due to weak coupling to the electromagnetic field. The reduction to one dimension in waveguide QED increases the electromagnetic field's directionality, which results in reduced losses. In this thesis, we first introduce circuit quantisation, giving the basis for the next part, where we investigate a transmon, a charge-insensitive artificial atom, coupled to a semi-infinite transmission line. An atom coupled to a semi-infinite waveguide is referred to as an atom in front of a mirror and is the subject of all appended papers. We proceed by summarising Paper I and III's main results: in Paper I, we investigate the spontaneous emission of a transmon coupled to a semi-infinite transmission line, where we take time-delay effects into account. We find that the system dynamics strongly depend on the coupling strength to the transmission line and the atom's position with respect to the electromagnetic field, leading to the Purcell effect or the convergence to a dark state with finite excitation probability. In the high-impedance regime, which we investigate in Paper III, the properties of the transmon coupled to the high-impedance transmission line change drastically. It becomes highly reflective and creates its own cavity with the mirror, resulting in the emergence of cavity modes and vacuum Rabi oscillations in the spontaneous emission dynamics. In the next chapter of the thesis, we demonstrate how to quantise an electromagnetic field and derive a light-matter interaction Hamiltonian within dipole approximation. We then give an introduction to open quantum systems and derive the quantum-optical master equation in Lindblad form. Furthermore, we introduce the dressed state picture, where the interaction of light and matter is so strong that the individual energy levels of light and matter are no longer separable. Both the quantum optical master equation and the dressed state picture are relevant in Paper II and IV. In Paper II, an experimental collaboration, we perform several experiments to characterise and discriminate different decay rates of a superconducting qubit coupled to the end of a transmission line. One experiment measured the atomic fluorescence spectral density, which shows an asymmetry for off-resonant driving, resulting from pure dephasing: an effect that we explain in more detail in this thesis and Paper II. In Paper IV, we theoretically investigate amplification mechanisms realised by different set-ups of an atom coupled to a semi-infinite waveguide. In the considered systems, the amplification of a probe field happens either due to population inversion between the pure states or dressed states or multi-photon processes. We find that compared to an open waveguide, we can achieve a higher gain in the amplification with a semi-infinite waveguide.
We propose a realistic circuit QED experiment to test the extraction of past-future vacuum entanglement to a pair of superconducting qubits. The qubit P interacts with the quantum field along an open transmission line for an interval T(on) and then, after a time-lapse T(off), the qubit F starts interacting for a time T(on) in a symmetric fashion. After that, past-future quantum correlations will have transferred to the qubits, even if the qubits do not coexist at the same time. We show that this experiment can be realized with current technology and discuss its utility as a possible implementation of a quantum memory.
Circuit Quantum Electrodynamics (cQED), the study of the interaction between superconducting circuits behaving as artificial atoms and 1-dimensional transmission-line resonators, has shown much promise for quantum information processing tasks.For the purposes of quantum computing it is usual to approximate the artificial atoms as 2-level qubits, and much effort has been expended on attempts to isolate these qubits from the environment and to invent ever more sophisticated control and measurement schemes.Rather than focussing on these technological aspects of the field, this thesis investigates the opportunities for using these carefully engineered systems for answering questions of fundamental physics.The low dissipation and small mode volume of the circuits allows easy access to the strong-coupling regime of quantum optics, where one can investigate the interaction of light and matter at the level of single atoms and photons.A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity-an effect known as vacuum Rabi splitting.The cQED architecture is ideally suited for going beyond this linear response effect.This thesis shows that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet, and the appearance of additional peaks with the characteristic √ n spacing of the Jaynes-Cummings ladder.These constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.This thesis also addresses the idea of Bell tests, which are experiments that aim to disprove certain types of classical theories, presenting a proposed method for preparing maximally entangled 3-qubit states via a 'preparation by measurement' scheme using an optimized filter on the time-dependent signal obtained via homodyne monitoring of the transmitted microwave field.
We propose a method to achieve photon pair propagation in an array of three-level superconducting circuits. Assuming experimentally accessible three-level artificial atoms with strong anharmonicity coupled via microwave transmission lines in both one and two dimensions we analyze the circuit quantum electrodynamics (QED) of the system. We explicitly show that, for a suitable choice of the coupling ratio between different levels, the single-photon propagation is suppressed and the propagation of photon pairs emerges. This propagation of photon pairs leads to the pair superfluid of polaritons associated with the system. We compute the complete phase diagram of the polariton quantum matter revealing the pair superfluid phase which is sandwiched between the vacuum and the Mott insulator state corresponding to the polariton density equal to 2 in the strong-coupling regime.
Experiments utilizing quantum optics have progressed rapidly in last few decades, particularly in the context of quantum computation, simulation, and communication. Early work in this field focused on implementations of cavity quantum electrodynamics (QED), where atoms, either natural or artificial, are strongly coupled to the confined photonic modes of cavities. However, in recent years, achieving strong coupling between atoms and itinerant photons has also gained significant interest for its applications in quantum networking. To this end, many atomic platforms are attempting to realize the waveguide QED architecture: atoms that interact with the continua of propagating photonic modes within a waveguide. In this thesis, we realize the strong-coupling regime of a waveguide QED architecture by coupling superconducting artificial atoms, typically operated as qubits, to one-dimensional transmission lines. We first demonstrate that superconducting qubits in a waveguide QED system can be used as high-quality quantum emitters. We then leverage the quantum interference between the simultaneous emission from multiple qubits in order to generate non-classical, spatially entangled, and directional itinerant microwave photons. These types of photons are particularly useful for remote entanglement and quantum communication protocols. Finally, we demonstrate that superconducting qubits can be engineered to enter novel regimes of light-matter interactions that are difficult, or even impossible, to achieve in other atomic platforms. In particular, we realize the giant-atom regime of waveguide QED, where the atom can no longer be treated as a point-like object. We use our giant atoms to implement tunable atom-waveguide couplings, as well as decoherence-free waveguide-mediated interactions between multiple atoms.