Superconducting microwave circuits provide a versatile platform for studying quantum optics with artificial atoms, mainly motivated by applications in quantum information. In addition, the circuits are promising for simulation of relativistic phenomena. This thesis is based on theoretical work along both these lines.Firstly, we consider a transmon coupled to an open transmission line. Using circuit quantization techniques and the master equation formalism, we theoretically describe scattering of coherent microwaves states on the transmon. The results agree with various recent experiments. As an example, we see a photon number redistribution leading to antibunching in the reflected field and superbunching in the transmitted field. Inspired by these results, we further investigate the possibility of generating single-photon states on demand in the system. We find that a single two-level system in an open transmission line is not a suitable single-photon source. With an asymmetric setup using two transmission lines, however, single-photon probabilities close to unity can be achieved.Secondly, we investigate simulation of a relativistically moving cavity containing a quantum field.Previously, in order to demonstrate the dynamical Casimir effect, a SQUID was used to tune a boundary condition in a way that mimics a moving mirror. Building on this idea, we extend the setup and use two SQUIDs to simulate the moving cavity. An experiment is proposed where the cavity is used as a clock and we show that time dilation should be observable for realistic circuit parameters. We also show how the size and the acceleration of the clock leads to a deviation from the ideal clock formula. Moreover, the effect of acceleration on the precision of the clock is analyzed.
Superconducting microwave circuits provide a versatile platform for studying quantum optics with artificial atoms, mainly motivated by applications in quantum information. In addition, the circuits are promising for simulation of relativistic phenomena. This thesis is based on theoretical work along both these lines.Firstly, we consider a transmon coupled to an open transmission line. Using circuit quantization techniques and the master equation formalism, we theoretically describe scattering of coherent microwaves states on the transmon. The results agree with various recent experiments. As an example, we see a photon number redistribution leading to antibunching in the reflected field and superbunching in the transmitted field. Inspired by these results, we further investigate the possibility of generating single-photon states on demand in the system. We find that a single two-level system in an open transmission line is not a suitable single-photon source. With an asymmetric setup using two transmission lines, however, single-photon probabilities close to unity can be achieved.Secondly, we investigate simulation of a relativistically moving cavity containing a quantum field.Previously, in order to demonstrate the dynamical Casimir effect, a SQUID was used to tune a boundary condition in a way that mimics a moving mirror. Building on this idea, we extend the setup and use two SQUIDs to simulate the moving cavity. An experiment is proposed where the cavity is used as a clock and we show that time dilation should be observable for realistic circuit parameters. We also show how the size and the acceleration of the clock leads to a deviation from the ideal clock formula. Moreover, the effect of acceleration on the precision of the clock is analyzed.
We address recent advances in quantum optics with propagating microwaves\nin superconducting circuits. This research field exploits on the fact that the coupling between a superconducting artificial atom and propagating microwave photons in a one-dimensional (1D) open transmission line can be made strong enough to observe quantum effects, without using any cavity to confine the microwave photons.\nWe embed an artificial atom, a superconducting transmon qubit, in a 1D open\ntransmission line and investigate the scattering properties of coherent microwaves. When an input coherent state, with an average photon number much less than 1, is on resonance with the artificial atom, we observe extinction of up to 99% in the forward propagating field. We observe the strong nonlinearity of the artificial atom and under strong driving we observe the Mollow triplet. We also study the statistics of the reflected and transmitted beams, which are predicted to be nonclassical states. In particular, we demonstrate photon antibunching in the reflected beam by measuring the second-order correlation function. By applying a second control tone, we observe the Autler-Townes splitting and a giant cross-Kerr effect.\nFurthermore, we demonstrate fast operation of a single-photon router using\nthe Autler-Townes splitting. This device provides important steps towards the realization of a quantum network. This thesis describes the motivation, theoretical background, design, implementation and measurement results.
Quantum optics in superconducting circuits, known as circuit QED, studies the interaction of photons at microwave frequencies with artificial atoms made of Josephson junctions. Although quite young, remarkable progress has been made in this field over the past decade, especially given the interest in building a quantum computer using superconducting circuits. In this thesis based on the appended papers, we look at generation, engineering and detection of microwave photons using superconducting circuits. We do this by taking advantage of the strong coupling, on-chip tunability and huge nonlinearity available in superconducting circuits. First, we present the strong photon-photon interaction measured experimentally, as shown in the giant cross-Kerr effect. In this work, conditional phase shift of about 20 degrees per photon was measured between two coherent fields at single photon level. Given this strong interaction, we propose and analyze a cascaded setup based on the cross-Kerr effect to detect itinerant microwave photons, a long outstanding problem with only recent experimental realizations. We show that a nondestructive detection of microwave photons is possible with few cascaded transmons. The on-chip tunability of Superconducting Quantum Interference Device (SQUID) is exploited to create a tunable superconducting resonator in the next presented experimental work. Finally, we show that by placing the atom at the end of a transmission line, microwave photons can be generated efficiently and on-demand. We also present a setup that can generate the photons in arbitrary wave packets.
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.
Artificially engineered atoms, built using superconducting electrical circuits, have had a broad impact on the field of quantum information and quantum computing. Based on the Josephson effect, superconducting qubits have provided a robust platform for engineering light-matter interactions at the single-photon level. The ability to precisely control and manipulate single photons using superconducting qubits and cavities, a field now popularly known as circuit quantum electrodynamics (circuit QED), has enabled new and novel regimes in quantum physics, which previously remained inaccessible. For instance, the coupling between individual photons and artificial atoms have been shown to reach the ultrastrong and deep-strong regimes, a feat which is difficult to achieve with natural atoms. The superconducting circuit platform is now a promising contender for building large-scale quantum processors, attracting large investments from academic, industry and government players. \n \nThis thesis uses superconducting circuits to engineer photon interactions in two separate studies. The first is aimed at studying the physics of ``giant" artificial-atoms. The second study explores the route towards building a quantum heat engine using two parametrically-coupled, superconducting microwave cavities. We review the theoretical ideas and concepts which motivate our work, along with discussions of the design methodology, simulations, fabrication, measurement setup and the experimental findings. \n \nIn the first study, we explore a giant artificial atom, formed from a transmon qubit, which is coupled to propagating microwaves at multiple points along an open transmission line. The multipoint coupling nature of the transmon allows its radiated field to interfere with itself leading to some striking ``giant" atom effects. For instance, we observe strong frequency dependent couplings of the transmon's transition levels to its electromagnetic environment, a feature which is not observed with ordinary artificial atoms. We measure large on/off ratios, as high as 380, for the coupling rate of the ket0−ket1 transition. Furthermore, we show that we can enhance or suppress the coupling rate of the ket1−ket2 transition relative to the ket0−ket1 transition, by more than a factor of 200. The relative modulation of the coupling rates was exploited to engineer a metastable state in the giant transmon and demonstrate electromagnetically-induced transparency (EIT), a typical signature of a lambda system. Our results show that we can transform the ladder structure of an ordinary transmon into a more interesting lambda system using a giant transmon, thereby paving the way for exploring new possibilities to study three-level physics in a waveguide-QED setting. \n \nExtending giant atom physics to multiple giant atoms, we then explore a device with two giant artificial atoms connected in a braided configuration to a transmission line. The braided topology of the qubits, offers an interesting regime where the qubits can interact with each other in a decoherence-free environment, where the interaction is mediated by virtual photons in the transmission line. We probe the resonant behavior of the qubits at two different frequency bias points, where we observe qualitatively different scattering behavior. Furthermore, when probing for the Autler-Townes Splitting (ATS), multiple resonances are observed for both resonant and off-resonant cases instead of the familiar doublet in the ATS spectroscopy. This comes as a surprise as the frequency-level spacings in both qubits are nominally identical. We believe these features could be an indication of a novel resonant interaction between the qubits facilitated by the braided topology. An effort to understand this theoretically is underway. \n \nFor our second study, we explore a system with two parametrically-coupled superconducting resonators, which implements an optomechanical-like interaction in an all-electrical network. The nonlinear nature of this interaction is mediated by a superconducting quantum interference device (SQUID), where the current in one resonator couples to the photon number in the other resonator. We propose to use this system to build a ``photonic piston" engine in the quantum regime. We motivate the feasibility of the proposal by reviewing key theoretical results which demonstrate an Otto-cycle by appropriately driving the system with noise. Our experimental findings demonstrate the crucial nonlinear coupling that is required for the engine to work. We also show that we can increase the coupling strength between the resonators depending on the chosen flux operating point.
In the last two decades, the field of circuit quantum electrodynamics, that studies the interaction between superconducting qubits and 1-dimensional waveguides, has been of great interest. It provides a great potential to build quantum devices, which are important for quantum computing, quantum communication and quantum information. The restriction to one dimension decreases losses and information can be transferred efficiently. Superconducting qubits are artificial atoms that consist of a non-linear Josephson element and work in the microwave regime. These superconducting qubits make on-chip tunable quantum experiments possible.In the appended paper, we investigate the spontaneous emission of an initially excited artificial atom (superconducting transmon qubit) which is capacitively coupled to a semi-infinite transmission line (atom in front of a mirror). We can choose the distance to the mirror arbitrarily so the interaction with the reflected field is delayed if the qubit is far away from the mirror and we have to take time-delay effects into account. We derive equations of motion for the transmon by circuit quantization and solve them semi-classically. In this thesis we give an introduction to circuit quantization, transmission lines and superconducting qubits. Then we discuss the methods and results of the appended paper which are based on the topics introduced.
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.