This thesis presents a series of circuit QED (cQED) experiments, in which artificial atoms consisting of superconducting circuits are strongly coupled to the electromagnetic field stored in a microwave resonator. This resonator can be used as a measurement apparatus for the atom, allowing both to address fundamental issues in quantum mechanics, and to develop building blocks for a quantum processor. In a first experiment we continuously monitored the evolution of a quantum system while varying the measurement strength. We observed the crossover from weak to strong measurement regimes, and, ultimately, the freezing of the dynamics by the Quantum Zeno Effect. In the weak measurement regime, we probed if the artificial atom complies with the macroscopic realism hypotheses, from which Leggett and Garg have derived a Bell's inequality in time. The violation of this inequality confirms that although macroscopic, the artificial atom is a truly quantum object. On the quantum information side, we have enriched the proposed cQED quantum processor architecture by demonstrating a high fidelity single-shot qubit readout, a crucial element for quantum processors. This new circuit relies on a dynamical transition of a non-linear resonator. The coupled system formed by the qubit and the non-linear resonator allows in addition to investigate the interplay between strong coupling and non-linear effects --parametric amplification, squeezing...-- opening the new field of non-linear cQED. Finally we have operated a circuit which would potentially be able to mediate operations between two arbitrary qubits: a superconducting resonator which is tunable in frequency.
This thesis presents a series of circuit QED (cQED) experiments, in which artificial atoms consisting of superconducting circuits are strongly coupled to the electromagnetic field stored in a microwave resonator. This resonator can be used as a measurement apparatus for the atom, allowing both to address fundamental issues in quantum mechanics, and to develop building blocks for a quantum processor. In a first experiment we continuously monitored the evolution of a quantum system while varying the measurement strength. We observed the crossover from weak to strong measurement regimes, and, ultimately, the freezing of the dynamics by the Quantum Zeno Effect. In the weak measurement regime, we probed if the artificial atom complies with the macroscopic realism hypotheses, from which Leggett and Garg have derived a Bell's inequality in time. The violation of this inequality confirms that although macroscopic, the artificial atom is a truly quantum object. On the quantum information side, we have enriched the proposed cQED quantum processor architecture by demonstrating a high fidelity single-shot qubit readout, a crucial element for quantum processors. This new circuit relies on a dynamical transition of a non-linear resonator. The coupled system formed by the qubit and the non-linear resonator allows in addition to investigate the interplay between strong coupling and non-linear effects --parametric amplification, squeezing...-- opening the new field of non-linear cQED. Finally we have operated a circuit which would potentially be able to mediate operations between two arbitrary qubits: a superconducting resonator which is tunable in frequency.
One of the most studied model systems in quantum optics is a two-level atom strongly coupled to a single mode of the electromagnetic field stored in a cavity, a research field named cavity quantum electrodynamics or CQED. CQED has recently received renewed attention due to its implementation with superconducting artificial atoms and coplanar resonators in the so-called circuit quantum electrodynamics (cQED) architecture. In cQED, the couplings can be much stronger than in CQED due to the design flexibility of superconducting circuits and to the enhanced field confinement in one-dimensional cavities. This enabled the realization of fundamental quantum physics and quantum information processing experiments with a degree of control comparable to that obtained in CQED. The purpose of this chapter is to investigate the situation where the resonator to which the atom is coupled is made nonlinear with a Kerr-type nonlinearity, causing its energy levels to be nonequidistant. The system is then described by a nonlinear Jaynes-Cummings Hamiltonian. This considerably enriches the physics since a pumped nonlinear resonator displays bistability, parametric amplification, and squeezing. The interplay of strong coupling and these nonlinear effects constitutes a novel model system for quantum optics that can be implemented experimentally with superconducting circuits. This chapter is organized as follows. In a first section we present the system consisting of a superconducting Kerr nonlinear resonator strongly coupled to a transmon qubit. In the second section, we describe the response of the sole nonlinear resonator to an external drive. In the third section, we show how the resonator bistability can be used to perform a high-fidelity readout of the transmon qubit. In the last section, we investigate the quantum backaction exerted by the intracavity field on the qubit.
Circuit quantum electrodynamics (cQED) is a prominent platform for quantum information processing, in which microwave photons are confined into resonant cavities coupled to superconducting quantum bits (qubits). The large effective dipole moment of the qubit, in combination with the high energy density of the quasi 1-D resonator allow these systems to enter the so-called strong coupling regime. The quantum state of the qubit can then be assessed by probing the frequency of the resonator, protecting the qubit from otherwise losing its energy to the environment. However, eventhough this so-called dispersive readout technique has proven useful, it is often in itself insufficient to render single-shot readout performance | one of the crucial tasks required for realizing a quantum computer. This thesis describes the demonstration of a single-shot readout technique forsuperconducting quantum bits, based on coupling the qubit to a frequency-tunable resonator. The backbone of our device is a 5 GHz quarter-wavelength coplanar waveguide resonator, terminated at one end by a non-linear inductance provided by a superconducting quantum interference device (SQUID). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using an on-chip transmission line. The modulation occurs on a timescale much faster than the photon loss out of the resonator and if the pump strength exceeds a threshold value set by the damping rate of the resonator, an intense photon field will build up inside the resonator | known as "parametric oscillations". By heterodyne detection of the output signal from the Josephson parametric oscillator (JPO), we first extracted two leading nonlinear effects of the system (dominating in different limits of applied magnetic flux). Next, we couple a qubit to the JPO and demonstrate that we can encode its quantum state onto the strong output field of the parametric oscillator (or lack thereof), rendering a signal-to-noise ratio sufficient for single-shot state detection and therefore also obviating a quantum limited parametric amplifier. The thesis also contains results from microscopic studies of the Josephson junctions, which we use to provide the necessary nonlinearities in the above mentioned devices. In particular, we show how the microstructure of the barrier layer and its atomic composition can be used to infer important electrical properties of the junctions. This knowledge allows us to better tailor the properties of Josephson-based devices.
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.
In this thesis, experimentally relevant aspects and open questions of quantum information processing and measurement in circuit quantum electrodynamics have been investigated theoretically. Circuit quantum electrodynamics is a relatively young field combining superconducting transmission line resonators on-chip with superconducting quantum bits which serve as artificial atoms. Remarkable experiments have underlined the prospects of circuit QED as a possible architecture for quantum information processing as well as a framework within which quantum optics experiments can be performed. In contrast to their optical counterparts, these experiments reach the ultra-strong coupling limit and allow e.g. the generation of Fock states, the study of decoherence and the observation of quantum jumps. We present the physics of superconducting circuits based on the Josephson junction as a non-linear circuit element. We discuss the various types of quantum bits (qubits) before turning to an introduction on cavity QED and conclude the introduction with a brief presentation of the most relevant experiments and a short introduction to the principles and prospects of quantum information processing. Building on the pioneering theoretical and experimental work in which up to three qubits have been integrated on a chip and successfully coupled via a cavity mode, we propose a scheme to overcome the natural limits concerning scalability in these systems. Usually, scalability is severely limited by the resonance width of the qubit transitions and the attainable frequency range for both qubit transition and cavity resonance frequencies. This limits the present setups to at most ten qubits. As a possible solution, we propose and investigate a cross-bar grid layout of cavities with qubits at the intersections. It turns out that this setup, allowing for up to about 1000 qubits, offers significant advantages over e.g. nearest-neighbor coupling schemes. In addition, it can serve as a building block for a truly scalable scheme for fault-tolerant quantum information processing with superconducting circuits by combining 7x7 arrays in a staircase manner. Furthermore, we discuss and simulate different possibilities to improve upon the suggested scheme by e.g. using resonant gates and optimal control theory. Another focus of the present thesis is measurement physics. In order to investigate e.g. the possibilities of using a circuit QED system to dispersively detect single microwave photons or to generate multi-qubit entangled states, we introduce in a pedagogical manner the basics of stochastic master equations which generate quantum trajectories before turning to concrete applications. Quantum trajectories have proven to be a state-of-the-art tool to analyze measurement situations in a very realistic manner by giving access to both the measurement record as well as the internal quantum dynamics conditioned on this record. Using the method of quantum trajectories as generated by stochastic master equations, we discuss a scheme to efficiently generate multi-qubit entangled states in a very flexible way. The method is based on a collective, dispersive qubit readout. By this measurement, a suitable product state of N qubits can be reliably converted into e.g. an N-qubit Greenberger-Horne-Zeilinger or W state. We propose and discuss the scheme and investigate the effects of decoherence and parameter spread as they would be encountered in experiment. Last but not least, we propose and fully analyze a scheme to dispersively detect single itinerant microwave photons. While experiments to generate single microwave photons have already been successfully performed, their single-shot quantum non-demolition detection has not been possible so far. The scheme presented in this thesis closes this gap in the circuit QED toolbox and reaches detection efficiencies of 30% only limited by fundamental quantum mechanics in this case the Quantum Zeno effect. This detection scheme could be used in quantum communication or quantum cryptography applications.
Real-time monitoring of a quantum state provides powerful tools for studying the backaction of quantum measurement and performing quantum feedback. Historically, this monitoring capability has been the exclusive province of atomic and optical physics. This thesis describes the implementation of the first such high-fidelity readout scheme in a solid state circuit, a superconducting quantum bit (qubit) coupled to a microwave cavity in the circuit quantum electrodynamics (circuit QED) architecture. The qubit-state-dependent resonance frequency of the cavity is probed with a microwave drive tone, and the resulting signal amplified using a fast, ultralow-noise superconducting parametric amplifier. This arrangement enables the observation of quantum jumps between the qubit states in real time. The ability to monitor the qubit continuously with high fidelity and resolve quantum jumps can be used to investigate the backaction of the measurement process on the qubit. This thesis examines the quantum Zeno effect--where strong measurement inhibits the evolution of a quantum system-- as well as the transition to non-ideal measurement with increasing measurement strength in the circuit QED architecture, a phenomenon shown to be due to the upconversion of low-frequency dephasing noise. These data allow probes of ``universal'' flux noise in previously inaccessible frequency ranges. The work presented here opens the door for quantum feedback and error correction in solid-state quantum systems using continuous weak measurement.
One of the key elements in circuit quantum electrodynamics (cQED) is the superconducting microwave resonator, which can enable strong coupling to and between nanoscale quantum systems, and as a result has emerged as an essential tool for both quantum information and quantum sensing. In this thesis, I will discuss new applications of superconducting resonators in both of these fields, which illustrates how quantum information and quantum sensing can be strongly tied together. As the field of quantum information continues to grow, various platforms for realizing a quantum computer have been proposed. One attractive platform is to control and manipulate the spin of an electron to form spin qubits, which have demonstrated a long coherence time, weak coupling to the environment, and high fidelity single- and two-qubit gates. However, scaling beyond two qubits has proven challenging, as has incorporating long-range coupling, although both are crucial for making spin qubits a scalable quantum computing platform. The confinement of electromagnetic fields in superconducting resonators enables strong coupling to small systems, such as the single electrons of a spin qubit. In the first part of this thesis, I will describe how a singlet-triplet spin qubit coupled to a high-impedance superconducting resonator constitutes a promising architecture for mediating long-ranged interactions based on a longitudinal coupling between the resonator and qubit. I will discuss the technical developments needed to successfully implement this novel type of interaction in a hybrid spin qubit-resonator device. This type of interaction has several advantages over the more commonly studied transverse coupling scheme: it does not require careful tuning of the qubit frequency to match that of the resonator, which facilitates scaling to a large number of qubits, and also avoids the loss of coherence, which is inevitable in resonant coupling. This type of interaction therefore opens promising paths for generating high-fidelity long-ranged two-qubit coupling by employing superconducting microwave resonators. By adapting techniques used in quantum information, we have also developed a new technique in quantum sensing, where we employ superconducting resonators as a probe of quantum materials such as mesoscopic systems, two-dimensional materials, and heterostructures, which are otherwise challenging to experimentally access with conventional techniques. In the second part of my thesis, I will discuss how implementing cQED techniques from quantum information allows us to probe the symmetry of the order parameter in unconventional superconductors. Unconventional superconductors are not readily available, and we therefore study an engineered system that comprises of interfacing a ferromagnet and superconductor, in which unconventional pairing can be induced into the ferromagnet. This platform allows us to simultaneously excite spin waves, a collective excitation of spins, in the ferromagnet, which opens new directions for studying interactions between coherently coupled magnons (quanta of spin waves) and unconventional superconducting states. Finally, by applying the same technique to a two-dimensional (2D) superconductor, tungsten ditelluride, we leverage this platform in an attempt to study the order parameter of its intrinsic superconducting phase. The nature of the order parameter in this material remains an open question, as both topological and superconducting phases can exist, possibly simultaneously. This work thus demonstrates a unique use of superconducting resonators beyond quantum information applications.