Structured Environments and Engineered Dissipation in Superconducting Circuits: Bound States, Dissipative Phase Transitions, Purcell Filtering and Power sensors
Superconducting circuits are a powerful platform for studying and controlling the interaction between light and matter at the quantum level. In these systems, superconducting qubits act as artificial atoms (with matter-like degrees of freedom), whereas microwave resonators play the role of oscillators hosting photons (with photonic-like degrees of freedom). A major advantage of this platform is the ability to tailor the electromagnetic environment to which the qubits are coupled. This degree of control makes it possible to realize well-known quantum optics models, like the Jaynes-Cummings model, as well as more complex systems, like quantum electrodynamics close to a bandgap. In this thesis, we engineer structured electromagnetic environments and couple superconducting qubits to them to experimentally study their interaction. By coupling multiple microwave resonators together, we create a metamaterial. When an atom interacts with the metamaterial, an atom-photon bound state emerges. We observe the dynamics of the creation and dissolution of the atom-photon bound state, as well as the spectral content of its photonic component, for the first time to our knowledge.Our metamaterial is intrinsically nonlinear because each resonator is formed by an array of Josephson junctions to serve as an inductor. When the system is pumped, its phase diagram exhibits multimode dissipative phase transitions with timescales on the order of hundred seconds. There is ongoing theoretical debate about whether such phase transitions can occur in one-dimensional systems, a question we address and resolve in this work.Furthermore, we engineer qubit decay using two different approaches. In the first one, we engineer the decay of two coupled atoms to two waveguides by using a symmetric–antisymmetric coupling configuration. This approach enables selective coupling to bright and dark states of the system. In the second one, we suppress the Purcell decay of a qubit using a compact lumped-element Purcell filter. In addition, we characterize the Purcell decay by employing an auxiliary superconducting qubit as a sensitive power detector directly coupled to the feedline waveguide used for the qubit readout.In summary, this thesis presents three different methods for controlling light–matter interactions in structured quantum systems, including decay suppression with both Purcell filters and symmetry-selective couplings. The thesis also introduces new experimental techniques for probing atom-photon bound states and provides direct evidence of collective phenomena in driven-dissipative quantum metamaterials.
Superconducting circuits are a powerful platform for studying and controlling the interaction between light and matter at the quantum level. In these systems, superconducting qubits act as artificial atoms (with matter-like degrees of freedom), whereas microwave resonators play the role of oscillators hosting photons (with photonic-like degrees of freedom). A major advantage of this platform is the ability to tailor the electromagnetic environment to which the qubits are coupled. This degree of control makes it possible to realize well-known quantum optics models, like the Jaynes-Cummings model, as well as more complex systems, like quantum electrodynamics close to a bandgap. In this thesis, we engineer structured electromagnetic environments and couple superconducting qubits to them to experimentally study their interaction. By coupling multiple microwave resonators together, we create a metamaterial. When an atom interacts with the metamaterial, an atom-photon bound state emerges. We observe the dynamics of the creation and dissolution of the atom-photon bound state, as well as the spectral content of its photonic component, for the first time to our knowledge.Our metamaterial is intrinsically nonlinear because each resonator is formed by an array of Josephson junctions to serve as an inductor. When the system is pumped, its phase diagram exhibits multimode dissipative phase transitions with timescales on the order of hundred seconds. There is ongoing theoretical debate about whether such phase transitions can occur in one-dimensional systems, a question we address and resolve in this work.Furthermore, we engineer qubit decay using two different approaches. In the first one, we engineer the decay of two coupled atoms to two waveguides by using a symmetric–antisymmetric coupling configuration. This approach enables selective coupling to bright and dark states of the system. In the second one, we suppress the Purcell decay of a qubit using a compact lumped-element Purcell filter. In addition, we characterize the Purcell decay by employing an auxiliary superconducting qubit as a sensitive power detector directly coupled to the feedline waveguide used for the qubit readout.In summary, this thesis presents three different methods for controlling light–matter interactions in structured quantum systems, including decay suppression with both Purcell filters and symmetry-selective couplings. The thesis also introduces new experimental techniques for probing atom-photon bound states and provides direct evidence of collective phenomena in driven-dissipative quantum metamaterials.
PhD Thesis: Superconducting circuit quantum electrodynamics (QED) has developed into a powerful platform for studying the interaction between matter and different states of light. In this context, superconducting quantum bits (qubits) act as artificial atoms interacting with quantized modes of the electromagnetic field. The field can be trapped in superconducting microwave resonators or propagating in transmission lines. In this thesis, we particularly study circuit QED systems where microwave fields are coupled with superconducting flux and transmon qubits. We optimize the coherence properties of the resonators, by analyzing loss mechanisms at excitation powers of approximately one photon on average. We find that two-level fluctuators associated with oxide layers at substrate and metal surfaces and metal-metal interfaces represent the predominant loss channel. Furthermore, we show how broadband thermal photon fields influence the relaxation and dephasing properties of a superconducting transmon qubit. To this end, we study several second-order loss channels of the transmon qubit and find that the broadband fields introduce a larger decay rate than expected from the Purcell filter defined by the resonator. Additionally, we show that qubit dephasing at the flux-insensitive point as well as low-frequency parameter fluctuations can be enhanced by thermal fields. Finally, we study how artificial atoms react to changes in inherent properties of the light fields. We perform a detailed analysis of the photon statistics of thermal fields using their relation to the qubits coherence properties. We quantitatively recover the expected n2+n-law for the photon number variance and confirm this result by direct correlation measurements. We then show a novel technique for the in-situ conversion of the interaction parity in light-matter interaction. To this end, we couple spatially controlled microwave fields to a flux qubit with two degrees of freedom.
Josephson junctions are a fundamental building block of superconducting quantum circuits. They provide the nonlinearity required to realize quantum bits and enable a wide range of nonlinear phenomena central to quantum technologies. This thesis explores two superconducting systems in which this nonlinearity plays a central role. In the first part, we investigate a superconducting resonator terminated by a superconducting quantum interference device (SQUID), an arrangement of two Josephson junctions connected in parallel. The SQUID provides a tunable Kerr nonlinearity and allows the resonator to be driven parametrically. Under the combined action of the parametric drive, Kerr nonlinearity, and dissipation to the environment, the state of the resonator can undergo abrupt changes as the pump frequency or amplitude is varied. We interpret these changes within the framework of dissipative phase transitions (DPTs). By implementing a finite-component thermodynamic limit, we experimentally and theoretically investigate both first- and second-order DPTs in this system. We characterize their steady-state and dynamical signatures, including squeezing below vacuum, phase coexistence, hysteresis, spontaneous symmetry breaking, and critical slowing down. Finally, we exploit the enhanced susceptibility near the second-order critical point to implement a frequency-estimation protocol. We show that the estimation precision scales quadratically with the effective system size, demonstrating that finite-component DPTs can provide a quantum advantage in a sensing protocol. In the second part, we investigate a novel architecture for the readout of superconducting qubits. Conventional dispersive readout relies on a transverse interaction between a transmon and a resonator, which can lead to Purcell decay and measurement-induced state transitions, ultimately limiting the readout fidelity. To overcome these limitations, we implement a nonlinear coupling by galvanically connecting the transmon and resonator through a Josephson junction. This interaction provides a strong cross-Kerr coupling for clear state discrimination, but also introduces a detrimental transverse interaction. We experimentally show that the exchange part of the transverse interaction can be suppressed by adding a capacitor in parallel with the coupling junction while preserving the strong cross-Kerr coupling. In addition, we show that the same circuit acts as an intrinsic Purcell filter, protecting the qubit against Purcell decay. The coupling junction also induces a Kerr nonlinearity in the resonator, which we exploit to implement a bifurcation readout with a 99.4 % fidelity in a 68 ns integration time. This performance is achieved without a dedicated Purcell filter or a near-quantum-limited amplifier. Overall, this thesis demonstrates the engineering of nonlinear superconducting circuits to investigate dissipative phase transitions, exploit criticality for enhanced quantum sensing, and develop a novel qubit readout architecture enabling fast, high-fidelity measurement.
Metamaterial resonant structures made from arrays of superconducting lumped-circuit elements can exhibit microwave-mode spectra with left-handed dispersion for the standing-wave resonances, resulting in a high density of modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this regime for multimode circuit quantum electrodynamics, we perform a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we observe the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we probe the qubit dispersively and characterize the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we investigate the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. Through numerical simulations, we explore designs based on this scheme with enhanced coupling so that the coupling energy between the qubit and the metamaterial modes can exceed the intermode spacing in future devices with achievable circuit parameters. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation with microwave photons and quantum memories.
Controlling Photons in Superconducting Electrical Circuits Blake Robert Johnson 2011 Circuit quantum electrodynamics (circuit QED) is a system that allows for strong coupling between microwave photons in transmission line cavities and superconducting qubits or artificial atoms. While circuit QED is often studied in the context of quantum information processing, it also provides an attractive platform for performing quantum optics experiments on-a-chip, because the level of control and coupling strengths available in circuit QED opens a vast array of possibilities for the creation, manipulation, and detection of quantum states of light. In this thesis, the extension of circuit QED to two cavities is examined, including design issues for cavities with very different Q-factors, and a new qubit design is proposed that couples to both cavities. The qubit-cavity interaction, while providing much of the utility of circuit QED, also introduces additional qubit relaxation. A powerful formalism for calculating this energy decay due to the classical admittance of the electromagnetic environment is presented in the context of circuit QED. Measurements of a wide range of samples validate this theory as providing an effective model for relaxation. A new circuit element, called the ‘Purcell filter’, is introduced and demonstrated to decouple the relationship between cavity Q and qubit relaxation. Finally, a new method for performing quantum nondemolition measurements of microwave photons is demonstrated. Controlling Photons in Superconducting Electrical Circuits A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Blake Robert Johnson Dissertation Director: Professor Robert J. Schoelkopf
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 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.