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arXiv:1904.03051 · Journal of the Physical Society of Japan

Microwave Scattering in the Subohmic Spin-Boson Systems of Superconducting Circuits

Tsuyoshi Yamamoto, Takeo Kato

Published Aug 8, 2019• 10 citations
arXivHTMLPDF

Abstract

We study quantum critical phenomena in the microwave scattering of the subohmic spin-boson system, which exhibits a quantum phase transition at a critical system-reservoir coupling. By relating the reflection coefficient of a microwave with the dynamic susceptibility of the subohmic spin-boson system, we clarify the appearance of quantum critical phenomena in microwave scattering. Further, we propose experimental setups to realize the subohmic spin-boson system in a superconducting circuit composed of a charge qubit and a dissipative transmission line.

DOI
10.7566/jpsj.88.094601

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We study quantum critical phenomena in the microwave scattering of the subohmic spin-boson system, which exhibits a quantum phase transition at a critical system-reservoir coupling. By relating the reflection coefficient of a microwave with the dynamic susceptibility of the subohmic spin-boson system, we clarify the appearance of quantum critical phenomena in microwave scattering. Further, we propose experimental setups to realize the subohmic spin-boson system in a superconducting circuit composed of a charge qubit and a dissipative transmission line.
Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on nonlinear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wave function over many charge states. Numerical renormalization group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, which are relevant for a large class of devices.
Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, both at the analog and digital levels. Their building blocks are often idealized as two-level qubits, drawing powerful analogies to quantum spin models. For a charge qubit that is capacitively coupled to a transmission line, this analogy leads to the celebrated spin-boson description of quantum dissipation. We put here into evidence a failure of the two-level paradigm for realistic superconducting devices, due to electrostatic constraints which limit the maximum strength of dissipation. These prevent the occurence of the spin-boson quantum phase transition for transmons, even up to relatively large non-linearities. A different picture for the many-body ground state describing strongly dissipative transmons is proposed, showing unusual zero point fluctuations.
We investigate coherent single-microwave-photon transport in the coupled superconducting transmission lines coupled to superconducting quantum interference device based charge qubits. The Fano resonance can be observed in the scattering spectra in both the linear and nonlinear regimes of the dispersion relation of the microwave photon. We further find that the degree of the two-qubit entanglement can vary from unity to zero when the Fano resonance occurs. There exists a correspondence between the entanglement and the Fano resonance.
A superconducting circuit is one of the prominent candidates for the realization of quantum computation, which is the grand challenge in 21st-century science.The superconducting circuit has several advantages in a high degree of freedom for designing, and its elementary ingredients, such as superconducting qubits, transmission lines, and hybrid structures called the circuit quantum electrodynamics (QED), have been utilized for the application of quantum computers.The superconducting circuit also provides an ideal and useful platform for the study of fundamental physics.In particular, coupling to environments and disorder, which are usually obstacles for the realization of quantum computers, provides fascinating problems on many-body effects, quantum phase transition, localization, and heat transport.In this thesis, we investigate three problems in superconducting circuits.First, we consider a quantum phase transition in the sub-Ohmic spin-boson system, which is realized by a charge qubit coupled to a transmission line, and study quantum critical phenomena in the frequency dependence of microwave scattering off this circuit.By performing the quantum Monte Carlo simulation, we find signatures of the quantum critical behavior as well as the Fermi-liquid-like feature indicated by the generalized Shiba-Korringa relation.We also describe how to construct the sub-Ohmic spin-boson system using superconducting circuits.Second, we study the transmission properties through a Josephson-junction chain.This system is not only useful for application as a superinductor but also suitable to study many-body effects induced by Coulomb interaction and disorder.When the disorder is added to this system, the interplay of Coulomb interaction and disorder makes the Josephson-junction chain undergo a transition into an intriguing glassy insulator: Bose glass.We focus on the deep insulating regime and show that the collective pinning affects the dynamical properties of the Josephson-junction chain in the whole frequency region.Finally, we study heat transport through an assembly consisting of a superconducting qubit sandwiched between superconducting harmonic resonators, which is described by the quantum Rabi model, a typical multi-level system.Using the non-perturbative approximation, we find a two-peak structure of the linear thermal conductance as a function temperature.This characteristic transport behavior comes from the fact that there are multiple levels in the assembly and is expected to be advantageous for the application of quantum heat devices.These studies will provide a concrete foundation for further research on the physics of superconducting circuits.We also expect that the results obtained in this thesis will be observed in the near future.
Critical slowing down of the time it takes a system to reach equilibrium is a key signature of bistability in dissipative first-order phase transitions. Understanding and characterizing this process can shed light on the underlying many-body dynamics that occur close to such a transition. Here, we explore the rich quantum activation dynamics and the appearance of critical slowing down in an engineered superconducting quantum circuit. Specifically, we investigate the intermediate bistable regime of the generalized Jaynes-Cummings Hamiltonian (GJC), realized by a circuit quantum electrodynamics (cQED) system consisting of a transmon qubit coupled to a microwave cavity. We find a previously unidentified regime of quantum activation in which the critical slowing down reaches saturation and, by comparing our experimental results with a range of models, we shed light on the fundamental role played by the qubit in this regime.