Spin-boson quantum phase transition in multilevel superconducting qubits

Abstract

Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on non-linear 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 wavefunction 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, that are relevant for a large class of devices.

5 pages, 3 figures, bundled with Supplementary Material

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• Fractional Josephson effect versus fractional charge in superconducting-normal metal hybrid circuits
• Inelastic decay from integrability
• Emergent quantum phase transition of a Josephson junction coupled to a high-impedance multimode resonator
• Direct detection of down-converted photons spontaneously produced at a single Josephson junction
• Driven anti-Bragg subradiant states in waveguide quantum electrodynamics
• Predicting topological quantum phase transition from dynamics via multisite entanglement
• Functional Renormalization Group Approach to Circuit Quantum Electrodynamics
• Limitations of Caldeira-Leggett model for description of phase transitions in superconducting circuits
• Dissipative phase transition: from qubits to qudits
• Resilience of the quantum critical line in the Schmid transition
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
• Inverse Superconductor-Insulator Transition in Weakly Monitored Josephson Junction Arrays