Motoaki Bamba

Hamiltonian of a flux qubit-LC oscillator circuit in the deep-strong-coupling regime

  1. Fumiki Yoshihara,
  2. Sahel Ashhab,
  3. Tomoko Fuse,
  4. Motoaki Bamba,
  5. and Kouichi Semba
We derive the Hamiltonian of a superconducting circuit that comprises a single-Josephson-junction flux qubit and an LC oscillator. If we keep the qubit’s lowest two energy levels,
the derived circuit Hamiltonian takes the form of the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator, regardless of the coupling strength. To investigate contributions from the qubit’s higher energy levels, we numerically calculate the transition frequencies of the circuit Hamiltonian. We find that the qubit’s higher energy levels mainly cause an overall shift of the entire spectrum, but the energy level structure up to the seventh excited states can still be fitted well by the quantum Rabi Hamiltonian even in the case where the coupling strength is larger than the frequencies of the qubit and the oscillator, i.e., when the qubit-oscillator circuit is in the deep-strong-coupling regime. We also confirm that some of the paradoxical properties of the quantum Rabi Hamiltonian in the deep-strong-coupling regime, e.g. the non-negligible number of photons and the nonzero expectation value of the flux in the oscillator in the ground state, arise from the circuit Hamiltonian as well.
arxiv pdf

Effects of an environment on the ground state of circuit QED systems in the deep-strong coupling regime

  1. Tomohiro Shitara,
  2. Motoaki Bamba,
  3. Fumiki Yoshihara,
  4. Tomoko Fuse,
  5. Sahel Ashhab,
  6. Kouichi Semba,
  7. and Kazuki Koshino
We investigate theoretically how the ground state of a qubit-resonator system in the deep-strong coupling (DSC) regime is affected by the coupling to an environment. We employ a superposition
of coherent states displaced in the qubit-state-dependent directions as a variational ansatz for the ground state of the qubit-resonator-environment system. We show that the reduced density matrix of the qubit-resonator system strongly depends on types of the resonator-waveguide and resonator-qubit coupling, i.e., capacitive or inductive, because of the broken rotational symmetry of the eigenstates of the DSC system in the resonator phase space. When the resonator couples to the qubit and the environment in different ways (for instance, one is inductive and the other is capacitive), the system is almost unaffected by the resonator-waveguide coupling. In contrast, when the types of two couplings are the same (for instance, both are inductive), by increasing the resonator-waveguide coupling strength, the average number of virtual photons increases and the quantum superposition realized in the qubit-resonator entangled ground state is partially degraded. Since the superposition becomes more fragile when the qubit-resonator coupling strength gets large, there exists an optimal strength of the qubit-resonator coupling to maximize the nonclassicality of the qubit-resonator system.
arxiv pdf