Double-well potentials in current qubits

Abstract

The effective potentials of the rf-SQUID and three-Josephson junction loop with a penetrating external magnetic flux are studied. Using the periodic boundary condition for the phase evolution of the wave function of Cooper pairs, we obtain new periodic potentials with cusp barriers in contrast with the usual smooth double-well potential. The tunneling through the cusp barrier becomes dominant for a parameter regime where the self inductance of the superconducting loop and the Josephson coupling energy are large. Calculating the tunneling frequency we see that the cusp potential may offer a more efficient qubit.

Ultrastrong coupling in a scalable design for circuit QED with superconducting flux qubits

“…Here we consider the usual Josephson junction energies such that E J 1 = 0.8E J 2 and E J 2 = E J 3 in the threejunction flux qubit of Fig. 2 [5,6,26]. In this case the phase difference α across the small Josephson junction can be obtained from Eq.…”

“…(23) of Ref. [6] with λ = E J 1 /E J 2 = 0.8 and η ≈ E L /E J 2 = 50 with E L being the characteristic inductive energy, resulting in α ≈ 0.38π .…”

“…This circuit quantum electrodynamics (QED) architecture [1,2] is a solid-state analog of cavity QED, providing a strong coupling strength between the qubit and resonator owing to the large dipole moment of the artificial qubit. The circuit QED scheme has been applied to superconducting qubits among which the flux qubit [3][4][5][6] has the advantage of fast gate operation because the flux qubit does not require low anharmonicity for long coherence time. There have been many studies for the circuit QED with the superconducting flux qubit [7,8].…”

Current biased gradiometric flux qubit in a circuit-QED architecture

“…We calculate numerically the qubit energy gap ∆ = 2t q with t q being the tunnelling amplitude across the one-dimensional potential well in Fig. 2(b) [33]. We can identify the parameter regime for a specific qubit energy gap ∆ with the ratio of the Josephson coupling energy to the charging energy E J /E C = 40 [34].…”

Ultrastrong coupling in a scalable design for circuit QED with superconducting flux qubits

“…This circuit quantum electrodynamics (QED) architecture [1,2] is a solid-state analog of cavity QED, providing a strong coupling strength between the qubit and resonator owing to the large dipole moment of the artificial qubit. The circuit QED scheme has been applied to superconducting qubits among which the flux qubit [3,4,5] has the advantage of fast gate operation because the flux qubit does not require low anharmonicity for long coherence time. There have been many studies for the circuit QED with the superconducting flux qubit [6,7].…”