Strong-Field Effects in the Rabi Oscillations of the Superconducting Phase Qubit

Abstract

Abstract-Rabi oscillations have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (qubits) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase qubit (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi frequency, and twophoton Rabi frequency are compared to measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.

Stark Effect and Generalized Bloch-Siegert Shift in a Strongly Driven Two-Level System

“…We refer to these additional changes in the qubit level splitting as the generalized Bloch-Siegert shift. This work differs from the previous studies on strong drive with superconducting or quantum dot qubits [5,6,[15][16][17][18][19][20][21][22][23][24][25][26], where the coupling of the drive to the qubit was linear.…”

Multifrequency control pulses for multilevel superconducting quantum circuits

“…Its reduction is due to the dressed eigenstates of the system, and has also been measured experimentally [21,22,23,32] IV. TWO-MODE FLOQUET THEORY: OPTIMIZED RABI OSCILLATION…”

“…SINGLE-MODE FLOQUET THEORY: THREE-LEVEL RABI OSCILLATIONS For Rabi oscillations in the presence of strong driving, there are deviations from two-level behavior that can be analyzed using a three-level model. Previous studies [11,12,31,32], using the rotating wave approximation, have identified three main features. First, the coherent oscillations between the ground and first excited state are accompanied by oscillations to the second excited state.…”

“…This corresponds to the anharmonicity of the system, being inversely proportional to N s . For Rabi frequencies near this value, three-level effects become important [12,32]. Therefore, to see deviations from two-level behavior, we use perturbation theory in the small parameters δ/Ω 01 and Ω 01 /∆, starting from the zeroth order eigenstates (|0, 0 ± |1, −1 )/ √ 2 and |2, −2 .…”

“…The resulting dynamics can be found by diagonalizing the Floquet matrix. For this Hamiltonian exact results are available [12,32]; here we will adopt a perturbative approach.…”