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Multiphoton transitions in Josephson-junction qubits (Review Article)

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10.1063/1.3701717

### Abstract

Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubitenergy levels and their populations and to read out the resonator’s state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent results for the driven superconducting qubit–resonator system, where the resonator can be realized as an *LC* circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconductingqubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing.

© 2012 American Institute of Physics

Published online 27 April 2012

Article outline:

I. INTRODUCTION

II. SEMICLASSICAL THEORY OF THE QUBIT–RESONATOR SYSTEM

A. Krylov–Bogolyubov formalism for qubit–resonator system

B. Inductive coupling with LCR resonator. Parametric inductance

1. Low-quality qubit (T_{1} ≪ T): Phase shift probes the parametric inductance of qubit

2. Higher-quality qubit (): Parametric resistance due to qubit’s lagging

C. Capacitive coupling with nanomechanical resonator. Parametric capacitance

III. DYNAMICAL BEHAVIOR OF A TWO-LEVEL SYSTEM

IV. EXCITATION OF A SUPERCONDUCTINGQUBIT

A. Inductance of superconductingqubits

B. Equilibrium-state measurement

C. Resonant transitions in the charge qubit

D. One- and multiphoton transitions in the flux qubit

E. Interferometry with nanoresonator

V. MULTI-QUBIT SYSTEMS

A. Equations for a system of coupled qubits

B. Weak-driving spectroscopy

C. Direct and ladder-type multiphoton transitions

D. Lasing in the two-qubit system

VI. CONCLUSIONS

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2012-04-27

2014-04-18

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