Multiphoton transitions in Josephson-junction qubits (Review Article)

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 qubit energy 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 superconducting qubits, 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. Contents

Delayed-response quantum back action in nanoelectromechanical systems

“…The effectiveness of this delayed-response method has been confirmed in different contexts [5][6][7]9,28,29]. In particular, the observation of Sisyphus cooling and amplification of an electrical LC circuit by a flux qubit [16] can be described by solving the master equation of the coalesced system [2,16]; the delayed-response method performs equally well in describing such a system [28,30]. In both cases, successful fitting of the experimental results yields a similar value for the key delay parameter, ω 0 T 1 ≈ 1, close to the optimal value for Sisyphus cooling and amplification.…”

“…Here a special case is when Q Sis → −Q 0 : this corresponds to the theoretical lasing limit [18,36], in which the regime of self-sustaining oscillations is realized. The delayed response can also be related to the work done on the resonator by the quantum system, QD [7,30]. The respective energy transfer during one period is given by…”

Effect of temperature on the coherence time of a parabolic quantum dot qubit

“…Based on a VMPT, Sun et al [15] calculated the effect of magnetic field on the coherence time of a PQD qubit. To obtain more information about the effects of temperature, the qubit and its coherence, the reader can refer to [16][17][18]. Such solutions would be useful to study the decoherence of the QD qubit.…”

Electromagnetically induced interference in a superconducting flux qubit

“…This transition is known as LandauZener (LZ) transition [10], which can be used to enhance the quantum tunneling rate [11,12], to prepare the quantum states [13], and to control the gate operations [14]. When the qubit is subjected to a strong periodic microwave field, consecutive LZ transitions between two states at the crossover may result in Landau-Zener-Stückelberg (LZS) interference [15,16], which has been demonstrated in many systems [17][18][19][20][21][22][23][24][25][26][27][28]. The strong driving could allow for fast and reliable control of the qubits, paving a way of demonstration of macroscopic quantum coherence and implementation of practical quantum processor.…”