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arXiv:0810.3111 · Physical Review B

Coherent Rabi response of a charge-phase qubit under microwave irradiation

V. I. Shnyrkov, Detlef Born, A. A. Soroka, Wolfram Krech

Published May 22, 2009• 8 citations

Abstract

We report on radio-frequency (rf) measurements of the charge-phase qubit being under continuous microwave irradiation in the state of weak coupling to a radio-frequency tank circuit. We studied the rf impedance dependence on the two important parameters such as the power of microwave irradiation, whose frequency is close to the gap between the two lowest qubit energy levels, and the temperature of the internal heat bath. We have found that backaction effects of the qubit on the rf tank and vice versa, tank on the qubit, lead to a negative as well as a positive real part of the qubit impedance $\text{Re}\text{ }Z(\ensuremath{\omega})$ seen by the tank. We have implemented noise spectroscopy measurements for direct impedance readout at the extreme points corresponding to maximum voltage response and obtained absolute values of about $0.017\text{ }\ensuremath{\Omega}$ for the negative and positive $\text{Re}\text{ }Z(\ensuremath{\omega})$. Our results demonstrate the existence and persistence of the coherent single- and multiphoton Rabi dynamics of the qubit with both negative and positive dynamic resistances inserted into the tank in the temperature range of 10--200 mK.

DOI: 10.1103/physrevb.79.184522

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We report on radio-frequency (rf) measurements of the charge-phase qubit being under continuous microwave irradiation in the state of weak coupling to a radio-frequency tank circuit. We studied the rf impedance dependence on the two important parameters such as the power of microwave irradiation, whose frequency is close to the gap between the two lowest qubit energy levels, and the temperature of the internal heat bath. We have found that backaction effects of the qubit on the rf tank and vice versa, tank on the qubit, lead to a negative as well as a positive real part of the qubit impedance

\text{Re}\text{ }Z(\ensuremath{\omega})

seen by the tank. We have implemented noise spectroscopy measurements for direct impedance readout at the extreme points corresponding to maximum voltage response and obtained absolute values of about

0.017\text{ }\ensuremath{\Omega}

for the negative and positive

0.017\text{ }\ensuremath{\Omega}

. Our results demonstrate the existence and persistence of the coherent single- and multiphoton Rabi dynamics of the qubit with both negative and positive dynamic resistances inserted into the tank in the temperature range of 10--200 mK.

We study theoretically dynamic properties of an interferometer-type Josephson charge qubit consisting of a single-Cooper-pair transistor (with capacitive gate) closed by a superconducting inductive loop. Analyzing the radio frequency response of the device to microwave fields within a two-band model, we present basic features of a method for observation of various Rabi oscillation modes. For this purpose, we apply the dressed-state approach in conjunction with the rotating-wave approximation to the strongly driven quantum bit. We demonstrate the existence of multiphoton excitations and Rabi frequency transitions between quantum levels connected with them. The resulting oscillations of the supercurrent in the interferometer modify the spectral loop susceptibility. This effect may be detected via the coil of a high-quality tank circuit inductively coupled to the qubit by measuring the tank-qubit impedance variations belonging to it.

Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop induce the voltage oscillations across the coil of a high quality resonant tank circuit, inductively coupled to the phase qubit. It is the presence of these voltage oscillations in the detected signal which reveals the existence of Rabi oscillations in the qubit. A detailed calculation for zero and nonzero temperatures are made for the case of persistent current qubit. According to the estimates for decoherence and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in the MHz range.

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector---namely, a spectrum of voltage fluctuations and an impedance---are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating-wave approximations. Back-action effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about the frequency and decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behavior as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.

We implemented experimentally an interferometer-type charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop that is in flip-chip configuration inductively coupled to a radio-frequency tank circuit. The tank permits us to readout the qubit state, acting as an inductance measuring apparatus. By applying continuous microwave power to the quantum device, we observed inductance alterations caused by redistributions of the energy-level populations. From the measured data we extracted the energy gap between ground and upper levels as a function of the transistor quasicharge as well as the Josephson phase across both junctions.

A superconducting charge-flux qubit coupled to a high-Q tank circuit was studied in a low-frequency electric field. A fine structure of the multiphoton resonance lines and quantum interference effects associated with the excitation of a quasi-two-level system due to the Landau–Zener–Stückelberg tunneling was observed. The results obtained for multiphoton resonant excitations and low-frequency oscillations of the average occupation of quantum levels were compared using different parameters of the measuring circuit. The mechanism responsible for the fine structure of resonance lines was considered. The method to measure the impedance arising in the tank circuit due to the oscillations of the superconducting current in the qubit and the main sources of decoherence were discussed.

The Josephson qubit based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-frequency driven tank circuit enabling the readout of the qubit states by measuring the effective Josephson inductance of the transistor. The effect of qubit dephasing and relaxation due to electric and magnetic control lines, as well as the measuring system, is evaluated. Recommendations for qubit operation with minimum decoherence are given.