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IEEE Transactions on Applied Superconductivity

Quantum Dynamics of the Interferometer-Type Charge Qubit Under Microwave Irradiation

Wolfram Krech, Detlef Born, V. I. Shnyrkov, Th. Wagner, M. Grajcar, E. V. Il’ichev, H.‐G. Meyer, Ya. S. Greenberg

Published Jun 1, 2005• 6 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2005.850093

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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.
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.
We have studied dynamic properties of a special Josephson charge qubit. The device consists of a single-Cooper-pair transistor (with capacitive gate) closed by a superconducting inductive loop. The phase bias is implemented by an external flux that threads the loop. Restricting ourselves to a two-band model, we have derived analytical expressions for the oppositely circulating ring currents in terms of gate charge and phase bias. They permit the determination of important device characteristics such as critical current, loop parameters, and Josephson inductance. For the purpose of measurements in connection with macroscopic quantum coherence, we investigate the qubit's microwave response within the frame of Bloch equations with phenomenological relaxation rates. We find the (nonlinear) qubit impedance in terms of quality, detuning, and the quantum resistance unit, which reflects the competition between irradiation and dephasing.
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.
We use the density matrix formalism to analyze the interaction of interferometer-type superconducting qubits with a high quality tank circuit, which frequency is well below the gap frequency of a qubit. We start with the ground state characterization of the superconducting flux and charge qubits. Then, by making use of a dressed state approach, we describe the qubits' spectroscopy when the qubit is irradiated by a microwave field which is tuned to the gap frequency. The last section of the paper is devoted to continuous monitoring of qubit states by using a dc superconducting quantum interference device in the inductive mode.
We investigated both theoretically and experimentally dynamic features of a phase-biased charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop. The effective inductance of the qubit was probed by a high-quality tank circuit. In the presence of a microwave power, with a frequency of the order of the qubit energy level separation, an alteration of the qubit inductance was observed. We demonstrate that this effect is caused by the redistribution of the qubit level population. The excitation of the qubit by one-, two-, and three-photon processes was detected. Quantitative agreement between theory and experimental data was found.
Using Bloch-type equations with phenomenological energy relaxation and dephasing terms, we investigate analytically the linear response of a superconducting charge qubit (single-Cooper-pair box) to a microwave field within a two-band model. Coherence of the macroscopic quantum states of the autonomous device is due to the competition of irradiation and dephasing. An extra qubit impedance arises from this quantum effect which can be expressed in terms of quantum resistance unit, quality and detuning. The theoretical results may support the design of microwave experiments with charge-type qubits. Especially, we present a proposal for determining the dephasing time by means of reflection measurements, anticipating a high quality of the extra (quantum) impedance.