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IEEE Transactions on Applied Superconductivity

Dynamic features of the phase-biased single-cooper-pair transistor

Wolfram Krech, Detlef Born, Th. Wagner, M. Grajcar, Evgeni V. Il’ichev, H.‐G. Meyer

Published Jun 1, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2003.814153

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We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, it behaves essentially like a single Cooper-pair box (SCB). The effective capacitance of a SCB can be defined as the derivative of the induced charge with respect to gate voltage and has two parts, the geometric capacitance, C(geom), and the quantum capacitance C(Q). The latter is due to the level anticrossing caused by the Josephson coupling and is dual to the Josephson inductance. It depends parametrically on the gate voltage and its magnitude may be substantially larger than C(geom). We have detected C(Q) in our CPT, by measuring the in phase and quadrature rf signal reflected from a resonant circuit in which the CPT is embedded. C(Q) can be used as the basis of a charge qubit readout by placing a Cooper-pair box in such a resonant circuit.
We have investigated the Josephson inductance LJ{L}_{J}LJ​ of a superconducting Cooper pair transistor (SCPT). We traced the inductance using microwave reflection measurements on a tuned resonance circuit in which a SCPT was mounted in parallel to a $\ensuremath{\sim}200\text{ }\text{pH}$ strip line inductance. When the inverse of the Josephson inductance, determined on the charge-phase bias plane for a SCPT with a Josephson to Coulomb energy ratio of EJ/EC=1.75{E}_{J}/{E}_{C}=1.75EJ​/EC​=1.75, is integrated over the phase, we obtain a current-phase relation, which is strongly nonsinusoidal near the charge degeneracy point.
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.
The single Cooper pair josephson transistor is a device that exhibits at the same time charge quantization and phase coherence. Coherent quantum phase slip phenomenon is “dual” the Josephson phase coherence, while the charge quantization is dual to the flux quantization. We present the experimental demonstration and the theoretical description of a new superconducting device–single flux transistor, which is dual to the single Cooper pair transistor. Our transport measurements show the periodic modulation of the critical voltage by the external magnetic field. The obtained current-voltage characteristics show the hysteretic behavior, which we attribute to the intrinsic self-heating of charge carriers.