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arXiv:cond-mat/0106597 · Physical Review Letters

Mechanical Cooper Pair Transportation as a Source of Long-Distance Superconducting Phase Coherence

Andreas Isacsson, L. Y. Gorelik, Robert I Shekhter, Y. M. Galperin, M. Jonson

Published Dec 18, 2002• 21 citations
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Abstract

Transportation of Cooper pairs by a movable single Cooper-pair box placed between two remote superconductors is shown to establish coherent coupling between them. This coupling is due to entanglement of the movable box with the leads and is manifested in the suppression of quantum fluctuations of the relative phase of the order parameters of the leads. It can be probed by attaching a high resistance Josephson junction between the leads and measuring the current through this junction. The current is suppressed with increasing temperature.

DOI
10.1103/physrevlett.89.277002

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Transportation of Cooper pairs by a movable single Cooper-pair box placed between two remote superconductors is shown to establish coherent coupling between them. This coupling is due to entanglement of the movable box with the leads and is manifested in the suppression of quantum fluctuations of the relative phase of the order parameters of the leads. It can be probed by attaching a high resistance Josephson junction between the leads and measuring the current through this junction. The current is suppressed with increasing temperature.
Abstract Superconducting circuits that incorporate Josephson junctions are of considerable experimental and theoretical interest, particularly in the context of quantum computing1, 2, 3, 4, 5. A nanometre-sized superconducting grain (commonly referred to as a Cooper-pair box2) connected to a reservoir by a Josephson junction is an important example of such a system. Although the grain contains a large number of electrons, it has been experimentally demonstrated6 that its states are given by a superposition of only two charge states (differing by 2e, where e is the electronic charge). Coupling between charge transfer and mechanical motion in nanometre-sized structures has also received considerable attention7, 8, 9, 10. Here we demonstrate theoretically that a movable Cooper-pair box oscillating periodically between two remote superconducting electrodes can serve as a mediator of Josephson coupling, leading to coherent transfer of Cooper pairs between the electrodes. Both the magnitude and the direction of the resulting Josephson current can be controlled by externally applied electrostatic fields.
We propose a nanomechanical device which can actuate and probe a flying qubit that can be used to facilitate quantum information transfer over a long distance. The flying qubit is formed by a movable Cooper pair box (CPB) consisting of a superconducting dot and a bulk superconductor which are entangled by removing the Coulomb blockade of Cooper pair tunneling electrostatically. We suggest that flying qubit states formed on movable CPB can be observed in electron transport to a normal electrode via Andreev reflections. The charge transfer due to periodic mechanical motion of CPB leads to nonzero current at zero voltage and its coherence can be identified through oscillatory dependence of the current on a gate voltage.
We have analyzed and measured the quantum coherent dynamics of a circuit containing two coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation ofthe qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pai1r after the manipulation. As expected from theory and observed experimentally the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result ofthe inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits' spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape the system remains entangled most ofthe time reaching maximally entangled states at certain instances.
We propose a superconducting nanomechanical device that can actuate and probe an oscillating flying qubit facilitating quantum information transfer over a distance. The flying qubit is formed by a movable Cooper-pair box (CPB) consisting of a superconducting dot and a bulk superconductor, which are entangled by lifting the Coulomb blockade of Cooper-pair tunneling electrostatically. We show that flying qubit states formed on a movable CPB can be observed in electron transport to a normal electrode via Andreev reflections. The charge transfer due to periodic mechanical motion of CPB leads to the occurrence of a nonzero current at zero bias voltage, and its coherence can be identified through the oscillatory current dependence of the current on a gate voltage. The proposed device provides a building block for dissipationless quantum information circuits.
We have succeeded in coupling two solid-state qubits and observing quantum coherent dynamics of such a system. Each qubit is a Cooper-pair box whose quantum states are manipulated by means of pulse technique. Coupling of the two qubits is done by using a small on-chip capacitor. For read-out of the state of each qubit, we use probe electrodes connected to the Cooper-pair boxes through resistive tunnel junctions. Quantum coherent oscillation of the two-qubit charge states results in the oscillation of the probe currents. The observed "beatings" as well as avoided level crossing in the energy spectrum is a direct evidence for the interaction of the two qubits. Although we could not measure the amount of entanglement directly, our simulations based on the experimental data show that during quantum evolution the qubits remain entangled most of the time. A straightforward continuation of this experiment is a demonstration of conditional gate operation, a prototype of a solid-state quantum logic gate.
We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.