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Physical review. B./Physical review. B

Andreev probing of a Cooper-pair flying qubit

Sunghun Park, L. Y. Gorelik, S. I. Kulinich, Hee Chul Park, Chulki Kim, R. I. Shekhter

Published Apr 3, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.111.165403

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 1, 2005•0 citations
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 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 suggest a nanoelectromechanical setup for designing a quantum-nanomechanical motion of a charge qubit in two-dimensional space. The quantum character of such motion comes through the fact that states of the qubit are entangled with nanomechanical cat states. The setup is based on mesoscopic terminal utilizing the ac Josephson effect between voltage-biased superconducting electrodes and mesoscopic superconducting grain—the charge qubit, vibrating in plane fixed on a nanomechanical cantilever. Required functionality is achieved by operating two external parameters: bias voltage between superconducting electrodes and controlling voltage applied over the gate electrodes. While the resonant tunneling of Cooper pairs between the superconductors and charge qubit builds nanomechanical coherent states comprising the cat state, gate voltage has a specific role of tuning their two-dimensional character in the form of the in-plane linear motion under the voltage-controlled direction. Controlling the spatial motion of a charge qubit opens a possibility of quantum communication between different terminals located in space. Directional control of nanomechanical motion entangled with charge qubit states we call the “quantum switch”.
We considered a nanoelectromechanical system consisting of a movable Cooper-pair box qubit, which is subject to an electrostatic field, and coupled to the two bulk superconductors via tunneling processes. We suggest that qubit dynamics is related to that of a quantum oscillator and demonstrate that a bias voltage applied between superconductors generates states represented by the entanglement of qubit states and coherent states of the oscillator if certain resonant conditions are fulfilled. It is shown that a structure of this entanglement may be controlled by the bias voltage in a way that gives rise to the entanglement incorporating so-called cat-states—the superposition of coherent states. We characterize the formation and development of such states analyzing the entropy of entanglement and corresponding Wigner function. The experimentally feasible detection of the effect by measuring the average current is also considered.
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.
Abstract A nanometre-scale superconducting electrode connected to a reservoir via a Josephson junction constitutes an artificial two-level electronic system: a single-Cooper-pair box. The two levels consist of charge states (differing by 2e, where e is the electronic charge) that are coupled by tunnelling of Cooper pairs through the junction. Although the two-level system is macroscopic, containing a large number of electrons, the two charge states can be coherently superposed1, 2, 3, 4. The Cooper-pair box has therefore been suggested5, 6, 7 as a candidate for a quantum bit or ‘qubit’—the basic component of a quantum computer. Here we report the observation of quantum oscillations in a single-Cooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modifies the energies of the two charge states non-adiabatically, bringing them into resonance. The resulting state—a superposition of the two charge states—is detected by a tunnelling current through a probe junction. Our results demonstrate electrical coherent control of a qubit in a solid-state electronic device.
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.