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Coherent control of macroscopic quantum states in a single-Cooper-pair box

Yasunobu Nakamura, Yu. A. Pashkin, J. S. Tsai

Published Apr 29, 1999• 1,507 citations
OpenAlex

Abstract

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.

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Quantum coherent dynamics of two coupled superconducting charge qubits

Yu. A. Pashkin, O. V. Astafiev, Tsuyoshi Yamamoto +5 more

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 1, 2005•0 citations

Qubit utilizing charge-number state in super conducting nanostructure

J. S. Tsai, Yasunobu Nakamura, Yu. A. Pashkin

In single-Cooper-pair box, the number of electrons in the box is quantized and they form a single macroscopic quantum charge-number state, corresponding to the number of excess electrons in the box. By making all the electrodes superconducting, we can couple two neighboring charge-number states coherently. In this way one can create an artificial two-level system. Qubit operations were demonstrated in two different control techniques, dc electric-field gate bias and ac field bias. The dc method was unique compared with the commonly used Rabi-oscillation-type operation. Here the system was biased at the degenerate point of the two states so that the dynamical phase does not develop during the operation. This was the first time that the quantum coherent oscillation was observed in a solid-state device whose quantum states involved a macroscopic number of quantum particles. Multiple-pulse experiments were also carried out and phase control was also demonstrated.

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Quantum Coherence and Entanglement in Two Coupled Josephson Charge Qubits

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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.

APS March Meeting Abstracts•Mar 1, 2004•0 citations

Quantum Coherence in the Single Cooper Pair Box

Kevin Bladh

This thesis presents measurements of quantum coherence in a single Cooper pair box, where quantum oscillations of charge between a reservoir and a small superconducting island have been observed. The single Cooper pair box (SCB) consists of a small metallic island which is connected to a reservoir via a tunnel junction. In the superconducting state, Cooper pairs are free to tunnel to and from the island, whose potential can be controlled by a gate voltage. A graded gap method was used to prevent quasiparticles from tunneling onto the island. For this purpose, a magnetic field suppressed the superconducting gap in the SCB leads more than in the island. This created an additional energy barrier for quasiparticles to tunnel to the island, making the gate voltage modulation periodic in Cooper pair charge. For a limited range of gate voltage, the SCB was found to behave as a model two-level quantum mechanical system. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with a frequency given by the energy level separation divided by Planck's constant. These oscillations had a longest coherence time of T2=9 ns at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate, ?1. Away from this point, the coherence time was limited by the dephasing rate, ??. Away from the charge degeneracy, the dependence of T2 on gate charge suggested that low frequency fluctuators were the main source of dephasing. The charge of the Cooper pair box was measured by coupling the SCB capacitively to a radio frequency single electron transistor (RF-SET). The RF-SET was used as an electrometer by measuring the amount of reflection from a resonant microwave circuit in which a single electron transistor (SET) was embedded. A best charge sensitivity of 2.3·10-6 e/sqrt(Hz) and a 7 MHz bandwidth was reached in an improved setup. Another part of this thesis concerns an investigation of electrical filters for use in single electronics experiments. The characteristics of seven different types of cryogenic filters were evaluated.

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In a system where two small-area (100 nm x 100 nm) superconducting tunnel junctions are connected in series, the Josephson effect which tends to impose the phase competes with the charging effects in the central electrode (the of the device) which tend to set the charge of the island. By applying a voltage on an electrode capacitively coupled to the island (the electrode) one can arbitrate this competition in favour of either effect. This is can be seen in particular on the supercurrent which can flow through the junctions : it is modulated periodically by the gate voltage (hence the name of given to the system). This modulation shows sharp peaks when two charge states of the island are degenerate with respect to the electrostatic energy. The system is then in a state which has no classical description : it is in a coherent superposition of states. In this thesis we demonstrate experimentally the behaviour of this transistor and we analyse the theoretical and practical problems which can prevent the observation of the coherent superposition of states through the modulation of the supercurrent. In particular we show that the parity of the electron number in the island must be rigorously controlled and that the impedance connected to the circuit plays a crucial role in setting the magnitude of the measured supercurrent.

•Mar 6, 1995•6 citations

Coherent transfer of Cooper pairs by a movable grain

L. Y. Gorelik, Andreas Isacsson, Y. M. Galperin +2 more

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.

•Jan 1, 2001•25 citations
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.
In single-Cooper-pair box, the number of electrons in the box is quantized and they form a single macroscopic quantum charge-number state, corresponding to the number of excess electrons in the box. By making all the electrodes superconducting, we can couple two neighboring charge-number states coherently. In this way one can create an artificial two-level system. Qubit operations were demonstrated in two different control techniques, dc electric-field gate bias and ac field bias. The dc method was unique compared with the commonly used Rabi-oscillation-type operation. Here the system was biased at the degenerate point of the two states so that the dynamical phase does not develop during the operation. This was the first time that the quantum coherent oscillation was observed in a solid-state device whose quantum states involved a macroscopic number of quantum particles. Multiple-pulse experiments were also carried out and phase control was also demonstrated.
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.
This thesis presents measurements of quantum coherence in a single Cooper pair box, where quantum oscillations of charge between a reservoir and a small superconducting island have been observed. The single Cooper pair box (SCB) consists of a small metallic island which is connected to a reservoir via a tunnel junction. In the superconducting state, Cooper pairs are free to tunnel to and from the island, whose potential can be controlled by a gate voltage. A graded gap method was used to prevent quasiparticles from tunneling onto the island. For this purpose, a magnetic field suppressed the superconducting gap in the SCB leads more than in the island. This created an additional energy barrier for quasiparticles to tunnel to the island, making the gate voltage modulation periodic in Cooper pair charge. For a limited range of gate voltage, the SCB was found to behave as a model two-level quantum mechanical system. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with a frequency given by the energy level separation divided by Planck's constant. These oscillations had a longest coherence time of T2=9 ns at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate, ?1. Away from this point, the coherence time was limited by the dephasing rate, ??. Away from the charge degeneracy, the dependence of T2 on gate charge suggested that low frequency fluctuators were the main source of dephasing. The charge of the Cooper pair box was measured by coupling the SCB capacitively to a radio frequency single electron transistor (RF-SET). The RF-SET was used as an electrometer by measuring the amount of reflection from a resonant microwave circuit in which a single electron transistor (SET) was embedded. A best charge sensitivity of 2.3·10-6 e/sqrt(Hz) and a 7 MHz bandwidth was reached in an improved setup. Another part of this thesis concerns an investigation of electrical filters for use in single electronics experiments. The characteristics of seven different types of cryogenic filters were evaluated.
In a system where two small-area (100 nm x 100 nm) superconducting tunnel junctions are connected in series, the Josephson effect which tends to impose the phase competes with the charging effects in the central electrode (the of the device) which tend to set the charge of the island. By applying a voltage on an electrode capacitively coupled to the island (the electrode) one can arbitrate this competition in favour of either effect. This is can be seen in particular on the supercurrent which can flow through the junctions : it is modulated periodically by the gate voltage (hence the name of given to the system). This modulation shows sharp peaks when two charge states of the island are degenerate with respect to the electrostatic energy. The system is then in a state which has no classical description : it is in a coherent superposition of states. In this thesis we demonstrate experimentally the behaviour of this transistor and we analyse the theoretical and practical problems which can prevent the observation of the coherent superposition of states through the modulation of the supercurrent. In particular we show that the parity of the electron number in the island must be rigorously controlled and that the impedance connected to the circuit plays a crucial role in setting the magnitude of the measured supercurrent.
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.