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Physica Scripta

Ramsey Fringe Measurement of Decoherence in a Novel Superconducting Quantum Bit Based on the Cooper Pair Box

D. Vion, A. Aassime, Audrey Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, Michel Devoret

Published Jan 1, 2002• 6 citations
Publisher

Abstract

We have designed and operated a novel superconducting tunnel junction circuit which behaves as a controllable atom, with a ground and first excited state forming an effective spin 1/2. These two states are the symmetric and antisymmetric combinations of two charge configurations of a Cooper pair box. Any spin orientation corresponding to an arbitrary superposition of these two states can be prepared by applying NMR-like microwave pulses to the gate of the box. The spin state is readout by measuring the voltage response to a probe current pulse applied to the bridge formed by the two junctions of the box and an additional large, shunting junction. In a sample whose transition period is 60 ps, coherent superpositions decay with a 0.5 μs time constant, as measured by a Ramsey fringes experiment. This result is a step towards the realization of a solid-state quantum information processor.

DOI
10.1238/physica.topical.102a00162

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Rabi oscillations, Ramsey fringes and spin echoes in an electrical circuit

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

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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

Josephson-Junction Qubits

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Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.

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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.

•Jan 1, 2005•3 citations

Experiments on a Quantum Gate Based on Charge-Current Superconducting Qubit

Michel Devoret

During this grant, we have invented, designed and successfully operated a new type of readout for charge-phase superconducting qubits. This new readout is based on the bifurcation of an RF-driven Josephson junction inserted in the loop of a split Cooper pair box. When the amplitude of the RF drive is in the vicinity of the bifurcation points a small change in the effective critical current of the junction is amplified into a large phase change in the reflected signal. The performance reached by the device is in agreement with theoretical predictions. The speed of this readout is unprecedented: we measure in 20ns the critical current increment corresponding to the transition between the 2 states of the qubit. The repetition rate is 10Mz. We have performed a series of experiments showing that the amplification mechanism behaves as expected. No quasiparticles are produced during the readout and the back-action on the qubit when the readout is OFF is minimal. We have performed decoherence measurements at dilution refrigerator temperatures on the quantronium qubit integrated with RF readout. These measurements involve all possible 1-qubit gate operations. Compared with the DC readout method we have gained in repetition rate (factor of 100), signal-to-noise ration on all coherence signals (factor of 10) but most importantly, on readout fidelity which now attains more than 60% (compared to 15%). This last improvement is very important for showing the entanglement produced by two-bit gate operations. The T1 has also been improved by 250%. We still have comparable T2 as before but we suspect this is due to insufficient filtering on the listening lines of our measurement apparatus and this problem is technically solvable. In parallel with this work on readout and decoherence of the quantronium qubit, we have designed a new 2-bit gate based on capacitive coupling between qubits and worked out the complete protocol of pulses.

•Aug 31, 2005•0 citations
We have designed and operated a novel superconducting tunnel junction circuit which behaves as a controllable atom, with a ground and first excited state forming an effective spin 1/2. These two states are the symmetric and antisymmetric combinations of two charge configurations of a Cooper pair box. Any spin orientation corresponding to an arbitrary superposition of these two states can be prepared by applying NMR-like microwave pulses to the gate of the box. The spin state is readout by measuring the voltage response to a probe current pulse applied to the bridge formed by the two junctions of the box and an additional large, shunting junction. In a sample whose transition period is 60 ps, coherent superpositions decay with a 0.5 μs time constant, as measured by a Ramsey fringes experiment. This result is a step towards the realization of a solid-state quantum information processor.
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.
Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.
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.
During this grant, we have invented, designed and successfully operated a new type of readout for charge-phase superconducting qubits. This new readout is based on the bifurcation of an RF-driven Josephson junction inserted in the loop of a split Cooper pair box. When the amplitude of the RF drive is in the vicinity of the bifurcation points a small change in the effective critical current of the junction is amplified into a large phase change in the reflected signal. The performance reached by the device is in agreement with theoretical predictions. The speed of this readout is unprecedented: we measure in 20ns the critical current increment corresponding to the transition between the 2 states of the qubit. The repetition rate is 10Mz. We have performed a series of experiments showing that the amplification mechanism behaves as expected. No quasiparticles are produced during the readout and the back-action on the qubit when the readout is OFF is minimal. We have performed decoherence measurements at dilution refrigerator temperatures on the quantronium qubit integrated with RF readout. These measurements involve all possible 1-qubit gate operations. Compared with the DC readout method we have gained in repetition rate (factor of 100), signal-to-noise ration on all coherence signals (factor of 10) but most importantly, on readout fidelity which now attains more than 60% (compared to 15%). This last improvement is very important for showing the entanglement produced by two-bit gate operations. The T1 has also been improved by 250%. We still have comparable T2 as before but we suspect this is due to insufficient filtering on the listening lines of our measurement apparatus and this problem is technically solvable. In parallel with this work on readout and decoherence of the quantronium qubit, we have designed a new 2-bit gate based on capacitive coupling between qubits and worked out the complete protocol of pulses.