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arXiv:cond-mat/0111402 · Physical Review Letters

Charge Echo in a Cooper-Pair Box

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

Published Jan 1, 2002• 322 citations
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Abstract

A spin-echo-type technique is applied to an artificial two-level system that utilizes a charge degree of freedom in a small superconducting electrode. Gate-voltage pulses are used to produce the necessary pulse sequence in order to eliminate the inhomogeneity effect in the time-ensemble measurement and to obtain refocused echo signals. Comparison of the decay time of the observed echo signal with an estimated decoherence time suggests that low-frequency energy-level fluctuations due to the 1/f charge noise dominate the dephasing in the system.

DOI
10.1103/physrevlett.88.047901

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 1, 2005•0 citations
A spin-echo-type technique is applied to an artificial two-level system that utilizes a charge degree of freedom in a small superconducting electrode. Gate-voltage pulses are used to produce the necessary pulse sequence in order to eliminate the inhomogeneity effect in the time-ensemble measurement and to obtain refocused echo signals. Comparison of the decay time of the observed echo signal with an estimated decoherence time suggests that low-frequency energy-level fluctuations due to the 1/f charge noise dominate the dephasing in the system.
We have investigated coherent properties of an artificial two-level system realized in a small-Josephson-junction circuit. Two charge-number states of a small superconducting electrode connected to a reservoir via a Josephson junction were used as the two relevant states. Coherent manipulations of the charge-number states by applying a gate-voltage pulse were demonstrated, and decoherence of the system was studied through a spin-echo-type experiment. The result suggested that low-frequency energy-level fluctuations due to 1/f background charge noise is a dominant source of the dephasing.
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.
Fast quantum oscillations of a charge qubit in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T2∗{T}_{2}^{*}T2∗​ ranges from 127 ps to 2.1 ns; it depends substantially on how the energy difference of the two qubit states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise (charge noise that changes the asymmetry of the qubit's double-well potential). In the regime with the shortest T2∗{T}_{2}^{*}T2∗​, applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127 to 760 ps, demonstrating that low-frequency noise processes are an important dephasing mechanism.
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.
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 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.