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arXiv:1208.0519 · Physical Review B

Coherent quantum oscillations and echo measurements of a Si charge qubit

Zhan Shi, C. B. Simmons, Daniel R. Ward, Jonathan R. Prance, Robert Mohr, Teck Seng Koh, John King Gamble, Xian Wu, D. E. Savage, M. G. Lagally, Mark G. Friesen, S. N. Coppersmith, M. A. Eriksson

Published Aug 13, 2013• 109 citations
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Abstract

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 ${T}_{2}^{*}$ 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 ${T}_{2}^{*}$, 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.

DOI
10.1103/physrevb.88.075416

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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.
In fulfilling the non-adiabatic requirement of pulse sequences, it is challenging to perform multi-pulse quantum control of a charge qubit. By optimizing our charge qubit and pulse parameters, we experimentally demonstrate the coherent control and echo process of a GaAs charge qubit. We firstly employed a single non-adiabatic voltage pulse to perform the Larmor oscillation experiment and determine the optimal operation pulses. Then, we produced Ramsey fringes using two pulses and extracted the decoherence time from the Ramsey fringes. More importantly, we successfully applied a charge echo pulse sequence to increase the extracted inhomogeneous dephasing time to ∼1360 ps. Our results show that the low-frequency noise is the important dephasing limiter of the coherence time of the charge qubit in the GaAs system.
Abstract Universal quantum computation requires high-fidelity single-qubit rotations and controlled two-qubit gates. Along with high-fidelity single-qubit gates, strong efforts have been made in developing robust two-qubit logic gates in electrically gated quantum dot systems to realise a compact and nanofabrication-compatible architecture. Here we perform measurements of state-conditional coherent oscillations of a charge qubit. Using a quadruple quantum dot formed in a Si/SiGe heterostructure, we show the first demonstration of coherent two-axis control of a double quantum dot charge qubit in undoped Si/SiGe, performing Larmor and Ramsey oscillation measurements. We extract the strength of the capacitive coupling between a pair of double quantum dots by measuring the detuning energy shift (≈75 μeV) of one double dot depending on the excess charge configuration of the other double dot. We further demonstrate that the strong capacitive coupling allows fast, state-conditional Landau–Zener–Stückelberg oscillations with a conditional π phase flip time of about 80 ps, showing a promising pathway towards multi-qubit entanglement and control in semiconductor quantum dots.
We discuss measurement and manipulation of a quantum dot hybrid qubit [1] formed in a Si/SiGe heterostructure. Xrotations on the Bloch sphere are performed by pulsing a gate voltage so that the detuning of a double quantum dot makes the (1,2) and (2,1) occupation ground states degenerate [2]. The resulting rotation rate is approximately 5 GHz and reveals an experimentally measured visibilty greater than 80 percent. Z-rotations on the Bloch sphere are performed by pulsing a gate voltage away from the (1,2)-(2,1) degeneracy point, resulting in oscillations at a rate of approximately 10 GHz and measured visibility greater than 85 percent. The T2* time at this detuning is greater than 15 ns, many times longer than the 100 ps gate operation time. In part because of the large ratio between the gate time and the dephasing time, improvements in the pulses used in the experiment are expected to enhance the visibility beyond that reported here and to enable high fidelity quantum gates. This work was supported in part by ARO (W911NF-12-0607), NSF (DMR-1206915), and the United States Department of Defense. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the US Government. This work was performed in collaboration with Dohun Kim, Zhan Shi, C. B. Simmons, D. R. Ward, J. R. Prance, Xian Wu, R. T. Mohr, Teck Seng Koh, John King Gamble, Ryan Foote, D. E. Savage, M. G. Lagally, Mark Friesen, and S. N. Coppersmith.
We study the dynamics of a pulse-gated semiconductor double-quantum-dot qubit. In our experiments, the qubit coherence times are relatively long, but the visibility of the quantum oscillations is low. We show that these observations are consistent with a theory that incorporates decoherence arising from charge noise that gives rise to detuning fluctuations of the double dot. Because effects from charge noise are largest near the singlet-triplet avoided level crossing, the visibility of the oscillations is low when the singlet-triplet avoided level crossing occurs in the vicinity of the charge degeneracy point crossed during the manipulation, but there is only modest dephasing at the large detuning value at which the quantum phase accumulates. This theory agrees well with experimental data and predicts that the visibility can be increased greatly by appropriate tuning of the interdot tunneling rate.
We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and noninvasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of ∼7 ns at the charge degeneracy point, where the qubit level splitting is first-order insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with numerical simulations and predictions from a 1/f noise model.
Abstract Quantum dots in silicon are a promising architecture for semiconductor quantum computing due to a high degree of electric control and compatibility with existing silicon fabrication processes. Although electron charge and spin are prominent methods for encoding the qubit state, valley states in silicon can also store quantum information via valley-orbit coupling with protection against charge noise. By observing coherent oscillations between valley states in a Si/SiGe double quantum dot device tuned to the two-electron charge configuration, we measure the valley energy splitting in both quantum dots individually. We further demonstrate two-axis quantum control of the valley qubit using gated pulse sequences with X and Z rotations occurring within a fast operation time of 300 ps. This control is used to completely map out the surface of the Bloch sphere in a single phase-space plot that is subsequently used for state and process tomography.