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arXiv:1701.00815 · npj Quantum Information

Coherent shuttle of electron-spin states

Takafumi Fujita, Timothy A. Baart, Christian Reichl, W. Wegscheider, Lieven M. K. Vandersypen

Published Jun 5, 2017• 133 citations
arXivHTMLPDF

Abstract

Abstract We demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third, or fourth dot. We observe that the separated spin-singlet evolves periodically into the m = 0 spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyze and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.

DOI
10.1038/s41534-017-0024-4

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•Jul 31, 2007•1 citation
Abstract We demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third, or fourth dot. We observe that the separated spin-singlet evolves periodically into the m = 0 spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyze and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.
We demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third, or fourth dot. We observe that the separated spin-singlet evolves periodically into the m = 0 spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyze and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.
Abstract Quantum information transport over micron to millimeter scale distances is critical for the operation of practical quantum processors based on spin qubits. One method of achieving a long-range interaction is by coherent electron spin shuttling through an array of silicon quantum dots. In order to execute many shuttling operations with high fidelity, it is essential to understand the dynamics of qubit dephasing and relaxation during the shuttling process in order to mitigate them. However, errors arising after many repeated shuttles are not yet well documented. Here, we probe decay dynamics contributing to dephasing and relaxation of a singlet-triplet qubit during coherent spin shuttling over many N repeated shuttle operations. We find that losses are dominated by magnetic dephasing for small N<\i> < 103 and by incoherent shuttle errors for large N<\i> > 103<\sup>. Additionally, we estimate shuttle error rates below 1×10-4<\sup> out to at least N<\i>=103<\sup>, representing an encouraging figure for future implementations of spin shuttling to entangle distant qubits.
A pair of self-assembled InGaAs quantum dots filled with two electrons can act as a singlet-triplet spin qubit that is robust against nuclear spin fluctuations as well as charge noise. This results in a T2* coherence time two orders of magnitude longer than that of a single electron, provided the qubit is operated at a particular "sweet spot" in gate voltage. However, at this fixed operating point the ground-state splitting can no longer be tuned into resonance with e.g. another qubit, limiting the options for coupling multiple qubits. Here, we propose using a four-electron coupled quantum dot to implement a singlet-triplet qubit that features a magnetically tunable level splitting. As a first step towards full experimental realization of this qubit design, we use optical spectroscopy to demonstrate the tunability of the four-electron singlet-triplet splitting in a moderate magnetic field.
Charge separation from the (4,0)(4,0)(4,0) to the (3,1)(3,1)(3,1) state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the (3,1)(3,1)(3,1) singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of ggg-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.
Connecting quantum processors over long distances using photon qubits would enable more complex quantum computing architectures and quantum networks. Recently a protocol to transfer a quantum state from a photonic qubit to a singlet-triplet spin qubit in GaAs/AlGaAs heterostructure has been theoretically demonstrated. In practice, the coherent transfer is facilitated by a hybrid device where a GaAs/AlGaAs gate-defined quantum dot (GDQD) is tunnel coupled to a self-assembled quantum dot (SAQD), in which a conversion between a photon state and a spin state takes place. This work addressed the three requirements of the optical-interface devices based on tunnel coupling between the GDQD and the SAQD: (i) a properly designed GaAs/AlGaAs heterostructure where the two-dimensional electron gas (2DEG) can be electrically tuned into resonance with the InAs SAQD; (ii) high-mobility 2DEG to form and operate a GDQD; (iii) precise alignment between the SAQD and the GDQD. It is proven that the InAs SAQD can be tuned to be charged, discharged, and resonant with the 2DEG by applying a local electric field.
We analyze the charge and spin dynamics in a DC biased double quantum dot driven by crossed DC and AC magnetic fields. In this configuration, spatial delocalization due to inter-dot tunnel competes with intra-dot spin rotations induced by the time dependent magnetic field, giving rise to a complicated time dependent behavior of the tunnelling current. When the Zeeman splitting has the same value in both dots and spin flip is negligible, the electrons remain in the triplet subspace (dark subspace) performing coherent spin rotations and the current does not flow. This electronic trapping is removed either by finite spin relaxation or when the Zeeman splitting is different in each quantum dot. In the first case, our results show that measuring the current will allow to get information on the spin relaxation time. In the last case, we will show that applying a resonant bichromatic magnetic field, the electrons become trapped in a coherent superposition of states and electronic transport is blocked. Then, manipulating AC magnetic fields, electrons are driven to perform coherent spin rotations which can be unambiguously detected by direct measurement of the tunneling current.