Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot

www.nature.com/scientificreports OPEN Received: 6 March 2018 Accepted: 14 August 2018 Published: xx xx xxxx Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot Xinyu Zhao & Xuedong Hu In this paper, we investigate how to achieve high-fidelity electron spin transport in a GaAs double quantum dot. Our study examines fidelity loss in spin transport from multiple perspectives. We first study incoherent fidelity loss due to hyperfine and spin-orbit interaction. We calculate fidelity loss due to the random Overhauser field from hyperfine interaction, and spin relaxation rate due to spin-orbit interaction in a wide range of experimental parameters with a focus on the occurrence of spin hot spots. A safe parameter regime is identified in order to avoid these spin hot spots. We then analyze systematic errors due to non-adiabatic transitions in the Landau-Zener process of sweeping the interdot detuning, and propose a scheme to take advantage of possible Landau-Zener-Stückelberg interference to achieve high-fidelity spin transport at a higher speed. At last, we study another systematic error caused by the correction to the electron g-factor from the double dot potential, which can lead to a notable phase error. In all, our results should provide a useful guidance for future experiments on coherent electron spin transport. In universal quantum computing, quantum information inevitably needs to be transferred over finite distances on chip or between chips. For spin qubits in semiconductor nanostructures1–9, there are a variety of ways such long-distance communication can be achieved10–17. One particularly straightforward way is to move the electrons themselves between quantum dots. Indeed, coherently transporting electrons between quantum confined states, with their spin states intact, could be a critical component of a wide range of future quantum coherent devices that utilize the electron spins. There are two major approaches to achieve coherent transport of spin qubits, one using surface acoustic waves10,18–26. the other by tuning the electric potentials on a series of surface gates11,12,27–31. We have studied the former in the past22,25, and will in this paper focus on the latter, which is an integral part of a concerted experimental effort towards making larger arrays of quantum dots30–32. Indeed, the importance of coherent spin transport goes well beyond quantum information transfer. Other important quantum operations, such as error correction and spin readout, also involve electron tunneling between quantum dots30,33–37. In the broader context of semiconductor heterostructures, an investigation of transport properties between quantum dots and nanowires is also an important element in the search and control of possible Majorana fermion excitations38,39. Practically, quantum tunneling of an electron is usually driven by tuning the bias voltage between neighboring quantum dots. During such a process, several factors could change the spin state of the electron and reduce the fidelity of spin transfer. A recent paper has already investigated the intrinsic errors in several aspects in the transport40, such as preparing the initial state, gate operations, and finalization. In this paper, we model the initialization, the transport, and the finalization as a continuous dynamical process, and study several external factors that can impact this process. For example, spin relaxation due to spin-orbit interaction (SOI)41,42 and phonon emission could be modified by the double-dot confinement as opposed to a single-dot confinement43. The degeneracy near zero bias causes an energy level anti-crossing, so that a time-dependent Hamiltonian for sweeping the electric field with a finite speed could cause non-adiabatic transitions, which usually reduce the fidelity of the electron spin transfer. Furthermore, the SOI together with the confinement potential causes corrections to the eigen-energies, leading to modification of the effective g-factor, which could be significant if a superposed spin state is being transferred. In this work, we study how to achieve high-fidelity spin and charge transfer through electron tunneling in a double dot. We first quantitatively study spin decoherence caused by hyperfine interaction and SOI to ensure that Department of Physics, University at Buffalo, SUNY, Buffalo, New York, 14260-1500, USA. Correspondence and requests for materials should be addressed to X.H. (email: ) Scientific Reports | (2018) 8:13968 | DOI:10.1038/s41598-018-31879-4 1 www.nature.com/scientificreports/ Figure 1. Sketch of our protocol for electron transport in a double quantum dot. The two-dimensional DQD resides at the interface of GaAs and the barrier material, with the growth-direction confinement much stronger than the in-plane confinement. The regions “QD1” and “QD2” label the two dots. Surface gates VL and VR can be used to adjust the detuning between the two dots, while Vt can be used to tune the tunnel coupling strength. there is no significant fidelity loss due to these incoherent processes. We explicitly calculate the residue coherence after the transport when taking spin relaxation and dephasing effects into consideration. After clarifying the decoherence errors caused by interaction with external environments, we analyze several systematic errors in the electron transport. In particular, we show that at finite sweeping speed for the interdot detuning, Landau-Zener (LZ) process leads to unwanted spin transitions that lower the spin transfer fidelity. We then show how pulse shaping can help reduce this population error by suppressing the LZ process. We also propose a scheme to achieve high-speed and high-fidelity electron transport through Landau-Zener-Stückelberg (LZS) interference, which can also be used to measure the tunnel barrier between the two dots. Last but not least, we study an important correction to the effective g-factor by SOI and the double dot potential. We point out that this correction can cause a significant error in the tracking of the phase difference between spin up and down states, and needs to be properly accounted for by mapping out the system parameters accurately during the detuning sweeping process. Results In this paper we study electron spin transport that is enabled by tuning the applied voltages on the metallic surface gates. While a dense array of gates together with optimized programming of voltages can probably achieve relatively smooth motion of a quantum dot potential, here we focus on a much simpler protocol. Assuming the existence of a double quantum dot (DQD) potential, as illustrated in Fig. 1, changing the interdot detuning via an applied electric field shifts the ground orbital state from one dot to the other, thereby achieving electron transport. In such a process, the only time-dependent variable is the electric field applied across the DQD, tunable by one or two surface gates. The goal of our (...truncated)