Quantum Interference between Three Two-Spin States in a Double Quantum Dot

S. A. Studenikin, G. C. Aers, G. Granger, L. Gaudreau, A. Kam, P. Zawadzki, Z. R. Wasilewski, and A. S. Sachrajda

Phys. Rev. Lett. 108, 226802 – Published 31 May 2012

Abstract

Qubits based on the singlet ( $S$ ) and the triplet ( $T_{0}$ , $T_{+}$ ) states in double quantum dots have been demonstrated in separate experiments. It has been recently proposed theoretically that under certain conditions a quantum interference could occur from the interplay between these two qubit species. Here we report experiments and modeling that confirm these theoretical predictions and identify the conditions under which this interference occurs. Density matrix calculations show that the interference pattern manifests primarily via the occupation of the common singlet state. The $S / T_{0}$ qubit is found to have a much longer coherence time as compared to the $S / T_{+}$ qubit.

Received 16 January 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.226802

Published by the American Physical Society

Authors & Affiliations

S. A. Studenikin¹, G. C. Aers¹, G. Granger¹, L. Gaudreau^1,2, A. Kam¹, P. Zawadzki¹, Z. R. Wasilewski¹, and A. S. Sachrajda^1,*

¹Institute for Microstructural Sciences, National Research Council Canada, Ottawa, Ontario Canada K1A 0R6
²Département de physique, Université de Sherbrooke, Sherbrooke, Québec Canada J1K 2R1

^*Andrew.Sachrajda@nrc.ca

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Vol. 108, Iss. 22 — 1 June 2012

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Images

Figure 1
(a) Electron micrograph of the triple-dot device. Fast voltage pulses ( $δ V_{1}$ , $δ V_{2}$ ) are applied to gates 1 and 2 in addition to dc voltages ( $V_{1}$ , $V_{2}$ ). Gate $C$ tunes the (1,1,1) region size and can be adjusted such that the pair of dots indicated by the white ovals operate independently of the right “spectator dot.” (b) Stability diagram obtained from numerically differentiating the left QPC detector conductance with respect to $V_{2}$ at $B = 0.2 T$ . Black is low, red [medium gray] is medium, and yellow [light gray] is high. Charge addition lines appear black, and charge transfer lines appear yellow [light gray] [3]. A detuning line is drawn across the (2,0,1)/(1,1,1) charge transfer line indicated by the white arrow. (c) Schematic energy diagram of the two-spin states near the (2,0,1)/(1,1,1) charge transfer line. (d) Examples of the pulse shapes for a pulse duration $τ = 15 ns$ after Gaussian filtering, leading to rise times of 8.0 (blue [dark gray]) and 0.8 ns (red [medium gray]).Reuse & Permissions
Figure 2
(a),(b) Left panels: experimental maps in the $τ − V_{2}$ plane from the numerical derivative of the QPC conductance with respect to initial detuning component $d V_{2}$ for the pulse rise times (a) 8.0 ns and (b) 0.8 ns. For (a)[(b)] the pulse involves $(δ V_{1}, δ V_{2}) = (- 5, 10) mV$ [ $(- 4, 8) mV$ ] to traverse the charge transfer line between (2,0) and (1,1) and repeats every $T_{m} = 0.5 μ s$ , $B = 0.08 T$ . Black is low, orange [medium gray] is medium, and yellow [light gray] is high transconductance. Right panels: calculated derivative with respect to detuning of singlet probability $P_{S}$ in the $τ − V_{2}$ plane for the rise times of the left panels. Black (white) is low (high). $T_{2}^{*} = 10 ns$ for $S / T_{+}$ . $d V_{2}$ shift is due to 2 mV pulse change between (a) and (b). The bright horizontal band around $d V_{2} = 0$ in (b), left panel, is the charge transfer line and is not generated by the theory.Reuse & Permissions
Figure 3
(a) Experimental map in the $τ − V_{2}$ plane from the numerical derivative of the QPC conductance with respect to initial detuning component $d V_{2}$ for an elliptical pulse rise shown in (c), repetition time $T_{m} = 2 μ s$ , $B = 0.2 T$ . Circle indicates region showing non-adiabatic structure on fringes. Black is low, orange [medium gray] is medium, and yellow [light gray] is high transconductance. (b) Calculated derivative with respect to detuning of $P_{S}$ in the $τ − V_{2}$ plane. Black (white) is low (high). The origin for the pulse detuning is the charge transfer line. (c) Pulse shape added to the DC detuning. (d) Energy diagram, including hyperfine splitting, showing the detuning ranges of the adiabatic ( $A$ ) and exchange ( $E$ ) steps. The effective energy/gate voltage lever arm used here is $38.1 μ eV / mV$ .Reuse & Permissions
Figure 4
(a) Schematic of $S / T_{0}$ Bloch sphere showing state vector motion corresponding to steps $A$ and $E$ of the “spin swap” pulse of Fig. 3c. Ideal rotation during the exchange step $E$ is around the $Z$ axis. (b) Schematic state vector motion corresponding to the “fast” square pulse of Fig. 1d. Axis of rotation is lowered towards the equator.Reuse & Permissions
Figure 5
(a) Experimental map in the $τ − V_{2}$ plane from the numerical derivative of the QPC conductance with respect to initial detuning component $d V_{2}$ for a pulse rise time of 1.0 ns. The pulse involves $(δ V_{1}, δ V_{2}) = (- 16.2, 20.0) mV$ to traverse the charge transfer line between (2,0) and (1,1) and repeats every $T_{m} = 2 μ s$ , $B = 0.2 T$ . Black is low, orange [medium gray] is medium, and yellow [light gray] is high transconductance. (b) Calculated derivative with respect to detuning of $P_{S}$ in the $τ − V_{2}$ plane for the same rise time as in (a). Black (white) is low (high). The origin for the detuning voltage is the charge transfer line. (c) Narrow detuning region with rectangular pulse, $(δ V_{1}, δ V_{2}) = (- 19.5, 25.0) mV$ , rise time $\approx 0.25 ns$ . (d) Time response of $P_{S}$ (black), $P_{T_{0}}$ (red [medium gray]) and $P_{T_{+}}$ (blue [dark gray]) to single pulse at point on Fig. 5b indicated by white dot.Reuse & Permissions

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