Demonstration of Quantum Entanglement between a Single Electron Spin Confined to an InAs Quantum Dot and a Photon

J. R. Schaibley, A. P. Burgers, G. A. McCracken, L.-M. Duan, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham

Phys. Rev. Lett. 110, 167401 – Published 16 April 2013

Abstract

The electron spin state of a singly charged semiconductor quantum dot has been shown to form a suitable single qubit for quantum computing architectures with fast gate times. A key challenge in realizing a useful quantum dot quantum computing architecture lies in demonstrating the ability to scale the system to many qubits. In this Letter, we report an all optical experimental demonstration of quantum entanglement between a single electron spin confined to a single charged semiconductor quantum dot and the polarization state of a photon spontaneously emitted from the quantum dot’s excited state. We obtain a lower bound on the fidelity of entanglement of $0.59 \pm 0.04$ , which is 84% of the maximum achievable given the timing resolution of available single photon detectors. In future applications, such as measurement-based spin-spin entanglement which does not require sub-nanosecond timing resolution, we estimate that this system would enable near ideal performance. The inferred (usable) entanglement generation rate is $3 \times 10^{3} s^{- 1}$ . This spin-photon entanglement is the first step to a scalable quantum dot quantum computing architecture relying on photon (flying) qubits to mediate entanglement between distant nodes of a quantum dot network.

Received 17 October 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.167401

Authors & Affiliations

J. R. Schaibley, A. P. Burgers, G. A. McCracken, L.-M. Duan, P. R. Berman, and D. G. Steel^*

The H. M. Randall Laboratory of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA

A. S. Bracker and D. Gammon

The Naval Research Laboratory, Washington, DC 20375, USA

L. J. Sham

Department of Physics, The University of California-San Diego, La Jolla, California 92093-0319, USA

^*dst@umich.edu

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Vol. 110, Iss. 16 — 19 April 2013

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Images

Figure 1
(a) The effective four-level system generated when a magnetic field is applied perpendicular to the QD growth axis. The selection rules are labeled horizontal ( $H$ ) and vertical ( $V$ ) where the $i$ is included to illustrate the relative phase between the matrix elements. The subscripts label the transitions in order of increasing energy. The excited state (heavy hole) splitting ( $Δ_{h} / 2 π$ ) and the ground state (electron) splitting ( $Δ_{e} / 2 π$ ) are shown. (b) Time histogram of integrated fluorescence showing QD emission from the excitation and readout pulses. The lower trace (red online) shows the background level when the QD transitions are Stark-shifted out of resonance with the excitation lasers. The arrow indicates the temporal location of the rotation pulse used in the $z$ basis measurements.Reuse & Permissions
Figure 2
(a) Pulse sequence used for $P (x + | H)$ measurement. After initialization, a 250 ps $π$ pulse excites to $| T_{x} - ⟩$ . Upon detection of an $H$ polarized photon, the spin state ideally collapses to $| x + ⟩$ where the population is read out by the next 4 ns pulse. (b) To show anticorrelation [ $P (x - | H)$ ] in an independent measurement, a second 250 ps $π$ pulse is used to readout the remaining $| x - ⟩$ population after an $H$ photon is detected. (c) To verify the entanglement, we perform the correlation measurement in the rotated ( $z$ ) basis. Here, we excite with $σ \pm$ and detect $σ \mp$ . A detuned $π / 2$ Raman pulse is used after the 250 ps pulse to rotate the spin coherence into a probability amplitude that is read out by the following 4 ns pulse. The photon detection time is binned relative to the Raman pulse ( $τ$ ) to observe the coincidence oscillations at the electron difference frequency.Reuse & Permissions
Figure 3
Conditional probabilities showing the correlated nature of the entangled spin-photon state in two bases. (a) For the $H$ , $V$ measurements, corrected data are shown. (b) For the $σ \pm$ measurements, the conditional probabilities are extracted from fits shown in Fig. 4.Reuse & Permissions
Figure 4
Time resolved coincidence oscillations showing the QD spin coherence generated by projecting of the photon state onto $σ \pm$ for the left and right figures, respectively. The time axis is taken relative to the QD spin rotation pulse which occurs at $t = 0$ . The first three periods of the normalized data are fit to Eq. (2) using the experimentally determined difference frequency (7.35 GHz). The data show fringe contrasts of $0.40 \pm 0.10$ for $σ +$ and $0.38 \pm 0.08$ for $σ -$ . Note that because we remove the exponential envelope by division, the relative noise increases with time.Reuse & Permissions

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