High-Rate, High-Fidelity Entanglement of Qubits Across an Elementary Quantum Network

Editors' Suggestion

High-Rate, High-Fidelity Entanglement of Qubits Across an Elementary Quantum Network

L. J. Stephenson, D. P. Nadlinger, B. C. Nichol, S. An, P. Drmota, T. G. Ballance, K. Thirumalai, J. F. Goodwin, D. M. Lucas, and C. J. Ballance

Phys. Rev. Lett. 124, 110501 – Published 16 March 2020

Abstract

We demonstrate remote entanglement of trapped-ion qubits via a quantum-optical fiber link with fidelity and rate approaching those of local operations. Two ${}^{88}{Sr}^{+}$ qubits are entangled via the polarization degree of freedom of two spontaneously emitted 422 nm photons which are coupled by high-numerical-aperture lenses into single-mode optical fibers and interfere on a beam splitter. A novel geometry allows high-efficiency photon collection while maintaining unit fidelity for ion-photon entanglement. We generate heralded Bell pairs with fidelity 94% at an average rate $182 s^{- 1}$ (success probability $2.18 \times 10^{- 4}$ ).

Received 3 December 2019
Accepted 6 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.110501

Published by the American Physical Society

Physics Subject Headings (PhySH)

Coherent control Entanglement detection Quantum information with atoms & light Quantum information with trapped ions Quantum networks Single photon sources

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

L. J. Stephenson^*, D. P. Nadlinger ^*, B. C. Nichol, S. An , P. Drmota , T. G. Ballance^‡, K. Thirumalai, J. F. Goodwin , D. M. Lucas, and C. J. Ballance ^†

Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom

^*These authors contributed equally to this work.
^†chris.ballance@physics.ox.ac.uk
^‡Present address: ColdQuanta UK Ltd, Oxford.

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 124, Iss. 11 — 20 March 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Intensity distribution of the light field for $σ^{+}$ and $π$ decay channels, relative to the quantization axis set by the static magnetic field $B$ , and the branching fractions for each decay due to atomic selection rules. At the fiber input face, photons from $σ^{+}$ ( $π$ ) decay map to the $H$ ( $V$ ) fiber polarization mode. (b) Maximum fraction of photons emitted by the ion that can be collected (red) and theoretical ion-photon entanglement fidelity (blue) versus collection optic numerical aperture. For free-space collection (dashed lines), polarization mixing leads to a loss in fidelity with increasing numerical aperture. To model the fiber-coupling (solid lines), we calculate the overlap of the light field with a Gaussian mode on the dashed plane in (a); a smaller fraction of the emission is collected, but the polarization mixing is completely suppressed. The vertical dashed line shows the NA 0.6 used in this Letter, where the fiber collection efficiency is 80% of that in free space.
Reuse & Permissions
Figure 2
(a) ${}^{88}{Sr}^{+}$ level diagram (not to scale). (b) The initial state preparation consists of optical pumping on the 422 nm transition, with a repumper at 1092 nm to clear the $D_{3 / 2}$ level. (c) A single $\sim 5 ps$ pulse from a frequency-doubled mode-locked Ti:sapphire laser coherently transfers the population to $P_{1 / 2}, m = + 1 / 2$ with $\approx 97 %$ probability. (d) The ion decays to a superposition of $| ↓ ⟩$ and $| ↑ ⟩$ , emitting a photon whose polarization state is entangled with the state of the ion. Decays to the $D_{3 / 2}$ manifold occur with probability 5.5%, but as the 1092 nm photons are not transmitted by the fiber, the only effect is to lower the overall rate. (e) Coherent manipulations are performed on the 674 nm transition to $| D ⟩$ in order to analyze the final ion qubit state. (f) Experimental sequence: the ions are Doppler cooled for $100 μ s$ before the attempt loop (lasting up to $500 μ s$ ) begins. The enlarged view shows a single attempt, with $\approx 400 ns$ of latency between state preparation turn-on signal (at $t = 0$ ) and light arriving at the ion. State preparation ( $\approx 350 ns$ ) is followed by a 100 ns delay to ensure that the beams are fully extinguished before the pulsed excitation. The 30 ns photon detection window begins 30 ns after the excitation pulse to allow for detector latency. A further 100 ns is required to decide whether to branch out of the attempt loop, in the event that a herald pattern is detected.
Reuse & Permissions
Figure 3
Overview of apparatus. Single pulses from a frequency-doubled mode-locked laser are split to simultaneously excite ions in Alice and Bob. The spontaneously emitted photons are collected into single-mode non-PM fibers, with wave plates directly after the fibers to rotate the polarization. The photons are then overlapped on a $50 ∶ 50$ NPBS, and detected on single-mode-fiber-coupled APDs following PBSs. To minimize the polarization dependence of the NPBS, we use a small angle of incidence ( $\approx 10 °$ ). The same apparatus is used for single-ion/single-photon experiments.
Reuse & Permissions
Figure 4
The remote ion-ion density matrices and corresponding herald patterns (i)–(iv) as per the detector arrangement in Fig. 3. Detector clicks on opposing sides of the $50 ∶ 50$ beam splitter (i), (ii) herald projection into $| Ψ_{ion}^{-} ⟩$ , while clicks on the same side (iii), (iv) herald $| Ψ_{ion}^{+} ⟩$ . The average fidelity of all four patterns to the nearest maximally entangled state is 94.0(5)%, at a heralded rate of $182 s^{- 1}$ . (In this diagram the area of each square gives the magnitude of the matrix element, with the color representing the complex phase, according to the key shown. A “clock hand” also indicates the phase on the same color wheel. See the Supplemental Material [33] for numerical information.)
Reuse & Permissions

Physical Review Letters