Photon-Mediated Quantum Gate between Two Neutral Atoms in an Optical Cavity

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Photon-Mediated Quantum Gate between Two Neutral Atoms in an Optical Cavity

Stephan Welte, Bastian Hacker, Severin Daiss, Stephan Ritter, and Gerhard Rempe

Phys. Rev. X 8, 011018 – Published 6 February 2018

Abstract

Quantum logic gates are fundamental building blocks of quantum computers. Their integration into quantum networks requires strong qubit coupling to network channels, as can be realized with neutral atoms and optical photons in cavity quantum electrodynamics. Here we demonstrate that the long-range interaction mediated by a flying photon performs a gate between two stationary atoms inside an optical cavity from which the photon is reflected. This single step executes the gate in $2 μ s$ . We show an entangling operation between the two atoms by generating a Bell state with 76(2)% fidelity. The gate also operates as a cnot. We demonstrate 74.1(1.6)% overlap between the observed and the ideal gate output, limited by the state preparation fidelity of 80.2(0.8)%. As the atoms are efficiently connected to a photonic channel, our gate paves the way towards quantum networking with multiqubit nodes and the distribution of entanglement in repeater-based long-distance quantum networks.

Received 29 September 2017
Revised 12 December 2017

DOI:https://doi.org/10.1103/PhysRevX.8.011018

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Entanglement production Optical quantum information processing Quantum entanglement Quantum gates Quantum information with atoms & light Quantum networks Quantum optics Quantum repeaters

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Stephan Welte^*, Bastian Hacker, Severin Daiss, Stephan Ritter^†, and Gerhard Rempe

Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany

^*To whom correspondence should be addressed. stephan.welte@mpq.mpg.de
^†Present address: TOPTICA Photonics AG, Lochhamer Schlag 19, 82166 Gräfelfing, Germany.

Popular Summary

The construction of a large-scale quantum network is a central goal in the field of quantum communication. The idea is that qubits (the quantum equivalent of a digital bit) in distant network nodes communicate with each other via propagating photons. Among many possibilities, this would allow for secure communication, ultimately on a global scale. Beyond the capability to send and retrieve single photons, such a network is based on the ability to process quantum information at each node. Our experiment demonstrates an important step towards this long-standing goal: the realization of a quantum gate by means of an optical photon propagating in a network channel.

Quantum gates are basic building blocks of a quantum computer, just as classical logic gates are the building blocks of a classical computer. In our experiment, the gate is performed between two neutral atoms trapped between highly reflecting mirrors forming a cavity. Usually, neutral atoms hardly interact with each other, but a single optical photon reflected off the cavity couples them. This allows one atom to change the state of the other atom in a controlled way. The gate mechanism is very powerful and facilitates, for example, the construction of a quantum repeater node for entanglement distribution over large distances.

Our mechanism is also applicable in other platforms for quantum information processing such as superconducting qubits or nitrogen vacancy centers, and it might therefore become a valuable tool in various fields of quantum communication and quantum computation.

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Vol. 8, Iss. 1 — January - March 2018

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Figure 1
Schematic representation of the setup. Two ${}^{87}{Rb}$ atoms are trapped at the center of a cavity with asymmetric mirror transmissions. Photons impinge on the mirror with higher transmission and are reflected. The inset on the upper left-hand side shows a simplified level scheme of the atoms with the two ground states $| ↓ ⟩$ , $| ↑ ⟩$ encoding the qubit and the excited state $| e ⟩$ . The cavity is tuned to the $| ↑ ⟩ \leftrightarrow | e ⟩$ transition. The inset on the upper right shows a fluorescence image of two trapped atoms in the cavity.
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Figure 2
Parity oscillations and populations of the entangled state produced by the gate and a subsequent $π / 4$ rotation. The populations ${\tilde{P}}_{↑ ↑}$ (blue squares), ${\tilde{P}}_{↑ ↓} + {\tilde{P}}_{↓ ↑}$ (red circles), and ${\tilde{P}}_{↓ ↓}$ (green diamonds) oscillate as a function of the phase of the analysis pulse $ϕ$ , which is scanned from 0 to $2 π$ . They yield the parity $Π (ϕ)$ , which we fitted with a sine of variable offset, phase, and amplitude. The values for the populations $P$ on the right-hand side come from a measurement without an analysis pulse. The overlap with the maximally entangled state $| Φ^{-} ⟩$ inferred from this data is $F = 76 (2) %$ . Error bars are statistical standard deviations of the mean within each bin. The slight offset in the phase is due to a residual two-photon Raman-laser detuning of $\pm 3 kHz$ .
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Figure 3
Fidelities of the experimentally generated states in the Bell basis. (a) Bar diagram of the fidelities of the four Bell states used as an input for our gate. (b) Measured fidelities of the two-atom states resulting from the gate operation on these input states. Error bars are statistical standard deviations of the mean. The truth tables for ideal input states and gate operations are shown as transparent bars for comparison.
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Figure 4
Complete quantum circuit diagram depicting initialization, preparation of Bell basis states, the two-atom gate, analysis state rotation, and final state detection. Rotations ( $R$ ) have a subscript indicating the rotation axis $x$ ( $| ↑ ⟩ + | ↓ ⟩$ ) or $y$ ( $| ↑ ⟩ + i | ↓ ⟩$ ) and a superscript denoting the rotation angle. The two techniques for state detection are labeled transmission and fluorescence, respectively. Whenever the result of an atomic state detection or a photon polarization measurement does not yield the desired result (OK), the protocol is restarted from the beginning. Initialization with parallel states allows us to prepare the triplet Bell states $| Ψ^{+} ⟩$ and $| Φ^{\pm} ⟩$ as gate input. The singlet state $| Ψ^{-} ⟩$ is prepared after initialization with an incoherent mixture of antiparallel states described by a density matrix $\frac{1}{2} (| ↑ ↓ ⟩ ⟨ ↑ ↓ | + | ↓ ↑ ⟩ ⟨ ↓ ↑ |)$ . The photon reflection with an antidiagonal ( $| A ⟩$ ) polarization realizes a Toffoli gate with an inversion of the photonic qubit. Experimentally, this means that the polarization of the reflected photon is flipped to $| D ⟩$ in all cases except the one where both atoms occupy $| ↓ ⟩$ . The dashed box in the Bell basis generation section is optional and needed only when transforming $| Ψ^{+} ⟩$ to $| Φ^{\pm} ⟩$ . Various two-atom states $| Ψ^{in} ⟩$ are prepared as gate input, then processed by the two-atom gate, and the result $| Ψ^{out} ⟩$ is characterized by state detection in a two-atom basis set by a preceding analysis rotation. The dashed box in the analysis section is optional. For a measurement of the populations $P_{i, j}$ it is omitted while for a measurement of the populations ${\tilde{P}}_{i, j}$ , with $i, j \in {↓, ↑}$ , it is applied.
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Figure 5
Parity signals of input and output states of the cnot gate. The left-hand column shows $Π (ϕ)$ for all four prepared Bell states used as input states for the gate. The right-hand column shows the respective parity signals after the gate. While the states $| Ψ^{\pm} ⟩$ remain basically unchanged by the gate operation, one can observe the swap $| Φ^{\pm} ⟩ \to | Φ^{\mp} ⟩$ as a $π / 2$ phase flip in the respective parity oscillation signal. Error bars are statistical standard errors of each data point. The solid lines are fitted sine curves with free offset, amplitude, and phase, which are used to compute the fidelities.
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