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arXiv:0912.3477 · New Journal of Physics

Analysis of the entanglement between two individual atoms using global Raman rotations

Alpha Gaétan, Charles Evellin, Janik Wolters, Philippe Grangier, Tatjana Wilk, Antoine Browaeys

Published Jun 28, 2010• 23 citations

Abstract

Making use of the Rydberg blockade, we generate entanglement between two atoms individually trapped in two optical tweezers. In this paper, we detail the analysis of the data and show that we can determine the amount of entanglement between the atoms in the presence of atom losses during the entangling sequence. Our model takes into account states outside the qubit basis and allows us to perform a partial reconstruction of the density matrix describing the two-atom state. With this method, we extract the amount of entanglement between pairs of atoms still trapped after the entangling sequence and measure the fidelity with respect to the expected Bell state. We find a fidelity F pairs =0.74(7) for the 62% of atom pairs remaining in the traps at the end of the entangling sequence.

DOI: 10.1088/1367-2630/12/6/065040

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Making use of the Rydberg blockade, we generate entanglement between two atoms individually trapped in two optical tweezers. In this paper, we detail the analysis of the data and show that we can determine the amount of entanglement between the atoms in the presence of atom losses during the entangling sequence. Our model takes into account states outside the qubit basis and allows us to perform a partial reconstruction of the density matrix describing the two-atom state. With this method, we extract the amount of entanglement between pairs of atoms still trapped after the entangling sequence and measure the fidelity with respect to the expected Bell state. We find a fidelity F pairs =0.74(7) for the 62% of atom pairs remaining in the traps at the end of the entangling sequence.

We report the generation of entanglement between two individual 87Rb atoms in hyperfine ground states |F=1,M=1> and |F=2,M=2> which are held in two optical tweezers separated by 4 microm. Our scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. The entangled state is generated in about 200 ns using pulsed two-photon excitation. We quantify the entanglement by applying global Raman rotations on both atoms. We measure that 61% of the initial pairs of atoms are still present at the end of the entangling sequence. These pairs are in the target entangled state with a fidelity of 0.75.

We report on our recent progress on the manipulation of single rubidium atoms trapped in optical tweezers and the generation of entanglement between two atoms, each individually trapped in neighboring tweezers. To create an entangled state of two atoms in their ground states, we make use of the Rydberg blockade mechanism. The degree of entanglement is measured using global rotations of the internal states of both atoms. Such internal state rotations on a single atom are demonstrated with a high fidelity.

We report results of a ground-state entanglement protocol for a pair of Cs atoms separated by 6 μ m, combining the Rydberg blockade mechanism with a two-photon Raman transition to prepare the Bell state with a loss-corrected fidelity of 0.81(5), equal to the best demonstrated fidelity for atoms trapped in optical tweezers but without the requirement for dynamically adjustable interatomic spacing. Qubit state coherence is also critical for quantum information applications, and we characterise both ground-state and ground-Rydberg dephasing rates using Ramsey spectroscopy. We demonstrate transverse dephasing times ms and s for the qubit levels and achieve long ground-Rydberg coherence times of as required for implementing high-fidelity multi-qubit gate sequences where a control atom remains in the Rydberg state while applying local operations on neighbouring target qubits.

In a neutral-atom quantum computer, the qubits are individual neutral atoms trapped in optical tweezers. Excitations to Rydberg states form the basis for the entanglement procedure that is at the basis of multiqubit quantum gates. However, these Rydberg atoms are often antitrapped, leading to decoherence and atom loss. In this work, we give a quantum-mechanical description of the antitrapping loss rates and determine the recapture probability after Rydberg excitation, distinguishing between having the laser traps turned on and off. We find that ample time ($\ensuremath{\approx}30\phantom{\rule{0.16em}{0ex}}\mathrm{\textmu{}}\mathrm{s}$, in a

^{88}\mathrm{Sr}

system) is needed for the wave functions to expand out of the trap. Therefore, even with traps on, $\ensuremath{\approx}100$% recapture probabilities can be expected for times in which significant entanglement operations between atoms can be performed. We find that for two-dimensional radial traps with bosonic

^{88}\mathrm{Sr}

atoms, the time in which perfect recapture can be achieved is of the same order of magnitude for traps turned on and off.

We demonstrate the deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-not gate. Parity oscillation measurements reveal a Bell state fidelity of $F=0.58\ifmmode\pm\else\textpm\fi{}0.04$, which is above the entanglement threshold of

F=0.5

, without any correction for atom loss, and $F=0.71\ifmmode\pm\else\textpm\fi{}0.05$ after correcting for background collisional losses. The fidelity results are shown to be in good agreement with a detailed error model.