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arXiv:1005.3584 · Physical Review A

Quantum-state tomography of a single nuclear spin qubit of an optically manipulated ytterbium atom

Atsushi Noguchi, Yujiro Eto, Masahito Ueda, Mikio Kozuma

Published Sep 9, 2011• 21 citations
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Abstract

A single Yb atom is loaded into a high-finesse optical cavity with a moving lattice, and its nuclear spin state is manipulated using a nuclear magnetic resonance technique. A highly reliable quantum state control with fidelity and purity greater than 0.98 and 0.96, respectively, is confirmed by the full quantum state tomography; a projective measurement with high speed $(500\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s})$ and high efficiency $(0.98)$ is accomplished using the cavity QED technique. Because a hyperfine coupling is induced only when the projective measurement is operational, the long coherence times (${T}_{1}=0.49$ s and ${T}_{2}=0.10$ s) are maintained.

DOI
10.1103/physreva.84.030301

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A single Yb atom is loaded into a high-finesse optical cavity with a moving lattice, and its nuclear spin state is manipulated using a nuclear magnetic resonance technique. A highly reliable quantum state control with fidelity and purity greater than 0.98 and 0.96, respectively, is confirmed by the full quantum state tomography; a projective measurement with high speed (500\ensuremathμs)(500\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s})(500\ensuremathμs) and high efficiency (0.98)(0.98)(0.98) is accomplished using the cavity QED technique. Because a hyperfine coupling is induced only when the projective measurement is operational, the long coherence times (T1=0.49{T}_{1}=0.49T1​=0.49 s and T2=0.10{T}_{2}=0.10T2​=0.10 s) are maintained.
We report the implementation of projective measurement on a single 1/2 nuclear spin of the (171)Yb atom by measuring the polarization of cavity-enhanced fluorescence. To obtain cavity-enhanced fluorescence having a nuclear-spin-dependent polarization, we construct a two-mode cavity QED system, in which two cyclic transitions are independently coupled to each of the orthogonally polarized cavity modes, by manipulating the energy level of (171)Yb. This system can associate the nuclear spin degrees of freedom with the polarization of photons, which will facilitate the development of hybrid quantum systems.
When an off-resonant light field is coupled with atomic spins, its polarization can rotate depending on the direction of the spins via Faraday rotation, which has been used for monitoring and controlling the atomic spins. We observed Faraday rotation by an angle of more than 10 deg for a single nuclear spin of 1/2 of a 171Yb^{171}\mathrm{Yb}171Yb atom in a high-finesse optical cavity. By employing the coupling between the single nuclear spin and a photon, we have also demonstrated that the spin can be projected or weakly measured through the projection of the transmitted single ancillary photon.
We constructed a cavity QED system with a diamagnetic atom of 171Yb^{171}\mathrm{Yb}171Yb and performed projective measurements on a single nuclear spin. Since Yb has no electronic spin and has 1/21/21/2 nuclear spin, the procedure of spin polarization and state verification can be dramatically simplified compared with the pseudo-spin-1/21/21/2 system. By enhancing the photon emission rate of the 1S0{}^{1}{S}_{0}1S0​-3P1{}^{3}{P}_{1}3P1​ transition, projective measurement is implemented for an atom with the measurement time of ${T}_{\mathrm{meas}}=30 \mathrm{\ensuremath{\mu}}\mathrm{s}$. Unwanted spin flip and dark counts of the detector lead to systematic error when the present technique is applied for the determination of diagonal elements of an unknown spin state, which is $\ensuremath{\delta}|\ensuremath{\beta}|{}^{2}\ensuremath{\leqslant}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$. Fast measurement on a long-lived qubit is key to the realization of large-scale one-way quantum computing.
We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+, with a measured coherence time of 2.5s2.5\phantom{\rule{0.3em}{0ex}}\mathrm{s}2.5s. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.
We demonstrate high-fidelity repetitive measurements of nuclear spin qubits in an array of neutral ytterbium-171 ( 171 Yb) atoms.We show that the qubit state can be measured with a spin-flip probability of 0.004(4) for a single tweezer and 0.012(3) averaged over the array.This is accomplished by high cyclicity of one of the nuclear spin qubit states with an optically excited state under a magnetic field of B = 58 G, resulting in a spin-flip probability of approximately 10 -5 per scattered photon during fluorescence readout.The performance improves further as ∼ 1/B 2 .The state discrimination fidelity is 0.993(4) with a state-averaged readout survival of 0.994(3), limited by off-resonant scattering to dark states.We combine our measurement technique with high-contrast rotations of the nuclear spin qubit via an ac magnetic field to explore two paradigmatic scenarios, including the noncommutativity of measurements in orthogonal bases, and the quantum Zeno mechanism in which measurements "freeze" coherent evolution.Finally, we employ real-time feedforward to repetitively and deterministically prepare the qubit in the +z or -z direction after initializing it in a different basis and performing a measurement in the Z basis.These capabilities constitute an important step towards adaptive quantum circuits with atom arrays.
We report on the realization of a fast, scalable, and high-fidelity qubit architecture, based on 171 Yb atoms in an optical tweezer array.We demonstrate several attractive properties of this atom for its use as a building block of a quantum information processing platform.Its nuclear spin of 1=2 serves as a long-lived and coherent two-level system, while its rich, alkaline-earth-like electronic structure allows for low-entropy preparation, fast qubit control, and high-fidelity readout.We present a near-deterministic loading protocol, which allows us to fill a 10 × 10 tweezer array with 92.73(8)% efficiency and a single tweezer with 96.0(1.4)%efficiency.In the future, this loading protocol will enable efficient and uniform loading of target arrays with high probability, an essential step in quantum simulation and information applications.Employing a robust optical approach, we perform submicrosecond qubit rotations and characterize their fidelity through randomized benchmarking, yielding 5.2ð5Þ × 10 -3 error per Clifford gate.For quantum memory applications, we measure the coherence of our qubits with T Ã 2 ¼ 3.7ð4Þ s and T 2 ¼ 7.9ð4Þ s, many orders of magnitude longer than our qubit rotation pulses.We measure spin depolarization times on the order of tens of seconds and find that this can be increased to the 100 s scale through the application of a several-gauss magnetic field.Finally, we use 3D Raman-sideband cooling to bring the atoms near their motional ground state, which will be central to future implementations of two-qubit gates that benefit from low motional entropy.