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arXiv:1012.1724 · Physical Review Letters

Projective Measurement of a Single Nuclear Spin Qubit by Using Two-Mode Cavity QED

Yujiro Eto, Atsushi Noguchi, Peng Zhang, Masahito Ueda, Mikio Kozuma

Published Apr 22, 2011• 33 citations
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Abstract

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.

DOI
10.1103/physrevlett.106.160501

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•Jan 31, 2007•0 citations
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.
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.
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)(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.
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 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.
The goal of this project was to improve our control over nuclear spins in the solid state, and to extend this control to coupled electron-nuclear spins. Our key results are summarized below. 1. We extended the control techniques developed in liquid state NMR quantum information processing to the control of a three-qubit solid state NMR quantum information processor. 2. To explore multi-body spin dynamics and their sensitivity to decoherence, we have measured the decay of NMR multiple quantum coherence intensities in the presence and absence of the dipolar Hamiltonian, in a cubic and a one-dimensional spin system. 3. We also studied the transport of polarization in the one-dimensional fluoroapatite system, both experimentally and theoretically, and created special states in which the polarization is localized to the ends of the chain. This enables both universal Quantum Computing and Quantum Simulation in 1-D systems. 4. We devised a novel scheme for electron-nuclear quantum information processing that exploits the anisotropic hyperfine coupling. This scheme enables universal control over a 1-electron, N-nuclear spin system, addressing only a single electron spin transition. Not having to address the nuclear spins directly significantly speeds up the control. We designed and fabricated a pulsed electron spin resonance spectrometer, along with a cryogenic probe which we used to experimentally implement this scheme on a single crystal sample of irradiated malonic acid. 5. We demonstrated the role of nuclear spin dipolar diffusion in dynamic nuclear polarization (DNP) experiments, in dielectric samples with abundant nuclear spins. We achieved a 29Si polarization of 8.3% at 66 GHz and 1.1 K in single crystal P-doped, the highest ever reported, using DNP.