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arXiv:0907.0336 · Physical Review A

Single-nuclear-spin cavity QED

Makoto Takeuchi, Nobuyuki Takei, Kodai Doi, Peng Zhang, Masahito Ueda, Mikio Kozuma

Published Jun 9, 2010• 12 citations
arXivHTMLPDF

Abstract

We constructed a cavity QED system with a diamagnetic atom of $^{171}\mathrm{Yb}$ and performed projective measurements on a single nuclear spin. Since Yb has no electronic spin and has $1/2$ nuclear spin, the procedure of spin polarization and state verification can be dramatically simplified compared with the pseudo-spin-$1/2$ system. By enhancing the photon emission rate of the ${}^{1}{S}_{0}$-${}^{3}{P}_{1}$ 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.

DOI
10.1103/physreva.81.062308

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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 Tmeas=30\ensuremathμs{T}_{\mathrm{meas}}=30 \mathrm{\ensuremath{\mu}}\mathrm{s}Tmeas​=30\ensuremathμs. 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 \ensuremathδ∣\ensuremathβ∣2\ensuremath⩽2\ifmmode×\else\texttimes\fi10\ensuremath−2\ensuremath{\delta}|\ensuremath{\beta}|{}^{2}\ensuremath{\leqslant}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\ensuremathδ∣\ensuremathβ∣2\ensuremath⩽2\ifmmode×\else\texttimes\fi10\ensuremath−2. Fast measurement on a long-lived qubit is key to the realization of large-scale one-way quantum computing.
Projective measurement of single electron and nuclear spins has evolved from a gedanken experiment to a problem relevant for applications in atomic-scale technologies like quantum computing. Although several approaches allow for detection of a spin of single atoms and molecules, multiple repetitions of the experiment that are usually required for achieving a detectable signal obscure the intrinsic quantum nature of the spin's behavior. We demonstrated single-shot, projective measurement of a single nuclear spin in diamond using a quantum nondemolition measurement scheme, which allows real-time observation of an individual nuclear spin's state in a room-temperature solid. Such an ideal measurement is crucial for realization of, for example, quantum error correction protocols in a quantum register.
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.
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.
Cavity quantum electrodynamic systems hosted in photonic integrated circuits are being explored as a potential platform for realizing quantum computers, owing to their compact size and scalability. The qubits can be encoded in the electronic states of a localized defect centre in some otherwise uniform host material that comprises a microscopic optical cavity. A particular defect centre of much recent interest is the ⁷⁷Se⁺ donor in silicon, which has a dipole-allowed transition at 2.9 μm. The ground state of the transition is split due to a hyperfi ne interaction with the donor's nuclear spin, resulting in long-lived singlet and triplet states, separated by an energy of 6.87 μeV. These two states can be used to encode the states of a qubit. The fundamental building block of the photonic integrated circuit quantum computing platform involves placing the donor in an optical microcavity with a resonance frequency tuned to the transition frequency of only the singlet or triplet state to the excited state. The quantum state of the spin qubit then controls the transmitted and reflected photon statistics of the cavity in such a way that single photon detectors located in waveguides coupled to the qubit-containing cavities can be used to measure and control the spin state of the qubits via projective measurements. To entangle more than one qubit with high fidelity, photon loss must be minimized, a quantum engineering task that requires a rigorous treatment of open quantum systems. In this thesis, we develop a scattering-matrix based formalism to analyze the photon statistics of multiple defect centres embedded in microcavities evanescently coupled to waveguides. This formalism is used to quantify the properties of a single ⁷⁷Se⁺ donor in a photonic crystal cavity with an experimentally-accessible quality factor. More generally, we look at ensembles of atoms in cavities subject to inhomogenous broadening and dipole-dipole interactions. Modelling ensembles of ⁷⁷Se⁺ donors enables us to study and characterize these systems before site-selective single impurity implantation techniques are perfected.