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arXiv:1107.4990 · Physical Review A

Coherence of a qubit stored in Zeeman levels of a single optically trapped atom

Wenjamin Rosenfeld, Jürgen Volz, Markus Weber, Harald Weinfurter

Published Aug 29, 2011• 17 citations
arXivHTMLPDF

Abstract

We experimentally investigate the coherence properties of a qubit stored in the Zeeman substates of the ${5}^{\phantom{\rule{0.16em}{0ex}}2}{S}_{1/2},\phantom{\rule{0.222222em}{0ex}}F=1$ hyperfine ground level of a single optically trapped ${}^{87}$Rb atom. Larmor precession of a single atomic spin-1 system is observed by preparing the atom in a defined initial spin state and then measuring the resulting state after a programmable period of free evolution. Additionally, by performing quantum-state tomography, maximum knowledge about the spin coherence is gathered. By using an active magnetic field stabilization and without application of a magnetic guiding field, we achieve transverse and longitudinal dephasing times of ${T}_{2}^{*}=75\ensuremath{-}150\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$ and ${T}_{1}>0.5\phantom{\rule{0.28em}{0ex}}\mathrm{ms},$ respectively. We derive the light-shift distribution of a single atom in the approximately harmonic potential of a dipole trap and show that the measured atomic spin coherence is limited mainly by residual position- and state-dependent effects in the optical trapping potential. The improved understanding enables longer coherence times, an important prerequisite for future applications in long-distance quantum communication and computation with atoms in optical lattices, or for a loophole-free test of Bell's inequality.

DOI
10.1103/physreva.84.022343

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We experimentally investigate the coherence properties of a qubit stored in the Zeeman substates of the 52S1/2,F=1{5}^{\phantom{\rule{0.16em}{0ex}}2}{S}_{1/2},\phantom{\rule{0.222222em}{0ex}}F=152S1/2​,F=1 hyperfine ground level of a single optically trapped 87{}^{87}87Rb atom. Larmor precession of a single atomic spin-1 system is observed by preparing the atom in a defined initial spin state and then measuring the resulting state after a programmable period of free evolution. Additionally, by performing quantum-state tomography, maximum knowledge about the spin coherence is gathered. By using an active magnetic field stabilization and without application of a magnetic guiding field, we achieve transverse and longitudinal dephasing times of T2∗=75\ensuremath−150\ensuremathμs{T}_{2}^{*}=75\ensuremath{-}150\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}T2∗​=75\ensuremath−150\ensuremathμs and T1>0.5ms,{T}_{1}>0.5\phantom{\rule{0.28em}{0ex}}\mathrm{ms},T1​>0.5ms, respectively. We derive the light-shift distribution of a single atom in the approximately harmonic potential of a dipole trap and show that the measured atomic spin coherence is limited mainly by residual position- and state-dependent effects in the optical trapping potential. The improved understanding enables longer coherence times, an important prerequisite for future applications in long-distance quantum communication and computation with atoms in optical lattices, or for a loophole-free test of Bell's inequality.
We investigate the interplay between Zeeman and light shifts in the transmission spectrum of an optically trapped, spin-polarized Rubidium atom. The spectral shape of the transmission changes from multiple, broad resonances to a single, narrow Lorentzian with a high resonant extinction value when we increase the magnetic field strength and lower the depth of the dipole trap. We present an experimental configuration well-suited for quantum information applications that enables not only efficient light-atom coupling, but also a long coherence time between ground state hyperfine levels.
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We demonstrate that the coherence of a single mobile atomic qubit can be well preserved during a transfer process among different optical dipole traps (ODTs). This is a prerequisite step in realizing a large-scale neutral atom quantum information processing platform. A qubit encoded in the hyperfine manifold of an ^{87}Rb atom is dynamically extracted from the static quantum register by an auxiliary moving ODT and reinserted into the static ODT. Previous experiments were limited by decoherences induced by the differential light shifts of qubit states. Here, we apply a magic-intensity trapping technique which mitigates the detrimental effects of light shifts and substantially enhances the coherence time to 225±21 ms. The experimentally demonstrated magic trapping technique relies on the previously neglected hyperpolarizability contribution to the light shifts, which makes the light shift dependence on the trapping laser intensity parabolic. Because of the parabolic dependence, at a certain "magic" intensity, the first order sensitivity to trapping light-intensity variations over ODT volume is eliminated. We experimentally demonstrate the utility of this approach and measure hyperpolarizability for the first time. Our results pave the way for constructing scalable quantum-computing architectures with single atoms trapped in an array of magic ODTs.
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We demonstrate an entirely new method to probe quantum measurement phenomena in semiconductor quantum dot (QD) spin qubits [1]. In addition to providing direct evidence for the quantum nature of solid state qubits, we show that our method has practical importance since it provides a completely alternative route for measuring ensemble and quantum dephasing times, T2* and T2, using only repeated projective measurements and without the need for coherent spin control. Our approach is based on measuring time-correlators of a spin qubit in an optically active QD beyond the second order. We utilize a quantum dot spin-storage structure to initialize a single electron spin in a quantum dot subject to a magnetic field applied in Voigt geometry through tunnel ionization and perform repeated projective measurements of the spin at times t1 and t2. This measurement is repeated, corresponding to ensemble averaging, and the resulting third-order time correlations reveals rich physics: For times t1 or t2 < T2* Larmor precession is observed which reveals the ensemble dephasing time T2*. Importantly, even though the time-correlators were obtained through averaging many measurements for times t1 and t2 > T2* oscillations are observed that decay with the dephasing time T2 and allow its determination even without the need for coherent spin control. Finally, combining the third-order time correlator with the second-order time correlator allows to demonstrate a violation of Leggett-Garg type inequalities for certain times providing clear evidence for the quantum nature of the quantum dot spin. [1] A. Bechtold et al. Phys. Rev. Lett. 117, 027402 (2016)
Summary form only given. We present experimental results that demonstrate a high degree of control over the spin state of an atom. The experiment is carried out on a sample of about 10/sup 7/ laser-cooled /sup 133/Cs atoms in their F=4 ground state hyperfine level released from a magneto-optical trap. Our method is to apply a static magnetic field B/sub 0/, a time-dependent transverse magnetic field B/sub x/(t), and a linearly polarized off-resonance laser field to the atoms. The Hamiltonian is H=-/spl mu//spl middot/B(t)+ M/sup 2//spl omega//sub E/|M><M|, where B(t)=B/sub 0/z+B/sub x/(t)x. B/sub 0/ induces a precession of the spins at the Larmor frequency /spl omega//sub L/=/spl mu//sub B/B/4/spl planck/. The second term in H arises from the laser field light shift; together with the static field B/sub 0/ it yields a finite anharmonic ladder of quantum states, labeled by the spin projection quantum number M=-F,...,F. Because of the anharmonicity, B/sub x/(t) induces motions of the spin that are not simply rotations of the initial state. Rather, through the application of quantum control theory, it is possible to find a pulse B/sub x/(t) that produces time evolution connecting arbitrary spin states.