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arXiv:quant-ph/0304188 · Optics Letters

Atomic qubit manipulations with an electro-optic modulator

P. J. Lee, B. B. Blinov, K. Brickman, Louis Deslauriers, M. J. Madsen, R. Miller, D. L. Moehring, D. Stick, C. Monroe

Published Sep 1, 2003• 36 citations
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Abstract

We report new techniques for driving high-fidelity stimulated Raman transitions in trapped-ion qubits. An electro-optic modulator induces sidebands on an optical source, and interference between the sidebands allows coherent Rabi transitions to be efficiently driven between hyperfine ground states separated by 14.53 GHz in a single trapped 111Cd+ ion.

DOI
10.1364/ol.28.001582

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We report new techniques for driving high-fidelity stimulated Raman transitions in trapped-ion qubits. An electro-optic modulator induces sidebands on an optical source, and interference between the sidebands allows coherent Rabi transitions to be efficiently driven between hyperfine ground states separated by 14.53 GHz in a single trapped 111Cd+ ion.
Single- and multi-qubit operations for trapped ion hyperfine or Zeeman qubits are typically implemented by continuous-wave lasers driving stimulated Raman transitions. Here we report two distinct regimes for driving these transitions with mode-locked pulsed lasers instead of cw systems. In the resolved-sideband regime, multiple pulses from a mode-locked laser constructively accumulate transition amplitude to drive the gate. In the regime where the pulse train is shorter than the oscillation period of motional modes, the mode spectrum is unresolvable and all allowed sidebands are driven simultaneously. We demonstrate a single qubit gate in about 50 ps in this regime, and discuss extensions to multi-qubit gates.
The authors design and implement a laser system using novel phase modulation and highly dispersive element techniques for realizing high-fidelity control over atomic hyperfine states, which are useful as qubits in quantum information processing. This approach is demonstrated in a neutral 87{}^{87}87Rb atomic system and could also be applied to trapped-ion systems.
Quantum computers are typically composed of an array of two-level systems, or qubits, encoded in some information carrier, such as an electron, photon, or quantized circuit. The size of this array is restricted by finite access to resources like laser power, cooling capacity, and control lines for trapping and manipulation. Under these constraints, the system's processing power can be increased by using more energy levels per information carrier, but common techniques for qubit control provide only limited connectivity between these additional states. We experimentally demonstrate transitions between electronic angular momentum states with a difference in magnetic quantum numbers $Δ\mathrm{m_J} = $ 3, 4, and 5 via resonant four- and six-photon stimulated Raman transitions in a single trapped atom. Derivation of the corresponding Rabi frequencies, which are verified experimentally, follows the standard treatment of two-photon transitions including the adiabatic elimination of intermediate states. Finally, we discuss pathways to increase the observed multi-photon transition fidelities to >99.99%>99.99\%>99.99%, providing a tool for efficient, high-fidelity control of qudits and single-atom logical qubits.
Two phase-coherent Raman laser beams with a frequency offset of 6.835 GHz were generated by sideband injection-locking technique. A master diode laser was phase-modulated at 6.835 GHz by a fiber electro-optic modulator. A slave diode was injection-locked to the -1 sideband of the phase-modulated beam, and another diode was locked to the master laser carrier. This method produced stable and spatially separated Raman lasers with a large frequency shift range (>180 MHz). The relative linewidth of these two beams was ∼1 Hz, and the unwanted carrier mode was suppressed down to -24 dB. Stimulated Raman transitions and Ramsey fringes were driven by Raman lasers in a cold atomic beam.
We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a 9Be+^{9}{\mathrm{Be}}^{+}9Be+ qubit ion is mapped to a 25Mg+^{25}{\mathrm{Mg}}^{+}25Mg+ readout ion using laser-driven Raman transitions. By partitioning the 9Be+^{9}{\mathrm{Be}}^{+}9Be+ ground-state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. We demonstrate combined readout and back-action errors for the two subspaces of ${1.2}_{\ensuremath{-}0.6}^{+1.1}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and ${0}_{\ensuremath{-}0}^{+1.9}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ with 68% confidence while avoiding decoherence of spectator qubits due to stray resonant light that is inherent to direct fluorescence detection.