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Physical Review A

Measurement and compensation of optical Stark shifts for manipulating the terahertz-separated qubit in C40a+

Shinsuke Haze, Rekishu Yamazaki, Kenji Toyoda, Shinji Urabe

Published Nov 11, 2009• 5 citations
Publisher

Abstract

We describe the measurement and compensation of optical Stark shifts induced by an off-resonant pulse for manipulating the terahertz-separated states $3\text{ }{^{2}D}_{3/2}--3\text{ }{^{2}D}_{5/2}$, in a single trapped ${^{40}\text{C}\text{a}}^{+}$ ion. These states can be used as a quantum bit and are coupled by a two-photon stimulated Raman transition with phase-locked light sources bridged by an optical comb generator. The induced optical Stark shift is measured by Ramsey interferometry. We estimate the power ratio of Raman beams that cancel the level shift with an uncertainty of 170 Hz. A shift of the same amount as this uncertainty is estimated to give rise to an infidelity of approximately $7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ during a $\ensuremath{\pi}/2$ rotation operation.

DOI
10.1103/physreva.80.053408

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We describe the measurement and compensation of optical Stark shifts induced by an off-resonant pulse for manipulating the terahertz-separated states 3 2D3/2−−3 2D5/23\text{ }{^{2}D}_{3/2}--3\text{ }{^{2}D}_{5/2}3 2D3/2​−−3 2D5/2​, in a single trapped 40Ca+{^{40}\text{C}\text{a}}^{+}40Ca+ ion. These states can be used as a quantum bit and are coupled by a two-photon stimulated Raman transition with phase-locked light sources bridged by an optical comb generator. The induced optical Stark shift is measured by Ramsey interferometry. We estimate the power ratio of Raman beams that cancel the level shift with an uncertainty of 170 Hz. A shift of the same amount as this uncertainty is estimated to give rise to an infidelity of approximately 7.6\ifmmode×\else\texttimes\fi10\ensuremath−47.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}7.6\ifmmode×\else\texttimes\fi10\ensuremath−4 during a \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 rotation operation.
Relaxation of the off-diagonal density-matrix elements between the metastable 3 2D3/23\text{ }{^{2}D}_{3/2}3 2D3/2​ and 3 2D5/23\text{ }{^{2}D}_{5/2}3 2D5/2​ states in a single 40Ca+{^{40}\text{C}\text{a}}^{+}40Ca+, which are separated from each other by 1.82 THz, is studied experimentally by using the Ramsey method of separated oscillating fields. The two metastable states are connected with a stimulated Raman transition by using two infrared lasers, which are phase locked with their frequency difference bridged by an optical frequency comb. By performing Ramsey measurements for two Zeeman components of the stimulated Raman transition with different sensitivities to magnetic fields, the coherence is investigated quantitatively and the effect of magnetic-field fluctuations on that is evaluated. By using a spin-echo $\ensuremath{\pi}$ pulse in a Ramsey sequence which is effective for inhomogeneous broadening processes, a visibility decay time of 5.1 ms is obtained. This is more than twice as long as that for normal sequences. This work is an essential step for realization of a qubit using the two metastable states and demonstrates coherent manipulation of the internal states separated by around a terahertz using phase-locked light sources.
Abstract Encoding qubit states in the ground states of zero nuclear spin trapped ions has the advantages of both long coherence time and simple energy structure. High-fidelity quantum operations on trapped-ion qubits are often hindered by the differential AC-Stark shift induced by state manipulation lasers. Here we propose and demonstrate a novel compensation approach that addresses this challenge without introducing additional laser sources or sacrificing the power of the manipulation lasers. Our method leverages an existing optical transition to induce a counteracting light shift on one of the qubit states. We experimentally validate this scheme using a single trapped 40 Ca + ion. We show that the differential AC-Stark shift induced by 393 nm Raman lasers on a ground-state Zeeman qubit can be compensated by a detuned 729 nm shelving laser. Conversely, we also demonstrate compensation of the shift induced by a 729 nm laser on a ground-to-metastable qubit using one of the 393 nm Raman beams. In both cases, the residual differential shift is suppressed by approximately two orders of magnitude compared to the uncompensated case. This method is universally applicable to various trapped-ion systems, offering a practical and power-effcient route to mitigate a key source of gate infidelity.
We describe the results of stimulated Raman spectroscopy between the fine-structure levels, specifically 3d2D3/23{d}^{2}{D}_{3/2}3d2D3/2​ and 3d2D5/23{d}^{2}{D}_{5/2}3d2D5/2​ metastable states, in a single trapped 40Ca+{^{40}\text{C}\text{a}}^{+}40Ca+. Transitions between different Zeeman sublevels, split by an applied magnetic field, are clearly observed and the fine-structure level separation of $\ensuremath{\nu}=1\text{ }819\text{ }599\text{ }021\text{ }504\ifmmode\pm\else\textpm\fi{}37\text{ }\text{Hz}$ is determined. This measurement provides a direct observation of this level separation. From the spectroscopic data, a prospect of using the DDD-fine structure levels as a qubit for the quantum information processing is reviewed.
A critical dependence of the quantum interference on the optical Stark spectral shift produced when two-color laser pulses interact with a two-level medium is observed. The four-wave mixing of two ultrashort phase-locked $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ laser pulses propagating coherently in a two-level system depends on the pulses' relative phase. The phase dominating the efficiency of the coupling to the anti-Stokes Raman component is found to be determined by the sign of the total ac Stark shift induced in the system, in such a way that the phase sensitivity disappears precisely where the ac Stark effect due to both pulses is compensated. A coherent control scheme based on this phenomenon can be contemplated as the basis for nonlinear optical spectroscopy techniques.