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arXiv:physics/0212040 · Physical Review Letters

Precision Measurement and Compensation of Optical Stark Shifts for an Ion-Trap Quantum Processor

Hartmut Häffner, S. Gulde, Mark Riebe, Gavin P. T. Lancaster, Christoph Becher, Jürgen Eschner, Ferdinand Schmidt‐Kaler, R. Blatt

Published Apr 9, 2003• 146 citations
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Abstract

Using optical Ramsey interferometry, we precisely measure the laser-induced ac-Stark shift on the S(1/2)-D(5/2) "quantum bit" transition near 729 nm in a single trapped 40Ca+ ion. We cancel this shift using an additional laser field. This technique is of particular importance for the implementation of quantum information processing with cold trapped ions. As a simple application we measure the atomic phase evolution during a n x 2 pi rotation of the quantum bit.

DOI
10.1103/physrevlett.90.143602

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Using optical Ramsey interferometry, we precisely measure the laser-induced ac-Stark shift on the S(1/2)-D(5/2) "quantum bit" transition near 729 nm in a single trapped 40Ca+ ion. We cancel this shift using an additional laser field. This technique is of particular importance for the implementation of quantum information processing with cold trapped ions. As a simple application we measure the atomic phase evolution during a n x 2 pi rotation of the quantum bit.
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 $7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ during a $\ensuremath{\pi}/2$ rotation operation.
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.
Quantum information processing is performed with single trapped Ca(+) ions, stored in a linear Paul trap and laser-cooled to the ground state of their harmonic quantum motion. Composite laser-pulse sequences were used to implement SWAP gate, phase gate and controlled-NOT gate operations. Stark shifts on the quantum-bit transitions were precisely measured and compensated. For a demonstration of quantum information processing, a Deutsch-Jozsa algorithm has been implemented using two quantum bits encoded on a single ion.
We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of Sr+{\mathrm{Sr}}^{+}Sr+ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. ac Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminating the need for an additional laser. Quantum process tomography is implemented on atomic and motional states by use of conditional pulse sequences. With these techniques, we demonstrate a Cirac-Zoller controlled-not gate in a single ion with a mean fidelity of 91(1)91(1)%91(1).
Abstract For the first time, we experimentally determine the infrared magic wavelength for the 40Ca+ 4 s 2 S 1 / 2 → 3 d 2 D 5 / 2 electric quadrupole transition by observation of the light shift canceling in 40Ca+ optical clock. A ‘magic’ magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9) nm, which is not only in good agreement with theoretical predictions (‘Dirac–Fock plus core polarization’ method) but also more precise by a factor of about 300. Using this measured magic wavelength, we also derive the differential static polarizability to be −44.32(32) a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of 40Ca+ optical clock.
We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, and we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mechanisms. Finally, we employ lattice-induced phase shifts for inferring the variation of the ion position over the 157 μm range along the trap axis at accuracies of better than 6 nm.