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arXiv:quant-ph/0103140 · Physical Review Letters

Light-Shift-Induced Quantum Gates for Ions in Thermal Motion

Daniel Jonathan, Martin Bodo Plenio

Published Sep 4, 2001• 83 citations
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Abstract

An effective interaction between trapped ions in thermal motion can be generated by illuminating them simultaneously with a single laser resonant with the ionic carrier frequency. The ac Stark shift induces simultaneous "virtual" two-phonon transitions via several motional modes. Within a certain laser intensity range these transitions can interfere constructively, resulting in a relatively fast, heating-resistant two-qubit logic gate.

DOI
10.1103/physrevlett.87.127901

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An effective interaction between trapped ions in thermal motion can be generated by illuminating them simultaneously with a single laser resonant with the ionic carrier frequency. The ac Stark shift induces simultaneous "virtual" two-phonon transitions via several motional modes. Within a certain laser intensity range these transitions can interfere constructively, resulting in a relatively fast, heating-resistant two-qubit logic gate.
We present an alternative scheme for the generation of a two-qubit quantum gate interaction between laser-cooled trapped ions. The scheme is based on the ac Stark shift (light shift) induced by laser light resonant with the ionic transition frequency. At specific laser intensities, the shift of the ionic levels allows the resonant excitation of transitions involving the exchange of motional quanta. We compare the performance of this scheme with respect to that of related ion-trap proposals and find that, for an experimental realization using traveling-wave radiation and working in the Lamb-Dicke regime, an improvement of over an order of magnitude in the gate switching rate is possible.
We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.
A single 40 Ca + -ion is trapped and laser-cooled to its motional ground state. Laser radiation which couples off-resonantly to a motional sideband of the ion's S 1/2 to D 5/2 transition causes a phase shift proportional to the ion's motional quantum state | n ⟩. As the phase shift is conditional upon the ion's motion, we are able to demonstrate a universal 2-qubit quantum gate operation where the electronic target state { S , D } is flipped depending on the motional qubit state | n ⟩ = {|0⟩,|1⟩}. Finally, we discuss scaling properties of this universal quantum gate for linear ion crystals and present numerical simulations for the generation of a maximally entangled state of five ions.
We present a scheme utilizing position-dependent ac Stark shifts for doing quantum logic with trapped ions. By a proper choice of direction, position, and size, as well as power and frequency of a far-off-resonant Gaussian laser beam, specific ac Stark shifts can be assigned to the individual ions, making them distinguishable in frequency space. In contrast to previous all-optical based quantum gates with trapped ions, the present scheme enables individual addressing of single ions and selective addressing of any pair of ions for two-ion quantum gates, without using tightly focused laser beams. Furthermore, the decoherence rate due to off-resonant excitations can be made negligible as compared with other sources of decoherence.
Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86 (2001) 910], a procedure is proposed for one-step realizing quantum control phase gates with two trapped ions in thermal motion. It is shown that the scheme can also be used to create a new special type of entangled states, i.e., cluster states of many trapped ions. In the scheme the two-trapped ions are simultaneously excited by a single laser beam and the frequency of the laser beam is slightly off resonance with the first lower vibration sideband of the trapped ions. The distinct advantage of the scheme is that it does not use the vibrational mode as the data bus. Furthermore, our scheme is insensitive to both the initial motional state and heating (or decay) as long as the system remains in the Lamb–Dicke regime.