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arXiv:1001.4600 · Physical Review A

Quantum gate using qubit states separated by terahertz

Kenji Toyoda, Shinsuke Haze, Rekishu Yamazaki, Shinji Urabe

Published Mar 24, 2010• 16 citations
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Abstract

A two-qubit quantum gate is realized using electronically excited states in a single ion with an energy separation on the order of a terahertz times the Planck constant as a qubit. Two phase-locked lasers are used to excite a stimulated Raman transition between two metastable states ${D}_{3/2}$ and ${D}_{5/2}$ separated by $1.82$ THz in a single trapped $^{40}\mathrm{Ca}$${}^{+}$ ion to construct a qubit, which is used as the target bit for the Cirac-Zoller two-qubit controlled NOT gate. Quantum dynamics conditioned on a motional qubit is clearly observed as a fringe reversal in Ramsey interferometry.

DOI
10.1103/physreva.81.032322

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A two-qubit quantum gate is realized using electronically excited states in a single ion with an energy separation on the order of a terahertz times the Planck constant as a qubit. Two phase-locked lasers are used to excite a stimulated Raman transition between two metastable states D3/2{D}_{3/2}D3/2​ and D5/2{D}_{5/2}D5/2​ separated by 1.821.821.82 THz in a single trapped ^{40}\mathrm{Ca}$${}^{+} ion to construct a qubit, which is used as the target bit for the Cirac-Zoller two-qubit controlled NOT gate. Quantum dynamics conditioned on a motional qubit is clearly observed as a fringe reversal in Ramsey interferometry.
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.
Realisation of controlled-NOT gate (CNOT) operation between two individual ions as a universal two-bit quantum gate based from the proposals of Cirac and Zoller, is presented. Two single /sup 40/Ca/sup +/ ions are held in a linear Paul trap and are individually addressed with focused laser beams. Superpositions of the S/sub 1/2 /and the D/sub 5/2/ long lived electronic states represent a qubit. A sequence of well suited laser pulses flips the state of the target ion conditional to the state of the control 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).
We present an alternative scheme to exactly implement one-qubit and two-qubit quantum gates with a single trapped cold ion driven by a travelling laser field. The internal degree of freedom of the ion acts as the target qubit and the control qubit is encoded by two Fock states of the external vibration of the ion. The conditions to realize these operations, including the duration of each applied laser pulse and Lamb-Dicke parameter, are derived. In our scheme neither the auxiliary atomic level nor the Lamb-Dicke approximation is required. The multiquantum transition between the internal and external degrees of freedom of the ion is considered.
A single 40Ca+ 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 S1/2 to D5/2 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.