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Optical Fiber Communication Conference

Observation of Long Decoherence Times in a Quantum Logic Gate using Trapped Ba137 Ions

Ralph G. DeVoe, Christian Kurtsiefer

Published Jan 1, 2001• 0 citations
Publisher

Abstract

We have measured a coherence lifetime > 1 millisecond for the phonons in a Cirac-Zoller quantum logic gate using the Ba137 ion. The microtrap of 80 microns radius does not show an anomalously fast decay.
DOI
10.1364/icqi.2001.pa37

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Summary form only given. Trapped ion quantum logic gates following the model of Cirac and Zoller have been constructed by the NIST and Innsbrueck groups using /sup 9/Be/sup +/ and /sup 40/Ca/sup +/ ions respectively. We are operating a new quantum logic gate using the /sup 137/Ba/sup +/ ion confined in a microscopic trap of 80 microns radius. Raman cooling to the ground state, with N < 1, is shown by the asymmetric sidebands shown. We have measured the decoherence time of a such a cooled phonon mode to be greater than 1 millisecond, which indicates that the anomalously fast decays seen by the NIST group is not dominant here.
We demonstrate long-lived coherence in internal hyperfine states of a single \Ca{43} trapped-ion qubit $[T_2=1.2(2)\s]$, and in external motional states of a single \Ca{40} trapped-ion qubit $[T_2'=0.18(4)\s]$, in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state T2T_2T2​ time that we observe in \Ca{43}, which has not previously been used as a trapped-ion qubit, is about one thousand times longer than that of physical qubits based on \Ca{40} ions. Using a single spin-echo pulse to ``re-phase'' the internal state, we can detect no decoherence after 1\s, implying an effective coherence time $T_2^{\mbox{\tiny SE}} \gtish 45\s$. This compares with timescales in this trap for single-qubit operations of \ish 1\us, and for two-qubit operations of \ish 10\us.
The intrinsic decoherence from vibrational coupling of the ions in the Cirac-Zoller quantum computer [Phys. Rev. Lett. 74, 4091 (1995)] is considered. Starting from a state in which the vibrational modes are at a temperature TTT, and each ion is in a superposition of an excited and a ground state, an adiabatic approximation is used to find the inclusive probability P(t)P(t)P(t) for the ions to evolve as they would without the vibrations, and for the vibrational modes to evolve into any final state. An analytic form is found for P(t)P(t)P(t) at T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0, and the decoherence time is found for all TTT. The decoherence is found to be quite small, even for 1000 ions.