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arXiv:1103.6050 · Journal of Physics B Atomic Molecular and Optical Physics

The quantum speed limit of optimal controlled phasegates for trapped neutral atoms

Michael H. Goerz, Tommaso Calarco, Christiane P. Koch

Published Jul 25, 2011• 71 citations
arXivHTMLPDF

Abstract

We study controlled phasegates for ultracold atoms in an optical potential. A shaped laser pulse drives transitions between the ground and electronically excited states where the atoms are subject to a long-range 1/ R 3 interaction. We fully account for this interaction and use optimal control theory to calculate the pulse shapes. This allows us to determine the minimum pulse duration, respectively, gate time T that is required to obtain high fidelity. We accurately analyse the speed limiting factors, and we find the gate time to be limited either by the interaction strength in the excited state or by the ground state vibrational motion in the trap. The latter needs to be resolved by the pulses in order to fully restore the motional state of the atoms at the end of the gate.

DOI
10.1088/0953-4075/44/15/154011

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We study controlled phasegates for ultracold atoms in an optical potential. A shaped laser pulse drives transitions between the ground and electronically excited states where the atoms are subject to a long-range 1/ R 3 interaction. We fully account for this interaction and use optimal control theory to calculate the pulse shapes. This allows us to determine the minimum pulse duration, respectively, gate time T that is required to obtain high fidelity. We accurately analyse the speed limiting factors, and we find the gate time to be limited either by the interaction strength in the excited state or by the ground state vibrational motion in the trap. The latter needs to be resolved by the pulses in order to fully restore the motional state of the atoms at the end of the gate.
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We use quantum optimal control to identify fast collision-based two-qubit SWAP\sqrt{\mathrm{SWAP}}SWAP​ gates in ultracold atoms. We show that a significant speedup can be achieved by optimizing the full gate instead of separately optimizing the merge-wait-separate sequence of the trapping potentials. Our optimal strategy does not rely on the atoms populating the lowest eigenstates of the merged potential, and it crucially includes the accumulation of quantum phases before the potentials are fully merged. Our analyses transcend the particular trapping geometry, but for comparison with previous works, we present systematic results for an optical lattice and find greatly improved gate durations and fidelities.
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