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Quantum dynamics simulator with the motional states of an ion in an anharmonic trap

par Santos, Ludovic ;Justum, Yves;Desouter-Lecomte, Michèle;Vaeck, Nathalie
Référence Conference on Cold Controlled Molecules and Ions (14-19/09/2014: Monté Verita, Suisse)
Publication Non publié, 2014-09-14

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Résumé :

Following a recent proposal [1], we theoretically illustrate the possibility of using the motional states of a Cd+ ion trapped in an anharmonic potential to realize a quantum dynamics simulator of a single-particle Schrödinger equation. The anharmonicity renders the states energetically non equidistant and allows the control of population transfer between states with an electromagnetic field.The simulated dynamics is discretized on spatial and temporal grids. The gate associated to an elementary evolution is estimated by the Split Operator formalism [2]. The radio-frequency field able to drive the corresponding unitary transformation among the qubit states encoded into the ion motional states is obtained by optimal control theory [3]. The field is unique for a given simulated potential. We also perform the computation of the field for the preparation of the initial simulated wave packet. This one needs to be adapted.The stability of the optimal electric fields driving the elementary evolution is checked by performing dissipative Lindblad dynamics [4-5] in order to consider fluctuations in the trap potential due to external fields [6].References[1] L. Wang and D. Babikov, J. Chemical Phys. 137, 064301 (2012).[2] M. D. Feit, Jr J. A. Fleck, and A. Steiger, J. Comput. Phys. 47, 412 (1982). [3] W. Zhu, J. Botina and H. Rabitz, J. Chem. Phys. 108, 1953 (1997).[4] G. Lindblad, Commun. Math. Phys. 48, 119 (1976).[5] W. Zhu and H. Rabitz, J. Chem. Phys. 118, 6751 (2003).[6] S. Schneider and G. J. Milburn, Phys. Rev. A 59, 3766 (1999).