[en] Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a Cd+ ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schrödinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolution operator corresponding to the time-dependent Schrödinger equation of the simulated system. The corresponding matrix can be estimated by any numerical algorithm. The radio-frequency field able to drive this unitary transformation among the qubit states of the ion is obtained by multi-target optimal control theory. The ion is assumed to be cooled in the ground motional state and the preliminary step consists in initializing the qubits with the amplitudes of the initial simulated wave packet. The time evolution of the localization probability at the grids points is then obtained by successive applications of the gate and reading out the motional state population. The gate field is always identical for a given simulated potential, only the field preparing the initial wave packet has to be optimized for different simulations. We check the stability of the simulation against decoherence due to fluctuating electric fields in the trap electrodes by applying dissipative Lindblad dynamics.
Disciplines :
Chemistry Physics
Author, co-author :
Santos, Ludovic; Université Libre de Bruxelles - ULB
Justum, Yves; Université Paris-Sud 11
Vaeck, Nathalie; Université Libre de Bruxelles - ULB
Desouter, Michèle ; Université de Liège > Département de chimie (sciences) > Département de chimie (sciences)
Language :
English
Title :
Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap
Publication date :
2015
Journal title :
Journal of Chemical Physics
ISSN :
0021-9606
eISSN :
1089-7690
Publisher :
American Institute of Physics, United States - New York
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