Adiabatic coherent control in the anharmonic ion trap: Numerical analysis of vibrational anharmonicities

Journal Article · Mon Feb 14 23:00:00 EST 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.022305· OSTI ID:21537122

Lei, Wang; Babikov, Dmitri ^[1]

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1. Chemistry Department, Marquette University, PO Box 1881, Milwaukee, Wisconsin 53201 (United States)

Anharmonicity of the quantized motional states of ions in a Paul trap can be utilized to address the state-to-state transitions selectively and control the motional modes of trapped ions coherently and adiabatically [Zhao and Babikov, Phys. Rev. A 77, 012338 (2008)]. In this paper we study two sources of the vibrational anharmonicity in the ion traps: the intrinsic Coulomb anharmonicity due to ion-ion interactions and the external anharmonicity of the trapping potential. An accurate numerical approach is used to compute energies and wave functions of vibrational eigenstates. The magnitude of the Coulomb anharmonicity is determined and shown to be insufficient for successful control. In contrast, anharmonicity of the trapping potential allows one to control the motion of ions very efficiently using the time-varying electric fields. Optimal control theory is used to derive the control pulses. One ion in a slightly anharmonic trap can be easily controlled. In the two- and three-ion systems the symmetric stretching mode is dark and cannot be controlled at all. The other two normal modes of the three-ion system can be controlled and used, for example, to encode a two-qubit system into the motional states of ions. A trap architecture that allows the necessary amount of vibrational anharmonicity to be achieved is proposed.

• OSTI ID: 21537122
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
CHARGED PARTICLES
COLLISIONS
CONTROL
EIGENSTATES
ELECTRIC FIELDS
ENERGY LEVELS
EXCITED STATES
FUNCTIONS
ION COLLISIONS
ION-ION COLLISIONS
IONS
MATHEMATICS
NUMERICAL ANALYSIS
OPTIMAL CONTROL
POTENTIALS
PULSES
TIME DEPENDENCE
TRAPPING
VIBRATIONAL STATES
WAVE FUNCTIONS