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arXiv:quant-ph/9807085

Quantum synthesis of 3D vibrational states of trapped ions

B. Hladký, G. Drobný, Vladimír Bužek

Published Jul 30, 1998• 0 citations
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Abstract

A universal algorithm for a deterministic preparation of arbitrary three--mode bosonic states is introduced. In particular, we consider preparation of entangled quantum states of a vibrational motion of an ion confined in a 3D trapping potential. The target states are established after a proper sequence of laser stimulated Raman transitions. Stability of the algorithm with respect to a technical noise is discussed and the distance (fidelity) of outputs with respect to target states is studied.

DOI
10.48550/arxiv.quant-ph/9807085

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A universal algorithm for a deterministic preparation of arbitrary three--mode bosonic states is introduced. In particular, we consider preparation of entangled quantum states of a vibrational motion of an ion confined in a 3D trapping potential. The target states are established after a proper sequence of laser stimulated Raman transitions. Stability of the algorithm with respect to a technical noise is discussed and the distance (fidelity) of outputs with respect to target states is studied.
A scheme is proposed to generate an arbitrary entangled state of the two-dimensional vibrational motion of a trapped ion. In the scheme the ion is excited by a sequence of laser pulses tuned to the appropriate vibrational sidebands. In order to generate a pure state with upper phonon numbers M and N in the X and Y directions, respectively, we require no more than (M+2)(N+1)(M+2)(N+1)(M+2)(N+1) operations.
We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We show that the method can be extended to realization of entangled coherent states for three vibrational modes of an ion in a three-dimensional anisotropic trap.
We consider a trapped ion with a quantized center-of-mass motion in 2D trap potential. With external laser fields the effective (non)linear coupling of two orthogonal vibrational modes can be established via stimulated Raman transition. Nonclassical vibrational states such as squeezed states or two-mode entangled states (Schroedinger cat-like states) can be generated. When the vibrational modes are entangled with internal energy levels the Greenberger-Horne-Zeilinger (GHZ) states can be prepared.