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arXiv:quant-ph/9801008 · Physical Review A

Quantum-state synthesis of multimode bosonic fields: Preparation of arbitrary states of two-dimensional vibrational motion of trapped ions

G. Drobný, B. Hladký, Vladimír Bužek

Published Sep 1, 1998• 20 citations
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Abstract

We present a universal algorithm for an efficient deterministic preparation of an arbitrary two-mode bosonic state. In particular, we discuss in detail preparation of entangled states of a two-dimensional vibrational motion of a trapped ion via a sequence of laser-stimulated Raman transitions. Our formalism can be generalized for multimode bosonic fields. We examine stability of our algorithm with respect to a technical noise.

DOI
10.1103/physreva.58.2481

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We present a universal algorithm for an efficient deterministic preparation of an arbitrary two-mode bosonic state. In particular, we discuss in detail preparation of entangled states of a two-dimensional vibrational motion of a trapped ion via a sequence of laser-stimulated Raman transitions. Our formalism can be generalized for multimode bosonic fields. We examine stability of our algorithm with respect to a technical noise.
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 present a scheme to generate an arbitrary two-dimensional quantum state of motion of a trapped ion. This proposal is based on a sequence of laser pulses, which are tuned appropriately to control transitions on the sidebands of two modes of vibration. Not more than (M+1)(N+1)(M+1)(N+1)(M+1)(N+1) laser pulses are needed to generate a pure state with a phonon number limit M and N.
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.
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.