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Mysteries, Puzzles, and Paradoxes in Quantum Mechanics

Entangled ions in thermal motion

Anders Søndberg Sørensen, Klaus Mølmer

Published Jan 1, 1999• 0 citations
Publisher

Abstract

We propose a method to entangle the internal states of traped ions via virtual vibrational excitations. Transition paths involving unpopulated, vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers, and our procedure is insensitive to the initial vibrational quantum state and to changes in the vibrational state occuring during operation.

DOI
10.1063/1.57857

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We propose a method to entangle the internal states of traped ions via virtual vibrational excitations. Transition paths involving unpopulated, vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers, and our procedure is insensitive to the initial vibrational quantum state and to changes in the vibrational state occuring during operation.
We present an alternative scheme to prepare entangled states of multiple trapped ions in thermal motion. In this scheme the vibrational degrees of freedom are only regarded as intermediate states and the ions exchange energy via the mediation of the vibration of the vibrational mode in coupling processes. The scheme is insensitive to both the initial vibrational state and heating if the system remains in the Lamb–Dicke regime. Since the effective Rabi frequency has a small dependence on the vibrational quantum number, the heating will have no direct effect on the internal state evolution. The scheme can also be used for the storage of entangled states.
This paper presents an alternative scheme to realize the storage of entangled states for multiple trapped ions including W state, Bell states, and GHZ states even with ions which exchange vibrational energy with a heating surrounding. Our scheme requires that the ions be simultaneously excited by two laser beams with different frequencies. In this scheme the vibrational degrees of freedom are only regarded as intermediate states and the ions exchange energy via the mediation of the vibration of the vibrational mode in coupling processes. The scheme is insensitive to both the initial vibrational state and heating if the system remains in the Lamb–Dicke regime. Since the effective Rabi frequency has a small dependence on the vibrational quantum number the heating will have no direct effect on the internal state evolution.
A robust scheme is proposed for producing maximally entangled states for many trapped ions in thermal motion. In the scheme the ions are simultaneously illuminated by two standing-wave laser fields. During the operation the phases of the lasers are inverted, which not only cancels the vibration-dependent parts in the evolution operator, but also suppresses direct off-resonant coupling of the internal states. Thus, our scheme allows the production of entanglement for hot trapped ions with laser fields of high intensity, which makes the entanglement speed extremely high.
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.