Flower-like squeezing in the motion of a laser-driven trapped ion

FLOWER-LIKE SQUEEZING IN THE MOTION OF A

LASER-DRIVEN TRAPPED ION

Due to quantum interference a superposition state may have properties qualitatively different from those of its component states (see, e.g. Refs. 1-8). For example, while coherent states are most classical states, their linear superpositions may exhibit various nonclassical behaviors. Inversely, an infinite superposition of Fock states with absolutely uncertain phases may result in a state with a definite certainty in phase.

The study of squeezed state has continuously progressed since its first introduc-tion in 1970⁹ because this state promises potential applications in communication networks, detecting extremely weak fields, waveguide tap, etc. (see, e.g. Ref. 10) and teleportation of entangled states.¹¹ Generalizations of squeezed states towards higher-order^12,13 and multi-mode¹⁴ -¹⁶ situations have also been made. Usually in an amplitude-squeezed state one quadrature phase reduces the quantum noise level below the standard quantum limit, i.e. squeezing occurs in one direction. Since the amplitude component along the squeezing direction could be exploited for practical applications more squeezing directions would be of physical relevance. In fact, in a recent paper¹⁷ multi-directional amplitude squeezing has been shown possible in the so called fan-state which is superposed from a finite number of multi-quantum nonlinear coherent states each of which is capable of possessing squeezing only in a single direction.

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