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arXiv:quant-ph/0403201

Hillery-type squeezing in fan-states

Truong, Minh Duc, Nguyen Ba An

Published Mar 29, 2004• 0 citations
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Abstract

We study the Hillery-type, i.e. $N$-th power, amplitude squeezing in the fan-state $| ξ;2k,f>_{F}$ characterized by $ξ\in \mathcal{C}$, $k=1,2,3,...$ and $f$ a nonlinear operator-valued function. We show that for a given $k$ there exists a critical $ξ_c$ such that for $0

DOI
10.48550/arxiv.quant-ph/0403201

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We study the Hillery-type, i.e. NNN-th power, amplitude squeezing in the fan-state ∣ξ;2k,f>F| ξ;2k,f>_{F}∣ξ;2k,f>F​ characterized by ξ∈Cξ\in \mathcal{C}ξ∈C, k=1,2,3,...k=1,2,3,...k=1,2,3,... and fff a nonlinear operator-valued function. We show that for a given kkk there exists a critical ξcξ_cξc​ such that for $0
Squeezing properties of the Hillery-type NNN-powered amplitude are investigated in the linear and nonlinear fan-state. For a given kkk, squeezing may appear to the even power N=2kN=2kN=2k and the number of directions along which the Nth-powered amplitude is squeezed is exactly equal to N,N,N, in both linear (the light field) and nonlinear (the vibrational motion of the trapped ion) fan-states.
We investigate the Nth order amplitude squeezing in the fan-state |ξ;2k,f> F which is a linear superposition of the 2k-quantum nonlinear coherent states. Unlike in usual states where an ellipse is the symbol of squeezing, a 4k-winged flower results in the fan state. We first derive the analytical expression of squeezing for arbitrary k, N, f and then study in detail the case of a laser-driven trapped ion characterized by a specific form of the nonlinear function f. We show that the lowest order in which squeezing may appear and the number of directions along which the amplitude may be squeezed depend only on k whereas the precise directions of squeezing are determined also by the other physical parameters involved. Finally, we present a scheme to produce such fan-states.