Generalized minimum-uncertainty squeezed states

Generalized squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing the properties of such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples we deal with nonlinear generalizations of quadrature squeezed states and deformed nonlinear squeezed states, which may be useful for optimized measurements at a reduced level of quantum noise. The realization of such states is studied for the quantized center-of-mass motion of a trapped ion.

Figure 1

(Color online) The $Q$ functions corresponding to the solutions of Eq. (16), with initial conditions ${\psi }_{\phi }\left(0\right)=0$ and ${\psi }_{\phi }^{\prime }\left(0\right)=e^{-i\phi }$, for $\beta =1$ and different values of $\lambda$. (a) $\lambda =0.2$ (b) $\lambda =0.5$ (c) $\lambda =1$ (d) $\lambda =2$ (e) $\lambda =5$ and (f) $\lambda =10$. Dark color corresponds to small values of $Q$ function and bright color corresponds to large values.

Figure 2

(Color online) The $Q$ functions corresponding to the solutions of Eq. (20) with the initial conditions ${\psi }_{\phi }\left(0\right)=1$, ${\psi }_{\phi }^{\prime }\left(0\right)=0$, and ${\psi }_{\phi }^{″}\left(0\right)=e^{-2i\phi }$ for $\beta =5$ and different values of $\lambda$. (a) $\lambda =0.2$ (b) $\lambda =0.5$ (c) $\lambda =1$ (d) $\lambda =2$ (e) $\lambda =5$ and (f) $\lambda =10$. Colors are used as in Fig. 1.

Figure 3

(Color online) Excitation scheme for the realizations of deformed nonlinear squeezed states.