Squeeze state

A squeeze state $\ket0_\gamma$ is created with the squeeze operator $S(\gamma)$ applied to the ground state

\begin{align*} \ket{0}_\gamma = S(\gamma) \ket 0 = e^{-\frac{1}{2} (\gamma\adj a^2 - \gamma (a\adj)^2)} \ket 0. \end{align*}

A squeeze state is a base state of the harmonic oscillator, squeezed in phase space in the direction of the complex number $\gamma$ . The figure illustrates a squeeze state compared to the ground state and a coherent state. The squeeze factor $\gamma$ in the figure is real, so the state is squeezed in the $x$ direction.

We can derive the squeeze state by considering a ground state of one oscillator defined by $m_1,\omega_1$ , in another oscillator $m_2,\omega_2$ . This ground state of one oscillator is “squeezed” compared to the ground state of another.