Chemistry - Squeezed coherent state

In physics, a squeezed coherent state is every state in the Hilbert space of quantum mechanics that saturates the uncertainty principle (the inequality becomes equality):

$\Delta x \Delta p = \frac{\hbar}2$

The simplest such state is the ground state of the quantum harmonic oscillator, namely $|0\rangle$ . A coherent state is a slight generalization. However the most general wavefunction that satisfies the identity above is the following squeezed coherent state (we work in units with $\hbar=1$ )

$\psi(x) = C\,\exp\left(-\frac{(x-x_0)^2}{2 w_0^2} + i p_0 x\right)$

where $C, x 0, w 0, p 0$ are constants (a normalization constant, the center of the wavepacket, its width, and its average momentum). The new feature relative to a coherent state is the free value of the width $w 0$ , which is the reason why the state is called "squeezed".

The squeezed state above is an eigenstate of a linear operator

$\hat x + i\hat p w_0^2$

and the corresponding eigenvalue equals $x_0+ip_0 w_0^2$ . In this sense, it is a generalization of the ground state as well as the coherent state.

Various squeezed coherent states, generalized to the case of many degrees of freedom, are used in various calculations in quantum field theory, for example Unruh effect and Hawking radiation (generally: particle production in curved backgrounds).

External links

An introduction to quantum optics of the light field

Squeezed coherent state

See also

External links