# sf.utils.coherent_state¶

coherent_state(r, phi, basis='fock', fock_dim=5, hbar=2.0)[source]

Returns the coherent state

This can be returned either in the Fock basis,

$|\alpha\rangle = e^{-|\alpha|^2/2} \sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle$

or as a Gaussian:

$\mu = (\text{Re}(\alpha),\text{Im}(\alpha)),~~~\sigma = I$

where $$\alpha$$ is the displacement.

Parameters
• r (float) – displacement magnitude

• phi (float) – displacement phase

• basis (str) – If ‘fock’, calculates the initial state in the Fock basis. If ‘gaussian’, returns the vector of means and the covariance matrix.

• fock_dim (int) – the size of the truncated Fock basis if using the Fock basis representation

• hbar (float) – (default 2) the value of $$\hbar$$ in the commutation relation $$[\x,\p]=i\hbar$$

Returns

the coherent state

Return type

array