qit.ho.coherent_state

qit.ho.coherent_state(alpha, n=30)

Coherent states of a harmonic oscillator.

Parameters

• alpha (complex) – displacement parameter

• n (int) – truncation dimension

Returns

coherent state

Return type

array[complex]

Returns the n-dimensional approximation to the coherent state $|\alpha ⟩$,

$$|\alpha ⟩:=D(\alpha )|0⟩=e^{-\frac{|\alpha {|}^2}{2}}\sum _{k=0}^{\mathrm{\infty }}\frac{{\alpha }^k}{\sqrt{k!}}|k⟩,$$

in the number basis. The coherent states are eigenstates of the annihilation operator, $a|\alpha ⟩=\alpha |\alpha ⟩$.