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 \(\ket{\alpha}\),

\[\ket{\alpha} := D(\alpha) \ket{0} = e^{-\frac{|\alpha|^2}{2}} \sum_{k=0}^\infty \frac{\alpha^k}{\sqrt{k!}} \ket{k},\]

in the number basis. The coherent states are eigenstates of the annihilation operator, \(a\ket{\alpha} = \alpha \ket{\alpha}\).