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, \(a\ket{\alpha} = \alpha \ket{\alpha}\).