qit.ho.displace¶
- qit.ho.displace(alpha, n=30)¶
Bosonic displacement operator.
- Parameters
alpha (complex) – displacement parameter
n (int) – truncation dimension
- Returns
displacement operator
- Return type
array[complex]
Returns the n-dimensional approximation for the bosonic phase space displacement operator
\[D(\alpha) := \exp\left(\alpha a^\dagger - \alpha^* a\right) = \exp\left( i \sqrt{2} \left(Q \: \im{\alpha} -P \: \re{\alpha}\right)\right)\]in the number basis. This yields
\[\begin{split}D^\dagger(\alpha) Q D(\alpha) &= Q +\sqrt{2} \: \re{\alpha} \: \mathbb{I},\\ D^\dagger(\alpha) P D(\alpha) &= P +\sqrt{2} \: \im{\alpha} \: \mathbb{I},\end{split}\]and thus the displacement operator displaces the state of a harmonic oscillator in phase space.