qit.ho.beamsplitter¶
- qit.ho.beamsplitter(theta, phi, n=30)¶
Bosonic beamsplitter operator.
- Parameters
theta (float) – rotation angle
phi (float) – phase angle
n (int) – truncation dimension
- Returns
beamsplitter operator
- Return type
array[complex]
Returns the n-dimensional approximation for the bosonic two-mode beamsplitter operator
\[\begin{split}B(\theta, \phi) :=& \exp\left(z a_1^\dagger a_2 -z^* a_1 a_2^\dagger\right)\\ =& \exp\left(\theta (e^{i\phi} a_1^\dagger a_2 -e^{-i\phi} a_1 a_2^\dagger)\right)\\ =& \exp\left(i \left((Q \otimes P - P \otimes Q) \re{z} + (Q \otimes Q + P \otimes P) \im{z} \right)\right)\end{split}\]in the number basis, where \(z = \theta e^{i \phi}\).