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

$$\begin{array}{rl}B(\theta ,\varphi ):=& \exp (z{a}_1^{†}{a}_2-z^{\ast }{a}_1{a}_2^{†})\\ =& \exp (\theta (e^{i\varphi }{a}_1^{†}{a}_2-e^{-i\varphi }{a}_1{a}_2^{†}))\\ =& \exp \left(i((Q\otimes P-P\otimes Q)\mathrm{Re}z+(Q\otimes Q+P\otimes P)\mathrm{Im}z)\right)\end{array}$$

in the number basis, where $z=\theta e^{i\varphi }$.