# sf.decompositions.mach_zehnder¶

mach_zehnder(m, n, internal_phase, external_phase, nmax)[source]

A two-mode Mach-Zehnder interferometer section.

This section is constructed by an external phase shifter on the input mode m, a symmetric beamsplitter combining modes m and n, an internal phase shifter on mode m, and another symmetric beamsplitter combining modes m and n.

The resulting matrix is

$\begin{split}M = i e^{i \phi_{i}/2} \left[\begin{matrix}\sin \left( \phi_{i}/2 \right) e^{i \phi_{e}} & \cos \left( \phi_{i}/2 \right) \\ \cos \left( \phi_{i}/2 \right) e^{i \phi_{e}} & - \sin \left( \phi_{i}/2 \right) \end{matrix}\right]\end{split}$
Parameters
• m (int) – mode number on which the phase shifters act

• n (int) – mode number which is combined with mode m by the beamsplitters

• internal_phase (float) – phase in between the symmetric beamsplitters

• external_phase (float) – phase acting before the first beamsplitter

• nmax (int) – maximum number of modes in the circuit

Returns

unitary matrix of the effective transformation the series of phaseshifters and beamsplitters.

Return type

array