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What is a general expression for a symmetric $N$-mode beam splitter?
It seems the matrix you want is just the Fourier matrix. Thus, if $\alpha^{2\pi i/N}$ so that $\alpha^N=1$, then
\begin{align}
\frac{1}{\sqrt{N}}\left(
\begin{array}{ccccc}
1&1&1&\ldots&...
- 45k
1
vote
Accepted
Applying a phase shift to a coherent state vs a phase-space rotation (Mach-Zhender)
It is the first case: The MZ produces
$$ |\alpha\rangle\rightarrow \left| \frac{1}{\sqrt{2}} \exp(i\phi)\alpha \right\rangle . $$
After the last beam splitter you then get
$$ |\alpha_{out}\rangle = \...
- 14.2k
1
vote
Accepted
What does a beam splitter look like in path-encoded notation for at most one photon?
To leave the vacuum unchanged, you need to put a $\sqrt{2}$ in the top left corner.
- 19.8k
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