Figure 1

Measurement of a differential phase shift. An (upper) mode $a_1$ in a coherent state $|\alpha ⟩$ and a (lower) mode $a_2$ in an arbitrary pure state $|\chi ⟩$ are incident on a $50:50$ beam splitter, which performs the unitary transformation $B$ of Eq. (1). After the beam splitter, phase shifts ${\phi }_1$ and ${\phi }_2$ are imposed in the two arms; the action of the phase shifters is contained in the unitary operator $U$ of Eq. (2). Finally, a measurement is made to detect the phase shifts. When the measurement is pushed beyond a second $50:50$ beam splitter, the result is a Mach-Zehnder interferometer, which is sensitive only to the differential phase shift ${\varphi }_d={\phi }_1-{\phi }_2$.Reuse & Permissions