Pass-through Mach-Zehnder topologies for macroscopic quantum measurements

Several relatively small-scale experimental setups, aimed on prototyping of future laser gravitational-wave detectors and testing of new methods of quantum measurements with macroscopic mechanical objects, are under development now. In these devices, not devoted directly to the gravitational-wave detection, Mach-Zehnder interferometer with pass-through Fabry-Perot cavities in the arms can be used instead of the standard Michelson/Fabry-Perot one. The advantage of this topology is that it does not contain high-reflectivity end mirrors with multilayer coatings, which Brownian noise could constitute the major part of the noise budget of the Michelson/Fabry-Perot interferometers. We consider here two variants of this topology: the “ordinary” position meter scheme, and a new variant of the quantum speed meter.

Figure 1

Simplified scheme of the Michelson interferometer topology of laser gravitational-wave detectors. ITM: input test masses; ETM: end test masses.

Figure 2

The scheme of Mach-Zehnder/Fabry-Perot interferometer.

Figure 3

Generalized scheme of the dual linear quantum meter.

Figure 4

The scheme of the Mach-Zehnder/Fabry-Perot quantum speed meter.

Figure 5

Generalized scheme of the Mach-Zehnder/Fabry-Perot quantum speed meter.

Figure 6

Plots of $\frac{\mu {\Omega }^2}{\hslash }{S}_{\mathrm{sum}}$ [see Eq. (31)] for $m/M=0.01$ (solid lines) and $m/M\to 0$ (dots). For all plots, ${\mathcal{K}}_0=2$.

Figure 7

To calculation of the Mach-Zehnder/Fabry-Perot interferometer quantum noises.

Figure 8

One arm of the two-port speed meter: top—optical scheme, bottom—mechanical scheme.

Figure 9

To calculation of the Mach-Zehnder/Fabry-Perot speed meter quantum noises.