Development of a Displacement- and Frequency-Noise-Free Interferometer in a 3D Configuration for Gravitational Wave Detection

The displacement- and frequency-noise-free interferometer (DFI) is a multiple laser interferometer array for gravitational-wave detection free from both the displacement noise of optics and laser frequency noise. So far, partial experimental demonstrations of the DFI have been done in 2D table top experiments. In this Letter, we report the complete demonstration of a 3D DFI. The DFI consists of four Mach-Zehnder interferometers with four mirrors and two beam splitters The attained maximum suppression of the displacement noise of both mirrors and beam splitters was 40 dB at about 50 MHz. The nonvanishing DFI response to a gravitational wave was successfully confirmed using multiple electro-optic modulators and computing methods.

Figure 1

Optical topology of 3D DFI. The pairs of ${\mathrm{IFO}}_1$ and ${\mathrm{IFO}}_3$ and of ${\mathrm{IFO}}_2$ and ${\mathrm{IFO}}_4$ are counterpropagating to each other, constructing two bidirectional Mach-Zehnder interferometers (MZIs). Right and left bidirectional MZIs share the two beam splitters.

Figure 2

Schematic of the experiment. The octahedron is pushed over sideways to be set up on an optical table. ${\mathrm{IFO}}_1$ and ${\mathrm{IFO}}_3$ comprise one bidirectional MZI, and so do ${\mathrm{IFO}}_2$ and ${\mathrm{IFO}}_4$. EOM1 simulates mirror $C_1$ displacement and EOM2 and EOM3 simulate beam splitter $B$ displacement.

Figure 3

The overhead view of the experimental setup. HWP: half wave plate, QWP: quarter wave plate, FI: Faraday islator, BS: beam splitter, DCPD: DC photo detector. ${\mathrm{IFO}}_1$ ($A-C_1$, $D_1$, $-B$), ${\mathrm{IFO}}_2$ ($A-C_2$, $D_2$, $-B$), ${\mathrm{IFO}}_3$ ($B-C_1$, $D_1$, $-C$) and ${\mathrm{IFO}}_4$ ($B-C_2$, $D_2$, $-A$). The black-dashed line indicates the optical lever method for the alignment of 3D configuration.

Figure 4

The solid green line is the transfer function from EOM3 to $tt4$ as a reference, and the solid black line is the transfer function from EOM3 to the DFI signal. In the DFI channel, from 1 to 2 orders of magnitude of the cancellation were attained from 500 kHz to 200 MHz.

Figure 5

The orange dots are the simulated DFI response to the gravitational wave obtained by being measured and computed, the gray solid line is the DFI response predicted by Eq. (4). The simulated response agreed with the theory.