Demonstration of Displacement- and Frequency-Noise-Free Laser Interferometry Using Bidirectional Mach-Zehnder Interferometers

We have demonstrated displacement- and frequency-noise-free laser interferometry (DFI) by partially implementing a recently proposed optical configuration using bidirectional Mach-Zehnder interferometers (MZIs). This partial implementation, the minimum necessary to be called DFI, has confirmed the essential feature of DFI: the combination of two MZI signals can be carried out in a way that cancels displacement noise of the mirrors while maintaining gravitational-wave signals. The attained maximum displacement-noise suppression was 45 dB.

Figure 1

Schematic of one possible 2D optical configuration of a displacement-noise-free interferometer. Light beams which follow common paths (thick, thin) travel in opposite directions, and the four MZIs share the two beam splitters (BS1 and BS2). The motion of each folding mirror (FM) is sensed by two MZIs, and the motion of the beam splitters is sensed by all four MZIs.

Figure 2

The experimental setup of partial DFI. MZI 1 and MZI 2 share a common laser source and Mach-Zehnder interferometer parts. The scale of the MZI was about 4 m, for which purpose the optical paths of the MZI arms had to be folded several times on the optical table, which does not affect the DFI features in this experiment.

Figure 3

The response functions from displacement noise to output signals. Dashed-red and dotted-blue curves are response to single detector HPD1 and HPD2, giving almost identical response in amplitude while opposite in sign. Therefore, summation of these two signals gives cancellation of displacement noise. The suppression depends on a delicate tuning of the balance between two signals. Approximately 30 dB of suppression can be seen in a wide frequency band from 10 kHz to 300 MHz in the green curve, meanwhile, the orange curve shows maximum suppression exceeding 45 dB at around 25 MHz.

Figure 4

The response functions from simulated-GW inputs to output signals. HPD1 and HPD2 response show almost the same response again in amplitude, whereas the phase delays in the higher frequency band are essentially different from that of displacement noise, which is the very reason why the summed signal (DFI signal) remains GW sensitive as is shown in the solid-green curve.

Figure 5

The effects of the response functions of EOMs and HPDs on the DFI signal (solid-green curve in Fig. 4) were compensated by using the response function to single detector, shown in red dots. This corresponds to an intrinsic DFI (bidirectional MZIs for this experiment) response function to a simulated GW signal. The solid curve is a fitted DFI response giving reasonable fitting parameters.