Broadband sensitivity enhancement of detuned dual-recycled Michelson interferometers with EPR entanglement

We demonstrate the applicability of the EPR entanglement squeezing scheme for enhancing the shot-noise-limited sensitivity of detuned dual-recycled Michelson interferometers. In particular, this scheme is applied to the GEO600 interferometer. The effect of losses throughout the interferometer, arm length asymmetries, and imperfect separation of the signal and idler beams is considered.

Figure 1

Simplified optical layout of the GEO600 detector with EPR squeezing. The main carrier light (green) is set to be resonant in the power recycling cavity (PRC). The signal (red) and idler (blue) are injected in the dark port and are resonant within the signal recycling cavity (SRC). On return from the interferometer they are separated and filtered by two output mode cleaner cavities (OMCs).

Figure 2

Sketch showing the frequency components and terms used for describing the EPR-squeezing scheme. ${\omega }_c$ is the optical frequency of a particular FSR of a cavity. The black lines show the signal recycling cavity resonances that the signal and idler fields resonate near, the dashed lines represent the $N-1$ FSRs between them.

Figure 3

Signal response of GEO600 with homodyne detection for different homodyne readout angles. This work assumes a 90 deg readout which allows for a direct comparison of the new scheme against the current DC readout scheme.

Figure 4

Optimization for $\mathrm{\Delta }$ and the ${\mathrm{LO}}_{\mathrm{B}}$ phase for EPR squeezing. The interferometer is detuned at ${\delta }_c=2\mathrm{kHz}$. The z-axis of the plot shows the noise output of ${\mathrm{HD}}_{\mathrm{AB}}$ at 2 kHz. We find two potential optimal parameters to choose from, the lower frequency one providing the correct broadband noise reduction. The resulting sensitivity of both are shown in Fig. 5.

Figure 5

The standard shot-noise limited sensitivity of the lossless GEO model (both tuned and detuned) is shown in black. For comparison we show that using 10 dB of squeezing with DC readout results in a slight improvement in the detuned case but with significantly narrower bandwidth. The EPR squeezing has two possible parameter choices to optimize the sensitivity at ${\delta }_c$ as shown in Fig. 4, however only one provides the required broadband improvement.

Figure 6

The two initial plots illustrate how the choice of the Schnupp asymmetry and the corresponding matching of $\mathrm{\Delta }$ to $N{\omega }_{\mathrm{SRC}}$ affects the sensitivity. Using a smaller Schnupp asymmetry reduces the additional resonance peak and results in less distortion near the peak sensitivity. The final plot shows how this additional resonance is affected by the PRM transmission due to the coupling of the SRC and PRC due to a Schnupp asymmetry. The optical power in the arm cavities was kept constant by adjusting the input power in each case to compare this effect.

Figure 7

Noise reduction through EPR squeezing as a function of the frequency $\mathrm{\Delta }$ given in units of free spectral range (FSR) of the signal recycling cavity (SRC). The current GEO OMC has an linewidth of 1.4 MHz and FSR of 435 MHz. The SRC FSR is 125 kHz. 13 dB of EPR-squeezed light is used to achieve a theoretical maximum noise reduction of 10 dB.

Figure 8

The effect of losses along the input path and output path on the detector sensitivity for EPR squeezing and for an ideal frequency-dependent squeezed source. Input and output loss of $X\%$ loss refer to an $X\%$ loss on input plus another $X\%$ on output. The lower plot shows the overall improvement of the EPR and ideal squeezing for identical losses. The peak seen here is due to the chosen Schnupp asymmetry.

Figure 9

Effect of internal symmetric losses on the sensitivity of the interferometer. The bottom plot shows the noise reduction achieved by the EPR squeezing and an ideal frequency-dependent source compared to no squeezing in both cases. Significant degradation around the detuning frequency is seen in this case.

Figure 10

Effect of asymmetric internal loss in the interferometer on the sensitivity using 10 dB of ideal frequency-dependent squeezing and 13 dB of EPR squeezing. Asymmetric losses adversely affect the sensitivity around the detuning frequency as well as at higher frequencies.

Figure 11

Shown are the powers in the PRC and SRC due to a single frequency optical field injected at the dark port. Figure 11 shows the phase of the field in the SRC. This field’s frequency is swept over a similar range to what the idler sidebands would be for $\mathrm{\Delta }\approx 80{\omega }_{\mathrm{SRC}}$, to visualize how they will react to a weak or strongly coupled cavity due to asymmetries. The sharper features seen are from the PRC resonance due to its higher finesse. As the asymmetric coupling is increased the PRC and SRC become strongly coupled and a split resonance is seen. The new resonances also alter the phase of the sidebands in the SRC affecting the correct squeezing angle rotation.

Figure 12

Entanglement through overlapping two squeezed fields.

Figure 13

Entangled squeezed input and magic beam splitter. In practice this frequency dependent splitting is achieved through an optical cavity, reflecting one frequency and transmitting another.

Figure 14

An entangled squeezed input reflected from a cavity can provide a frequency independent squeezing when recombined.