Quantum noise limits in white-light-cavity-enhanced gravitational wave detectors

Abstract

Previously, we had proposed a gravitational wave detector that incorporates the white light cavity (WLC) effect using a compound cavity for signal recycling (CC-SR).Here, we first use an idealized model for the negative dispersion medium (NDM), and use the so-called Caves model for phase-insensitive linear amplifier to account for the quantum noise (QN) contributed by the NDM, in order to determine the upper bound of the enhancement in the sensitivity-bandwidth product. We calculate the quantum noise limited sensitivity curves for the CC-SR design, and find that the broadening of sensitivity predicted by the classical analysis is also present in these curves, but is somewhat reduced. Furthermore, we find that the curves always stay above the standard quantum limit (SQL). To circumvent this limitation, we modify the dispersion to compensate the non-linear phase variation produced by the opto-mechanical (OM) resonance effects. We find that the upper bound of the factor by which the sensitivitybandwidth product is increased, compared to the highest sensitivity result predicted by Bunanno and Chen [Phys. Rev. D 64, 042006 (2001)], is ~14. We also present a simpler scheme (WLC-SR) where a dispersion medium is inserted in the SR cavity. For this scheme, we found the upper bound of the enhancement factor to be ~18. We then consider an explicit system for realizing the NDM, which makes use of five energy levels in M-configuration to produce Gain, accompanied by Electromagnetically Induced Transparency (the GEIT system). For this explicit system, we employ the rigorous 2 approach based on Master Equation (ME) to compute the QN contributed by the NDM, thus enabling us to determine the enhancement in the sensitivity-bandwidth product definitively rather than the upper bound thereof. Specifically, we identify a set of parameters for which the sensitivity-bandwidth product is enhanced by a factor of 17.66.

Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation

“…It broadens the cavity resonance without changing the finesse, in which case the uncertainty of the amplitude quadrature must increase above the vacuum level. Recently, it was proposed that the white-light cavity effect can be achieved by using an anomalously dispersive medium inside the interferometer [13][14][15][16][17][18][19][20][21][22].…”

Catastrophic breakdown of the Caves model for quantum noise in some phase-insensitive linear amplifiers or attenuators based on atomic systems

“…As a result, this four-level atomic system is not suitable for our WLC-SR scheme [15], which requires very low QN. In Sec.…”

“…In Ref. [15], we have used both the SC-CM and the ME approaches to determine the QN-limited enhancement in the sensitivity-bandwidth product. For the case where !…”

“…Finally, in Sec. VI, we describe a scheme called gain-EIT (GEIT) that has the desired properties for enhancing the sensitivitybandwidth product of the WLC-SR scheme [15] and analyze its QN. In Appendix A, we show the details of the steps for the ME approach for a two-level atomic system discussed in Sec.…”

“…Recently, we have proposed a gravitational wave detector that incorporates the white light cavity (WLC) [4,5,6,7,8,9,10] effect by adding a negative dispersion medium (NDM) in the signal recycling cavity in the advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) [11,12,13,14] design, which we call WLC-SR [15]. To calculate the QN for the detector, we need to consider the QN due to the NDM.…”