Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics

Abstract

The LIGO-II gravitational-wave interferometers (ca. 2006–2008) are designed to have sensitivities near the standard quantum limit (SQL) in the vicinity of 100 Hz. This paper describes and analyzes possible designs for subsequent LIGO-III interferometers that can beat the SQL. These designs are identical to a conventional broad band interferometer (without signal recycling), except for new input and/or output optics. Three designs are analyzed: (i) a squeezed-input interferometer (conceived by Unruh based on earlier work of Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is injected into the interferometer’s dark port; (ii) a variational-output interferometer (conceived in a different form by Vyatchanin, Matsko and Zubova), in which homodyne detection with FD homodyne phase is performed on the output light; and (iii) a squeezed-variational interferometer with squeezed input and FD-homodyne output. It is shown that the FD squeezed-input light can be produced by sending ordinary squeezed light through two successive Fabry-Pérot filter cavities before injection into the interferometer, and FD-homodyne detection can be achieved by sending the output light through two filter cavities before ordinary homodyne detection. With anticipated technology (power squeeze factor $e^{-2R}=0.1\mathrm{}$ for input squeezed vacuum and net fractional loss of signal power in arm cavities and output optical train ${\epsilon }_{*}=0.01)$ and using an input laser power $I_o$ in units of that required to reach the SQL (the planned LIGO-II power, $I_{\mathrm{SQL}}),$ the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts $\mu \equiv \sqrt{S_h}/\sqrt{S_h^{\mathrm{SQL}}}$ and with the following corresponding increase $\mathcal{V}=1/{\mu }^3$ in the volume of the universe that can be searched for a given noncosmological source: $\mathrm{Squeezed}\mathrm{input}—\mu \simeq \sqrt{e^{-2R}}\simeq 0.3$ and $\mathcal{V}\simeq {1/0.3}^3\simeq 30$ using $I_o{/I}_{\mathrm{SQL}}=1.\mathrm{}$ $Variational-output—\mu \simeq {\epsilon }_{*}^{1/4}\simeq 0.3$ and $\mathcal{V}\simeq 30$ but only if the optics can handle a ten times larger power: $I_o{/I}_{\mathrm{SQL}}\simeq 1/\sqrt{{\epsilon }_{*}}=10.\mathrm{}$ $\mathrm{Squeezed}\mathrm{varational}—\mu {=1.3(e}^{-2R}{\epsilon }_{*}{)}^{1/4}\simeq 0.24$ and $\mathcal{V}\simeq 80$ using $I_o{/I}_{\mathrm{SQL}}=1;$ and $\mu \simeq {(e}^{-2R}{\epsilon }_{*}{)}^{1/4}\simeq 0.18$ and $\mathcal{V}\simeq 180$ using $I_o{/I}_{\mathrm{SQL}}=\sqrt{e^{-2R}/{\epsilon }_{*}}\simeq \mathrm{3.2.}$