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

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 for input squeezed vacuum and net fractional loss of signal power in arm cavities and output optical train ɛ_*=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_SQL), the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts μ≡(S_h)/(S^SQL_h) and with the following corresponding increase V=1/μ³ in the volume of the universe that can be searched for a given noncosmological source: Squeezed input-μ~=(e^-2R)~=0.3 and V~=1/0.3³~=30 using I_o/I_SQL=1. Variational-output-μ~=ɛ^1/4_*~=0.3 and V~=30 but only if the optics can handle a ten times larger power: I_o/I_SQL~=1/(ɛ_*)=10. Squeezed varational-μ=1.3(e^-2Rɛ_*)^1/4~=0.24 and V~=80 using I_o/I_SQL=1; and μ~=(e^-2Rɛ_*)^1/4~=0.18 and V~=180 using I_o/I_SQL=(e^-2R/ɛ_*)~=3.2.