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-Perot 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 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-SQL), the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts mu =rootS(h)/ rootS(h)(SQL) and with the following corresponding increase V=1/mu(3) the volume of the universe that can be searched for a given noncosmological source: Squeezed input-mu similar or equal toroote(-2R)similar or equal to0.3 and Vsimilar or equal to1/0.3(3)similar or equal to30 using I-o/I-SQL=1. Variational-output-musimilar or equal toepsilon(1/4)similar or equal to0.3 and Vsimilar or equal to30 but only if the optics can handle a ten times larger power: I-o/I(SQL)similar or equal to1/rootepsilon(*)=10. Squeezed varational-mu = 1.3(e(-2R)epsilon(*))(1/4)similar or equal to0.24 and Vsimilar or equal to80 using I-o/I-SQL = 1; and musimilar or equal to(e(-2R)epsilon(*))(1/4)similar or equal to0.18 and Vsimilar or equal to180 using I-o/I-SQL = roote(-2R)/epsilon(*)similar or equal to3.2.