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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-P\'erot 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 *=0. 01) and using an input laser power I₎ in units of that required to reach the SQL (the planned LIGO-II power, Iₒₐ₋), the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts S₇/S₇^{SQL} and with the following corresponding increase V=1/^3 in the volume of the universe that can be searched for a given noncosmological source: Squeezedinput---e^{-2R}0. 3 and V1/0. 3^330 using I₎/Iₒₐ₋=1. Variational-output---*^1/40. 3 and V30 but only if the optics can handle a ten times larger power: I₎/Iₒₐ₋1/{*}=10. Squeezedvarational---=1. 3 (e^-2R*) ^1/40. 24 and V80 using I₎/Iₒₐ₋=1; and (e^-2R*) ^1/40. 18 and V180 using I₎/Iₒₐ₋=e^{-2R/*}3. 2.
Kimble et al. (Wed,) studied this question.