Practical speed meter designs for QND gravitational-wave interferometers

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors (e.g., LIGO-III and EURO), one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. A previous paper analyzed a straightforward but impractical design for a {\it speed-meter interferometer} that accomplishes this. This paper describes some practical variants of speed-meter interferometers. Like the original interferometric speed meter, these designs {\it in principle} can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies. These variants essentially consist of a Michelson interferometer plus an extra "sloshing" cavity that sends the signal back into the interferometer with opposite phase shift, thereby cancelling the position information and leaving a net phase shift proportional to the relative velocity. {\it In practice}, the sensitivity of these variants will be limited by the maximum light power $W_{\rm circ}$ circulating in the arm cavities that the mirrors can support and by the leakage of vacuum into the optical train at dissipation points. In the absence of dissipation and with a squeezed vacuum of power squeeze factor ~ 0.1 inserted into the output port so as to keep the circulating power down, the SQL can be beat by a factor 10 in power at all frequencies below some chosen $f_{\rm opt}\simeq 100$ Hz, with $W_{\rm circ}\simeq 800$ kW. Estimates are given of the amount by which vacuum leakage at dissipation points will debilitate this sensitivity; these losses are 10% or less over most of the frequency range of interest.