Practical speed meter designs for quantum nondemolition 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 speed-meter interferometer that accomplishes this. This paper describes some practical variants of speed-meter interferometers. Like the original interferometric speed meter, these designs 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. In practice, the sensitivity of these variants will be limited by the maximum light power Wcirc 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 squeezed vacuum ~power squeeze factor e.0.1) inserted into the output port so as to keep the circulating power down, the SQL can be beat by h/hSQL ;AWcirc e/Wcirc at all frequencies below some chosen f opt.100 Hz. Here Wcirc SQL