Double optical spring enhancement for gravitational-wave detectors

Abstract

Currently planned second-generation gravitational-wave laser interferometers such as Advanced LIGO exploit the extensively investigated signal-recycling technique. Candidate Advanced LIGO configurations are usually designed to have two resonances within the detection band, around which the sensitivity is enhanced: a stable optical resonance and an unstable optomechanical resonance-which is upshifted from the pendulum frequency due to the so-called optical-spring effect. As an alternative to a feedback control system, we propose an all-optical stabilization scheme, in which a second optical spring is employed, and the test mass is trapped by a stable ponderomotive potential well induced by two carrier light fields whose detunings have opposite signs. The double optical spring also brings additional flexibility in reshaping the noise spectral density and optimizing toward specific gravitational-wave sources. The presented scheme can be extended easily to a multi-optical-spring system that allows further optimization.

Experimental demonstration of coupled optical springs

“…Were this a physical effect upon the loop gain, this ought to result in a unity gain instability at this frequency; this backs up the notion that this effect is imposed upon the measurement only due to the apparent reduced motion of the CTM, rather than on the loop gain itself. Note the similarity between this measurement and the "annihilation" double-spring regime proposed by Rehbein et al [9], whereby the two springs are tuned to "trap" the CTM longitudinally by application of equal optical force on either side.…”

“…This may be required in a system such as that proposed by Rehbein et al [9] in which an anti-spring is combined with …”

“…These instabilities are ordinarily corrected by the application of electronic feedback systems shaped in such a way as to stop the system from going unstable; however, with a second optical spring of appropriate detuning the system may be stabilised purely optically [9]. Configurations involving two or more optical springs can also allow reshaping of the noise spectral density of the system.…”

“…We show that this can be achieved via a modification to the measurement technique, whereby the signal injections required for measurement of opto-mechanical effects are performed simultaneously in both cavities of the doubly-resonant system. This measurement technique can also be applied to demonstrate suppression of test-mass motion by the application of appropriately-tuned opto-mechanical stiffnesses, in the regime termed "annihilation" by Rehbein et al [9].…”

“…However, the sensitivity increase would be restricted to a narrow band around the resonance, and hence be of limited benefit. Further, a single optical spring is inherently unstable, requiring control systems to maintain stability of the opto-mechanical system [9,10]. Proposals exist to employ multiple optical springs in a single system, relatively tuned such that their combination is stable without requiring further complexity in the control loops [9].…”