Quantum noise in ring-laser gyros. II. Numerical results

Abstract

This is the second of three papers dealing with the effects of quantum noise on the operation of a ring-laser gyro. Exact expressions for the spectrum and the mean beat frequency of the beat signal are obtained in terms of infinite continued fractions. The spectrum is found to be always separable into a "coherent" $\delta$-function contribution at zero frequency, representing the effects of locking, and an "incoherent" part of nonzero band-width. Computed forms for the spectrum and the frequency response curve are presented for parameter values appropriate to the ring-laser gyro. The results obtained show that for laser rotation rates corresponding to the locked zone in the absence of noise, the tendency for locking as measured by the strength of the coherent contribution continues to dominate, but this effect rapidly becomes negligibly small outside this zone. In addition, the transition in beat frequency between the locked and unlocked zones which is discontinuous in the noise-free case ceases to be well defined in the presence of noise. Finally, the higher harmonics predicted to occur in the unlocked zone in the absence of noise are found to reoccur in the presence of noise except that the individual harmonics are now found to be broadened.