Effects of Field Fluctuations,Losses, and Aberrations on the Sensitivity of a Michelson GW Antenna Using Squeezed Radiation

The sensitivity of an interferometric gravitational wave (GW) antenna operating above a few hundred Hertz is shot-noise limited. Sub-shot-noise sensitivity can be achieved by superimposing squeezed light on the laser field. The benefits of this approach are reduced in nonideal interferometers having fringe visibility less than unity, as pointed out by Gea-Banacloche and Leuchs and recently discussed by Chickarmane. Here, we consider an interferometer described by a set of coefficients V_l^(k), V_sq^(k), V_lsq^(k) depending on the misalignment, mismatching, and aberrations of the optical systems, as well as on the asymmetry of the beam splitter and the two-arm losses. Due to the presence of terms proportional to the product of laser times squeezed fields, we have taken into account the amplitude fluctuations of a_l. A simple model of the squeezed vacuum light, produced by a degenerate optical parametric oscillator (OPO), is used for calculating the dependence of the spectral density of the output of a GW antenna on the fluctuations of the OPO-cavity resonance frequency, the pump amplitude fluctuation, and the nonlinear-crystal-temperature drift. A set of figures η_sq± and r_lsq±⁽²⁾ are introduced for describing the effects of the amplitude fluctuations and the relative line width γ_la on the spectral density of the quadrature phase operator X = a_la_sq⁺ h.c.