Fig. 1 Possible squeezing as a function of the total effective losses 100 × (1 − η) and total squeezed quadrature fluctuations, in the absence of technical noise. Here pump power is optimized for best squeezing given the level of quadrature fluctuations. Squeezing levels in decibels relative to shot noise are negative for an improvement in sensitivity.

Fig. 2 The LIGO interferometer with a squeezed vacuum source. The pump laser, locked to the LIGO main laser frequency through an optical fiber, pumps the second harmonic generator (SHG) [19] and the optical parametric oscillator (OPO) [18]. The control laser – for the quadrature control scheme – is offset locked 29.5 MHz above the pump laser frequency, and injected into the OPO where the nonlinear interaction generates a symmetric sideband 29.5 MHz below the pump with, under ideal conditions, a phase determined by the phase of the circulating pump [19, 20]. The phase of the control laser is then locked relative to the phase of the circulating pump by the coherent field photo-detector (CF PD). The squeezed field, with coherent control sidebands, reflects off the interferometer after which the quadrature control photo-detector senses the phase between the interferometer beam and the coherent sidebands. This error signal is used to adjust the pump laser phase and control the quadrature angle. The output mode cleaner (OMC) reflects the coherent sidebands and transmits the carrier towards the gravitational wave readout photo-detectors (GW PD) where the squeezing is measured.

Fig. 3 Variance (in dB relative to vacuum fluctuations) in one quadrature of the OPO output field as a function of the phase of the incident second harmonic pump. With no detuning and ideal phase matching (red trace), the minimum variance occurs at θ_B = π, and the pump phase alone determines the squeezed quadrature θ_sqz = θ_B/2. However small changes in the cavity length or crystal temperature shift the location of the minimum variance, introducing a relative shift between the squeezed quadrature angle and the pump phase. The green trace shows the variance with the cavity length shifted 6 nm away from resonance, while the blue trace shows the variance produced when the temperature deviates by 0.01 K from the phase matching temperature. These predictions assume $\mathrm{\Omega }\ll {\gamma }_a^{\text{tot}}$, $\left|x\right|=1/\sqrt{2}$, η_esc = 0.96, ${\gamma }_a^{\text{tot}}=2\pi \times 12\hspace{0.17em}\text{MHz}$, and ${\gamma }_{\text{b}}^{\text{tot}}=2\pi \times 30\hspace{0.17em}\text{MHz}$.

Fig. 4 Expected variances of the squeezed (solid lines) and anti-squeezed (dashed lines) quadratures as a function of nonlinear gain, based on Eq. (1). The level of anti-squeezing is sensitive to the total losses, while at high gains the level of squeezing is sensitive to the quadrature fluctuations. Left panel: θ̃ =50 mrad and η= 90% (blue) 70% (green) and 50% (red). Right panel: η=70%, and θ̃ =30 (blue), 50 (green), and 100 (red) mrad. Blue and green dashed lines are below the red dashed line in the right panel.

Fig. 5 Characterization of Enhanced LIGO interferometer as a squeezing detector. Red points show measured squeezing and anti squeezing between 1.9 kHz and 3.7 kHz. Blue trace is a fit to the red points with η = 38 ± 3% and θ̃ = 81 ± 6 mrad. Control bandwidths were consistent for measurements at different nonlinear gains. The black and green points were measured at a later date with η = 42 ± 7%. After measurement of the black point (θ̃ = 109 ± 9 mrad), the interferometer alignment was adjusted slightly and the squeezing angle lock point adjusted, reducing the quadrature fluctuations to (θ̃ = 37 ± 6 mrad) as shown by the green point.

Fig. 6 Squeezing targets for gravitational wave detectors, in decibels relative to shot noise. This experiment measured −2.1 dB of squeezing in Enhanced LIGO, with 55% losses and at least 37 ± 6 mrad squeezing angle fluctuations. For Advanced LIGO we would like to be able to measure at least −6 dB of squeezing in an initial implementation. Since the total losses are expected to be 20–28%, planning for 15 mrad or less of phase noise would allow for −6 dB of squeezing. Designs for third generation detectors call for even higher levels of squeezing [31], which will place very stringent limits on the total quadrature fluctuations and losses.