Squeezed-state source using radiation-pressure-induced rigidity

We propose an experiment to extract ponderomotive squeezing from an interferometer with high circulating power and low mass mirrors. In this interferometer, optical resonances of the arm cavities are detuned from the laser frequency, creating a mechanical rigidity that dramatically suppresses displacement noises. After taking into account imperfection of optical elements, laser noise, and other technical noise consistent with existing laser and optical technologies and typical laboratory environments, we expect the output light from the interferometer to have measurable squeezing of $5\mathrm{dB}$, with a frequency-independent squeeze angle for frequencies below $1\mathrm{kHz}$. This squeeze source is well suited for injection into a gravitational-wave interferometer, leading to improved sensitivity from reduction in the quantum noise. Furthermore, this design provides an experimental test of quantum-limited radiation pressure effects, which have not previously been tested.

Figure 1

(Color online) Schematic of a interferometer designed to extract ponderomotively squeezed light due to radiation-pressure-induced motion of the low-mass end mirrors. Light from a highly amplitude- and phase-stabilized laser source is incident on the beam splitter. High-finesse Fabry-Perot cavities in the arms of the Michelson interferometer are used to build up the carrier field incident on the end mirrors of the cavity. All interferometer components in the shaded triangle are mounted on a seismically isolated platform in vacuum. The input optical path comprises a pre-stabilized $10\text{Watt}$ laser, equipped with both an intensity stabilization servo and a frequency stabilization servo. FI is a Faraday isolator.

Figure 2

(Color online) Front and side view of the end mirror suspension. The dot represents the center of mass of the mirror. The fibers are attached to a point a distance $h$, which could be negative, above the mirror center of mass. The distance between the attachment points at the mirror is $2b$, and at the top of the suspension is $2a$. Not drawn to scale.

Figure 3

(Color online) Left panel, the different noise sources relative to the vacuum level, as a function of frequency. The dominant noise below $1\mathrm{kHz}$ is optical losses, which are primarily comprised of detection losses (10%) and the optimization losses (13% in one arm). Right panel, the same noise sources in terms of equivalent displacement of a free mass (the displacement noise that each noise source would exhibit if the optical spring were not present). We estimate that a sensitivity of $5\times {10}^{-16}\mathrm{m}{\mathrm{Hz}}^{-1∕2}$ is necessary to measure squeezing at $100\mathrm{Hz}$, and the required sensitivity drops as frequency to the second power at higher frequencies.

Figure 4

(Color online) Block diagram for the feedback loop. $a$ and $b$ are the input and output quadrature fields; $n_i$ are vacuum noise fields entering the different port of the beamsplitter (BS) that has power reflectivity $R$ and transmission $T$. A small fraction of the output (squeezed) field $u=\sqrt{R}b$ is used to generate a shot-noise-limited error signal for a feedback loop to control the position of the differential mode of the ponderomotive interferometer (IFO), while the remainder $y=\sqrt{T}b$ is used to make sub-quantum-noise-limited measurements. The sample beam $u$ is filtered by $F\left(s\right)$, a transfer function that converts quadrature fields into force, and $Q\left(s\right)$ converts force back into quadrature fields. $f$ are spurious forces that act on the interferometer mirrors.

Figure 5

(Color online) The coupling of laser noise to the antisymmetric port is shown for the unoptimized and optimized cases. The optimized case includes a Michelson detuning and intentional loss in one of the arms.

Figure 6

(Color online) The coupling of laser and antisymmetric port noise to the output as a function of the homodyne measurement quadrature for the unoptimized case. The solid (red) curves represent the quantum optical noise, the dashed (blue) curves represent laser intensity noise, the dotted (green) curves represent laser phase noise and the dash-dotted (cyan) curves represent the total noise. In (a), the minimal noise quadratures for the different noise sources are not the same. In (b), the minimal noise quadratures for the laser intensity noise and the vacuum fluctuations are now the same. For this case, only a Michelson detuning has been added. In (c), the minimal noise quadratures for the laser intensity noise, laser frequency noise and the vacuum fluctuations are now the same. For this case, a Michelson detuning and a controlled loss in one arm (between the beamsplitter and the input mirror) were used.