Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry

We show that the generation of entanglement of two heavily macroscopic mirrors is feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the standard quantum limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and provides a measure of when macroscopic entanglement can be observed in the presence of realistic decoherence processes.

Figure 1

Schematic plot of a power-recycled (PR) Michelson interferometer. Suspended test-mass mirrors are much lighter than other suspended optics. Differential motion of test-mass mirrors detected at dark (south) port and common motion at bright (west) port. A Faraday rotator might be used to access all of the back reflected light.

Figure 2

Noise spectral densities (left panel) in arbitrary units with ${\Omega }_F=2\pi 230\mathrm{Hz}$ and ${\Omega }_x=2\pi 1270\mathrm{Hz}$, and optimized ${\Omega }_{\alpha }^c=2\pi 1600\mathrm{Hz}$, ${\Omega }_{\alpha }^d=2\pi 184\mathrm{Hz}$. Test-mass entanglement of $E_{\mathcal{N}}=0.35$. Squeezing ellipses of position and momentum operators (right panel) with respect to common (red) and differential (blue) mode. Second-order moments are normalized to the ground state of harmonic oscillator at frequency $({\Omega }_{\alpha }^c+{\Omega }_{\alpha }^d)/2$.

Figure 3

Logarithmic negativity versus ${\Omega }_x/{\Omega }_F$, maximized with respect to ${\Omega }_{\alpha }^c$ and ${\Omega }_{\alpha }^d$ (example values marked) for 0 dB (solid line), 5 dB (dashed line) and 10 dB (dotted line) technical laser noise, in both, amplitude and phase quadrature.