Quantum-enhanced interferometer using Kerr squeezing

Abstract

One of the prime applications of squeezed light is enhancing the sensitivity of an interferometer below the quantum shot-noise limit, but so far, no such experimental demonstration was reported when using the optical Kerr effect. In prior setups involving Kerr-squeezed light, the role of the interferometer was merely to characterize the noise pattern. The lack of such a demonstration was largely due to the cumbersome tilting of the squeezed ellipse in phase space. Here, we present the first experimental observation of phase-sensitivity enhancement in an interferometer using Kerr squeezing.

Keywords: fiber squeezing; interferometric sensitivity; optical Kerr effect; squeezed light.

Figure 1:

Two-rail sketch. Kerr-squeezed phase-coherent light beams of equal power are launched into rails a and b. The squeezing ellipses are tilted with respect to the amplitude quadrature and, without the central beam splitter, when measuring the Stokes parameter do not improve the interference sensitivity. On the contrary, it is much worse than it would be for coherent input states of similar power because the interferometer is sensitive to the relative phase and the Kerr squeezing increases the phase noise. Without the beam splitter, the phase differences before (δφ) and after (δψ) it are equivalent. With the beam splitter, a basis transformation is introduced that, if appropriately chosen, leads to a sensitivity beyond the SNL for δψ, but not for δφ.

Figure 2:

Poincaré-sphere representation of the state in the two-rail system just before interference in the Stokes parameter detector. Without the central beam splitter in Figure 1, the state just before the interference in the detector rotates along the black geodesic (great circle) in the S ₂–S ₃ plane as a function of optical arm length difference δφ. The joint effect of the squeezing in the two arms is a squeezed ellipsoid which is tilted with respect to the geodesic. The sensitivity is worse than the SNL because of the anti-squeezing. With the central beam splitter, the Stokes basis is changed such that the new $S_1^{\prime }$ axis has the same orientation as the major axis of the ellipsoid. Then further ‘downstream’, an arm length difference δψ lets the state rotate along the tilted red geodesic leading to a sensitivity improvement beyond the SNL. In the inset, we have a top view of the motion of the ellipsoid due to phase difference before (δφ) and after (δψ) the beam splitter.

Figure 3:

Scheme of a Kerr-squeezed interferometer. (a) General free-space scheme of a Kerr-squeezed interferometer. The polarization-squeezed state is prepared in the blue box, then the basis is rotated with a half-wave plate, and in the green box a phase change is introduced that can be measured with sensitivity below the SNL. The polarization modes in the boxes may share the same spatial mode (in this case no PBSs are used) and are drawn separately for clarity. (b) The scheme of our experimental setup. The boxes correspond to those in (a). PBS — polarizing beam splitters, L — lenses, λ/2 — half-wave plates, λ/4 — quarter-wave plates, WP — Wollaston prism.

Figure 4:

Spectra of the Stokes parameter measured with the birefringence modulator in action: bottom (blue crosses) – modulating the squeezed Stokes parameter, middle (red circles) – modulating a coherent state of the same power (background equivalent to shot-noise level), top (green pluses) – modulating the anti-squeezed Stokes parameter for comparison. The uneven background level is due to the amplifier response.