Squeezed light

The field of a light wave can be written as two quadratures, the components in phase and in quadrature with a reference oscillation, which for a bright beam correspond to fluctuations in amplitude and in phase. In a coherent state, the output of an ideal laser, both quadratures carry the same quantum noise, and that noise is the shot-noise floor every classical measurement meets. The uncertainty principle constrains only the product of the two variances, not each one separately. A squeezed state uses that freedom: the noise in one quadrature falls below the shot-noise level while the noise in the other, the anti-squeezed quadrature, rises above it. A measurement that reads only the squeezed quadrature sees less noise than any classical light could give it. Squeezing in the amplitude quadrature is the same thing as the photon-number squeezing described in the shot-noise entry.

Generating squeezing requires a nonlinearity that correlates photons in pairs. The standard source is a degenerate optical parametric oscillator operated below threshold: a crystal with a second-order nonlinearity, often periodically poled KTP, inside a cavity and pumped at twice the optical frequency by second-harmonic generation of the same laser. Third-order processes do the same job through four-wave mixing, in fiber and in silicon nitride microresonators, which is how squeezing reaches photonic chips. Detection uses balanced homodyne detection: the squeezed beam is mixed on a beam splitter with a strong local oscillator at the same frequency, the two outputs are subtracted as in balanced detection, and the local oscillator phase selects which quadrature is measured. Squeezing is quoted in dB relative to the shot noise measured with the squeezed input blocked.

Loss limits what can be used. Every loss point replaces part of the state with vacuum, which carries exactly shot noise, so a variance $V$ (normalized to shot noise) becomes $\eta V + (1-\eta)$ after a total efficiency $\eta$. With 15 dB of squeezing generated, a path efficiency of 90% leaves 8.91 dB at the detector and 80% leaves 6.47 dB; at 90% no amount of generated squeezing can show more than 10 dB. Photodiodes with quantum efficiency above 99%, low-loss optics and careful mode matching are therefore as important as the source. The highest directly measured value, 15 dB, was reported in 2016 from a PPKTP oscillator at 1064 nm.

The main application is interferometry limited by shot noise. GEO 600 began injecting squeezed vacuum into its dark port in 2010, and Advanced LIGO and Virgo followed in their third observing run in 2019, lowering the high-frequency noise floor. Because the anti-squeezed quadrature raises radiation-pressure noise at low frequencies, later detectors add a filter cavity that rotates the squeezed quadrature with frequency, so each band sees the quadrature that helps it. Squeezed states are also the working resource of continuous-variable quantum key distribution and of Gaussian boson sampling on quantum photonic chips.

References: D. F. Walls, Nature 306, 141 (1983); H. Vahlbruch, M. Mehmet, K. Danzmann, R. Schnabel, Phys. Rev. Lett. 117, 110801 (2016); M. Tse et al., Phys. Rev. Lett. 123, 231107 (2019).