We present a direct measurement of bright two-mode quadrature squeezing, by mixing the two mode squeezed oscillation with itself, or with a second two-mode squeezed source.

Parametric oscillators are known for their ability to generate quadrature squeezed modes, i.e. oscillating modes that have a reduced noise level in one quadrature and an increased level in the other. Squeezing can be both classical (squeezed classical noise) and quantum (squeezed vacuum fluctuations), semi classical analysis provides a good description also of quantum squeezing when the light intensity is high, near the oscillation threshold and above it [1]. A standard method to measure the level of squeezing is by mixing the oscillation with a local oscillator (LO) of the same frequency, tuning the LO's phase to match the squeezed quadrature. In the standard measurement the oscillation is kept under threshold, allowing comparison of the measured noise levels of the two quadratures, since above threshold the increased noise quadrature contains a strong oscillation, preventing measurement of the noise level.  

Although two-mode squeezing is the most general and easily produced form of squeezing, most current parametric oscillators in quantum optics applications generate single frequency (degenerate) squeezed light. The reason is that detection of two-mode squeezing is complicated as it requires a phase-correlated pair of LO's, which are not easy to come by [2, 3]. Thus, most measurements so far relied on the incomplete characterization of intensity correlation only [4]. We propose and demonstrate a simple scheme to detect two mode squeezing, by mixing the oscillation with a second identical two-mode squeezed source which acts as two-mode LO. Interestingly, the bright two-mode oscillation is an advantage for the squeezing measurement, since it allows measurement of the noise in both quadratures, even when the oscillation is above threshold, by shifting the bright oscillation to a high frequency at the mixing output. Classically, the strong two mode oscillation serves as an internal two-mode LO that is useful to measure its own quadrature noise levels, without the need for an external LO.

We demonstrate this method for detection of classical squeezing using parametric oscillators in the RF domain. The outputs of the two parametric oscillators are mixed in a frequency mixer, and then analyzed in an RF spectrum analyzer, demonstrating a ~20dB difference between the DC noise of the two quadratures, indicating a significant reduction from the non-squeezed noise.

References:

1. S. Chaturvedi, K. Dechoum and P. D. Drummond, "Limits to squeezing in the degenerate optical parametric oscillator" Phys. Rev. A, 65, 33805 (2002).
2. A. S Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli and P. Nussenzveig, "Generation of bright two-color continues variable entanglement", Phy. Rev. Lett. 95, 24603 (2005).
3. A. M Marino, V. Boyer and P.D. Lett," Violation of the Cauchy-Schwarz inequality in the macroscopic regime", Phys. Rev. Lett. 100, 233601 (2008).
4. C. D. Nabors and R. M. Shelby, "Two color squeezing and sub-shot-noise signal recovery in doubly resonant optical parametric oscillators", Phys. Rev. A, 42, 556 (1990).