Sum-frequency generation as a detector of high-power two-mode squeezing

Abstract

We introduce sum-frequency generation (SFG) as an effective physical two-photon detector for high power two-mode squeezed coherent states with arbitrary frequency separation, as produced by parametric oscillators well above the threshold. Using a formalism of "collective modes", we describe both two-mode squeezing and degenerate squeezing on equal footing and derive simple relations between the input degree of squeezing and the measured SFG quadrature noise. We compare the proposed SFG detection to standard homodyne measurement, and show advantages in robustness to detection inefficiency (loss of SFG photons) and acceptance bandwidth.PACS numbers: 42.50. Dv, 42.50.St, 42.65.Lm, 42.65.Ky Quantum mechanical squeezing -the reduction of fluctuations of an observable below the standard quantum limit (SQL -1/ √ N , N the total number of photons detected) at the expense of increased fluctuations of the conjugate observable -is a major resource in quantum information and quantum measurement. In optics, squeezed states of light are key to methods of phase measurement with precision beyond SQL, approaching the ultimate Heisenberg limit 1/N [1, 2]. Due to the potential for a dramatic improvement in precision, sub-SQL methods are appealing for metrology applications, such as detection of gravitational waves [3], precision spectroscopy [4] and next generation atomic clocks [5].Two major limitations exist for measurement of squeezing by standard homodyne detection. The first is sensitivity to photo-detection inefficiency, which reduces the usable squeezing. Since squeezing is very sensitive to photon loss, and since detection inefficiency in standard homodyne is indistinguishable from loss, near unity detection efficiency is crucial to exploit the squeezing resource [11,12]. Another limitation of homodyne detection is detection bandwidth -while parametric downconversion (PDC) can produce two-mode squeezed states with arbitrary frequency separation, the photo detectors bandwidth is restricted to several GHz at most. Consequently, standard homodyne detection is effective only for narrowband degenerate squeezing and cannot be used for two-mode or broadband squeezing, especially above the oscillation threshold. Detection of the phase correlation in two-mode squeezing requires a stable reference for the phase-sum, which is not easy to obtain for spectrallyseparated mode pairs. Reports so far relied on delicate referencing to optical cavities and were limited to few nanometer separation between the modes [10].We suggest a simple method to detect high-power twomode squeezing, as produced by parametric oscillators above threshold [10,13,14]. The method, shown in Fig. 1, utilizes sum-frequency generation (SFG) as a detector of quantum correlation that is robust to detection inefficiency and accepts arbitrary frequency separation between the two modes. Previously, SFG was explored as an ultra-broadband two-photon detector in the FIG. 1: (Color online) (a) The proposed SFG scheme for measurement of squeezing: a narrowband pump local ...