We introduce sum-frequency generation (SFG) as a physical detector for high-power two-mode squeezed coherent states with arbitrary frequency separation, as produced by parametric oscillators above 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 show that the SFG quadratures provide a direct measure of the input squeezing and discuss the sensitivity limits of the proposed method.
We introduce sum-frequency generation (SFG) as a physical detector for high-power two-mode squeezed coherent states with arbitrary frequency separation, as produced by parametric oscillators above 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 show that the SFG quadratures provide a direct measure of the input squeezing and discuss the sensitivity limits of the proposed method.
Abstract We present a theoretical investigation of two-mode squeezing and bipartite entanglement in the nondegenerate sum-frequency generation (NSFG) process, based on a second-order Hamiltonian under the short-time approximation. Both first- and second-order amplitude squeezing are shown to depend strongly on the coherent input amplitudes, nonlinear coupling strength, and relative phase. Asymmetric input configurations, especially those with enhanced signal-mode intensity, substantially enhance squeezing and deepen nonclassicality. In particular, second-order quadrature squeezing proves highly sensitive to phase and amplitude imbalances, making it a robust probe of higher-order quantum correlations. Entanglement is assessed using the Duan inseparability criterion and both variants of the Hillery–Zubairy (HZ) criteria. Under coherent excitation, the Duan condition approaches the separability threshold, indicating notable entanglement. Both HZ-1 and HZ-2 reveal bipartite entanglement under suitable field configurations, with HZ-2 displaying greater sensitivity at higher field intensities. The entanglement primarily resides in the pump modes, which symmetrically engage in the nonlinear interaction. These findings highlight the critical role of field asymmetry and higher-order effects in quantum-state engineering, establishing NSFG as a promising, tunable platform for generating nonclassical light in integrated photonics and continuous-variable quantum technologies.
We report on the experimental demonstration of strong quadrature EPR entanglement and squeezing at very low noise sideband frequencies produced by a single type-II, self-phase-locked, frequency degenerate optical parametric oscillator below threshold. The generated two-mode squeezed vacuum state is preserved for noise frequencies as low as 50 kHz. Designing simple setups able to generate non-classical states of light in the kHz regime is a key challenge for high sensitivity detection of ultra-weak physical effects such as gravitational wave or small beam displacement.
Quantum frequency conversion, the process of shifting the frequency of an optical quantum state while preserving quantum coherence, can be used to produce non-classical light at otherwise unapproachable wavelengths. We present experimental results based on highly efficient sum-frequency generation (SFG) between a vacuum squeezed state at 1064 nm and a tunable pump source at 850 nm ± 50 nm for the generation of bright squeezed light at 472 nm ± 4 nm, currently limited by the phase-matching of the used nonlinear crystal. We demonstrate that the SFG process conserves part of the quantum coherence as a 4.2(±0.2) dB 1064 nm vacuum squeezed state is converted to a 1.6(±0.2) dB tunable bright blue squeezed state. We furthermore demonstrate simultaneous frequency- and spatial-mode conversion of the 1064-nm vacuum squeezed state, and measure 1.1(±0.2) dB and 0.4(±0.2) dB of squeezing in the TEM01 and TEM02 modes, respectively. With further development, we foresee that the source may find use within fields such as sensing, metrology, spectroscopy, and imaging.
Quantum squeezing, a major resource for quantum information processing and quantum metrology, is best analyzed in terms of the field quadratures - the quantum optical analogues of position and momentum, which form the continuous-variable formalism of quantum light. Degenerate squeezing admits a very helpful and simple description in terms of the single-mode quadrature operators, but the non-degenerate case, i.e. when the squeezing involves pairs of modes, requires a more complicated treatment involving correlations between the quadratures of the different modes. We introduce a generalized set of complex quadrature operators that treats degenerate and non-degenerate squeezing on equal footing. We describe the mode-pairs (and photon-pairs) as a single entity, generalizing the concept of single-mode quadrature operators to two-mode fields of any bandwidth. These complex operators completely describe the SU(1,1) algebra of two-photon devices and directly relate to observable physical quantities, like power and visibility. Based on this formalism, we discuss the measurement of optically-broad squeezed signals with direct detection, and present a compact set of phase-dependent observables that completely and intuitively determine the two-mode squeezed state, and quantify the degree of inseparability and entanglement between the modes.
We propose non-phase-matched sum frequency generation (SFG) as a method for characterizing broadband multimode light. Both the central wavelength and the bandwidth are in this case not limited by the phase matching condition. As an example, we consider bright squeezed vacuum (BSV) generated through high-gain parametric down conversion (PDC). In the spectrum of SFG from BSV, we observe the coherent peak and the incoherent background. We show that the ratio of their widths is equal to the number of frequency modes in BSV, which in the case of low-gain PDC gives the degree of frequency entanglement for photon pairs. By generating the sum frequency in the near-surface region of a nonlinear crystal, we increase the SFG efficiency and get rid of the modulation caused by chromatic dispersion, known as Maker fringes. This allows one to use non-phasematched SFG as a wavelength-independent autocorrelator. Furthermore, we demonstrate efficient non-phase-matched three- and four-frequency summation of broadband multimode light, hardly possible under phase matching. We show that the latter contains the coherent peak while the former does not.
Quantum frequency conversion, the process of shifting the frequency of an optical quantum state while preserving quantum coherence, can be used to produce non-classical light at otherwise unapproachable wavelengths. We present experimental results based on highly efficient sum-frequency generation (SFG) between a vacuum squeezed state at 1064 nm and a tunable pump source at 850 nm ± 50 nm for the generation of bright squeezed light at 472~nm ± 4~nm, currently limited by the phase-matching of the used nonlinear crystal. We demonstrate that the SFG process conserves part of the quantum coherence as a 4.2(±0.2)~dB 1064 nm vacuum squeezed state is converted to a 1.6($\pm0.2)dBtunablebrightbluesqueezedstate.Wefurthermoredemonstratesimultaneousfrequency−andspatial−modeconversionofthe1064−nmvacuumsqueezedstate,andmeasure1.1(\pm0.2)dBand0.4(\pm0.2)dBofsqueezingintheTEM_{01}$ and TEM02 modes, respectively. With further development, we foresee that the source may find use within fields such as sensing, metrology, spectroscopy, and imaging.