Coherent anti-Stokes Raman Spectroscopy (CARS) has become one of the most useful label-free spectroscopic techniques whereby chemical composition can be determined based on molecular vibrational-spectra. While providing greatly enhanced gain over standard Raman spectroscopic methods, a major technical difficulty in this method has been the usual presence of a strong non-resonant background from surrounding molecules, such as a solvent or a background lattice, which greatly outnumber the molecules of interest and thus can mask the vibrationally resonant spectra.
Here we present the theoretical study of a new method for Raman spectroscopy by measuring the nonlinear phase shift induced by the resonant Four-Wave mixing (FWM) Raman interaction, using an SU(1,1) interferometer. We show that addition of a non-linear medium (such as a Raman sample) in-between the two OPAs (Optical parametric amplifiers) of the interferometer couples between the gain of the amplifiers and the Raman sample, resulting in sub-shot noise signal detection. In addition to the enhancement of the resonant Raman signal by the generated squeezed light, this scheme distinguishes the inherent phase shift between the resonant Raman signal and the non-resonant FWM background, allowing for complete suppression of the non-resonant background down to the vacuum level.
Figure 1: Crossed Raman scheme. a) Quantum-mechanical view of the Crossed Raman method in the phase picture. The input state is the vacuum for both the signal and the idler. Signal and Idler pairs are parametrically amplified from the vacuum in the first OPA. After the first amplification, the FWM light interferes parametrically on the Raman sample at an intermediate phase, inducing a nonlinear phase shift. Lastly, destructive interference occurs on OPA2 at completely negating all parametric amplification performed by OPA1. If no nonlinear phase shift is present, the output state is identical to the input state (vacuum). Thus, any changes to the signal intensity correspond to a phase shift induced by the sample. b) Illustration of the crossed-amplifiers concept in the quadrature picture. Red axis: quadrature axis. Blue circular shapes: uncertainty area of the quantum state. Blue arrow: Amplification axis of amplifier. OPA1 generates quadrature-squeezed light by amplifying the X quadrature (as indicated by the amplification axis of OPA1) and attenuating the Y quadrature of the vacuum. Upon interacting with the Raman sample, off-axis parametric amplification occurs, where the squeezing ellipse experiences slight rotation. Lastly, OPA2 is set to undo the squeezing of OPA1 by attenuating the X quadrature and amplifying the Y quadrature.
