Spectrally multimode integrated SU(1,1) interferometer

Abstract

Nonlinear SU(1,1) interferometers are fruitful and promising tools for spectral engineering and precise measurements with phase sensitivity below the classical bound. Such interferometers have been successfully realized in bulk and fiber-based configurations. However, rapidly developing integrated technologies provide higher efficiencies, smaller footprints, and pave the way to quantum-enhanced on-chip interferometry. In this work, we theoretically realised an integrated architecture of the multimode SU(1,1) interferometer which can be applied to various integrated platforms. The presented interferometer includes a polarization converter between two photon sources and utilizes a continuous-wave (CW) pump. Based on the potassium titanyl phosphate (KTP) platform, we show that this configuration results in almost perfect destructive interference at the output and supersensitivity regions below the classical limit. In addition, we discuss the fundamental difference between single-mode and highly multimode SU(1,1) interferometers in the properties of phase sensitivity and its limits. Finally, we explore how to improve the phase sensitivity by filtering the output radiation and using different seeding states in different modes with various detection strategies.

Two-Colour Spectrally Multimode Integrated SU(1,1) Interferometer

“…The presence of this noise is caused by the fact that our technique for compensating the group velocities of signal and idler photons succeeds in the proximity of the central frequencies (namely, where the main peaks of the intensity spectra are expected), whereas it fails for frequencies far from ω s0 and ω i0 , resulting in the emergence of residual photons. The same issue was already observed in the degenerate SU(1,1) interferometer [28]. In both degenerate and two-colour frameworks, the presence of this residual radiation hinders the perfect interference and, therefore, affects the precision of the interferometer, which can be estimated by means of the phase sensitivity [14]:…”

“…The regime of destructive interference is very important for reducing noise and improving phase sensitivity in SU(1,1) interferometers [8]. Analysing a degenerate multimode SU(1,1) interferometer, we already found that the shape of the JSI and the number of generated photons at different imparted phase ϕ are strongly conditioned by the arrangement of various components within the integrated device [28]. In this section, in order to improve the phase sensitivity of the non-degenerate two-colour SU(1,1) interferometer, we elaborate a strategy for reducing the number of generated photons in the destructive interference regime by properly placing polarisation converters.…”

“…This concretely means that the degree of freedom given by the choice of the periodic pole allows us to determine the central frequencies of the signal and idler photons, and consequently the separation of their spectra. In order to realise the fully spectral distinguishability of signal and idler photons, we firstly estimate the full width at half maximum (FWHM) of their spectra ∆ω in the case of the degenerate PDC source with the polling period Λ deg [28]; note that the spectra of signal and idler photons are identical in this case due to the use of the CW laser. The variation of the polling period allows signal and idler photons to be generated at different central frequencies with a proper spectral separation.…”

“…Then, the new value of the polling period Λ, which allows the photon pair creation at frequencies ω s0 and ω i0 , is calculated by means of the momentum conservation in Equation (3). In contrast to the single-colour SU(1,1) interferometer described in [28], the current device is characterised by two polarisation converters (PCs), which are required for the proper compensation of the group velocities of signal and idler photons.…”

“…It is therefore reasonable to believe that any specific realisation of the SU(1,1) interferometer based on realistic nonlinear photon sources should take the multimode structure of the emitted radiation into account. Thus, in [28], it was already demonstrated how a proper state engineering [29] of the photon source allows one to reduce the dispersion within the interferometer and therefore improve both the visibility of the interference pattern and the accuracy in the phase scanning. In addition, proper spectral engineering of PDC sources allows the creation of correlated photons of different colours.…”