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Arising out of a Non-local non-relativistic BEC, we present an Analoguegravity model upto $\mathcal{O}(\xi^{2})$ accuracy in the presence of thequantum potential term for a canonical acoustic BH in $(3+1)$-d spacetime wherethe series solution of the free minimally coupled KG equation for the largelength scale massive scalar modes is derived. We systematically address theissues of the presence of the quantum potential term being the root cause of aUV-IR coupling between short wavelength `primary' modes which are supposedlyHawking radiated through the sonic horizon and the large wavelength `secondary'modes. In the quantum gravity experiments of analogue Hawking radiation in thelaboratory, this UV-IR coupling is inevitable and one can not get rid of theselarge wavelength excitations which would grow over space by gaining energy fromthe short wavelength Hawking radiated modes. We identify the characteristicfeature in the growth rate(s) that would distinguish these primary andsecondary modes.

Quantum Potential induced UV-IR coupling in Analogue Hawking radiation: From Bose-Einstein Condensates to canonical acoustic black holes