Quantum-coherent nonlinear interferometry using electron-phonon systems for entanglement-assisted terahertz sensing

Abstract

We present a theoretical framework for quantum-coherent nonlinear interferometry in which the nonlinear medium is modeled as active electron-phonon quantum systems rather than a passive $χ^{(2)}$ converter. By explicitly retaining the quantum coherence of the coupled electron-phonon-photon dynamics, our model describes a two-stage buildup of entanglement - first between signal and idler photons and subsequently between idler photons mediated by material coherence. This coherent light-matter interaction imprints the internal dynamics of the medium onto the interferometer output, yielding phase-sensitive interference that enables indirect readout of terahertz-band signal modes via near-infrared detection. The results reveal a route toward entanglement-assisted terahertz sensing and establish a general framework for treating nonlinear quantum media as active components in interferometric architectures.

Figures (6)

• Figure 1: Schematic of electron-phonon-photon model used to describe SPDC process in the interferometer.
• Figure 2: Schematic of the Mach-Zehnder-type interferometer with two identical electron-phonon coupled systems (A and B). (a) Configuration C1: the signal mode generated in A is injected into B, so that both media share the same signal field. (b) Configuration C2: the signal path from A to B is blocked, so each medium interacts only with its local signal mode.
• Figure 3: (a) The average number of pump photons $N_{1j}(t)= \ev{c^{\dagger}_{1j}c_{1j}}$ for $j=A, B$, (b) The average number of idler photons $N_{2j}(t) = \ev{c^{\dagger}_{2j}c_{2j}}$ for $j=A, B$, (c) The average number of signal photons $N_{3}(t) = \ev{c^{\dagger}_{3}c_{3}}$
• Figure 4: Quantum mutual information $I_{M}(t)$. (a) Signal-idler $j$$(j=A,B)$. (b) Idler $A$-idler $B$. The solid and dash-dotted lines correspond to those for C1 and C2, respectively.
• Figure 5: Output idler photon number from BS2, $N_{BS2}=\langle c_{2'A}^\dagger c_{2'A} \rangle$. The solid and dash-dotted lines correspond to C1 and C2, respectively.