Sensing coherent phonons with two-photon interference

Abstract

Detecting coherent phonons pose different challenges compared to coherent photons due to the much stronger interaction between phonons and matter.This is especially true for high frequency heat carrying phonons, which are intrinsic lattice vibrations experiencing many decoherence events with the environment, and are thus generally assumed to be incoherent.Two photon interference techniques, especially coherent population trapping (CPT) and electromagnetically induced transparency (EIT), have led to extremely sensitive detection, spectroscopy and metrology.Here, we propose the use of two photon interference in a three-level system to sense coherent phonons.Unlike prior works which have treated phonon coupling as damping, we account for coherent phonon coupling using a full quantum-mechanical treatment.We observe strong asymmetry in absorption spectrum in CPT and negative dispersion in EIT susceptibility in the presence of coherent phonon coupling which cannot be accounted for if only pure phonon damping is considered.Our proposal has application in sensing heat carrying coherent phonons effects and understanding coherent bosonic multi-pathway interference effects in three coupled oscillator systems.Phonons are packets of vibrational energy that shares many similarities with its bosonic cousin photons.Advances in nanofabrication has enabled many parallels between the development of photon and phonon control.Parallel developments in passive control techniques include photonic [1] versus phonoic crystals [2], optical [3] versus acoustic metamaterials [4] etc. Development in active manipulation of electromagnetic waves through light-matter interaction have led to creation of nanoscale optical emitters [5] and gates [6] and similar progress have been made in controlling phonons using their interaction with matter especially in the realms of optomechanics [7] and phononic devices [8,9].Phonons span a vast frequency range and while techniques to control and sense lower frequency coherent phonons have been well-developed [10-19], heat carrying coherent terahertz acoustic phonons have been harder to measure directly due to the small wavelength and numerous scattering mechanism at these small wavelengths [20].In the past, THz crystal phonons have been generated and detected in low temperature experiments with defect doped crystals [21-24], with experimental evidence of coherent phonon generation [25][26][27].At the same time, interpretation of non-equilibrium phonon transport, with the advancement of nanoscale electrical heating and ultrafast optical pump-probe techniques, have allowed us to infer phonon coherence from broadband thermal conductivity measurements [28][29][30][31][32].There have been also interest of using defect-based techniques as a thermal probe using perturbation to energy levels due to changes in temperature [33].Furthermore, surface deflection techniques with ultrafast optics have also been used to generate phonons close to THz frequencies in materials [34][35][36][37].Defect-based techniques are attractive compared to both thermal conductivity measurement and deflection techniques due to its ability to directly access atomic length scales where THz phonon wavelength resides.Also, the energy levels in the excited state [21,38,39] and ground state [25,40] electron manifold of these defects can match the phonon energy precisely, resulting in a narrow band phonon detector.In light of the success of defect-based optical absorption techniques in coupling directly to high frequency phonons, we propose the use of two photon interference to measure the coherence properties of these phonons.