Photon-phonon interaction is a powerful mechanism for all-optical signal processing, slow (fast) light, microscopy, spectroscopy, microwave photonics, and sensing. Here, we demonstrate a photon-echo-like phenomenon induced by a phonon, whose mechanism is represented by a coherent photon-phonon chain interaction (PPCI) theory referring to the alternating evolution between Stokes scattering and anti-Stokes scattering. An analytical solution, including the impulse response of the coherent PPCI theory, is derived to quantitatively analyze the energy conversion between photon and phonon, showing a damped photoacoustic oscillation. All theoretical analysis, numerical simulation, and experiments confirm that the adjacent order echoes have a phase difference of \ensuremath{\pi}, i.e., phase flip, and the echoes generated by using photon and phonon as the initial excitation sources, respectively, are in inverse phase. As a result, the echoes up to the third-order are theoretically analyzed by the proposed coherent PPCI theory and verified by the experiment. This physical mechanism bodes well for a class of photonics applications in telecommunications, optical metrology, and optical computation.
Photon-phonon interaction is a powerful mechanism for all-optical signal processing, slow (fast) light, microscopy, spectroscopy, microwave photonics, and sensing. Here, we demonstrate a photon-echo-like phenomenon induced by a phonon, whose mechanism is represented by a coherent photon-phonon chain interaction (PPCI) theory referring to the alternating evolution between Stokes scattering and anti-Stokes scattering. An analytical solution, including the impulse response of the coherent PPCI theory, is derived to quantitatively analyze the energy conversion between photon and phonon, showing a damped photoacoustic oscillation. All theoretical analysis, numerical simulation, and experiments confirm that the adjacent order echoes have a phase difference of \ensuremath{\pi}, i.e., phase flip, and the echoes generated by using photon and phonon as the initial excitation sources, respectively, are in inverse phase. As a result, the echoes up to the third-order are theoretically analyzed by the proposed coherent PPCI theory and verified by the experiment. This physical mechanism bodes well for a class of photonics applications in telecommunications, optical metrology, and optical computation.
The photon wave function formalism provides an alternative description of some quantum optical phenomena in a more intuitive way. We use this formalism to describe the Stokesanti-Stokes (SaS) correlated scattering process present in Raman scattering. In this process, two photons from a laser beam are inelastically scattered by a phonon created by the first photon (Stokes processes) and annihilated by the second photon (anti-Stokes process), producing a pair of Stokes–anti-Sokes (SaS) photons. . We arrive at an expression for the two-photon wavefunction, in the time and frequency domains, of the scattered SaS photon pair, which is in agreement with a number of experimental results. It was shown, from the phase matching analysis, that the scattering pattern is compatible with the experiments. It was seen that, in the application for Pump-and-probe experiments, it was possible to generate the correct curves for the decay of the population of phonons in the sample. Finally, it was verified that, through the analysis of the joint spectrum of the pairs, information was obtained about the entanglement in frequency of the scattered photons. Thus, it is concluded that, from the results, the photon wave function formalism provides an intuitive and robust way to calculate the SaS scattering properties.
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.
Raman scattering of photons into phonons gives rise to entangled photon pairs when the phonon emitted in a Stokes process is coherently absorbed in antiStokes scattering, forming the photonic analog of Cooper pairs. We present a nonperturbative theory for the time evolution of photonic Cooper pairs that treats interacting photons and phonons as a hybrid excitation, the Ramaniton. As the Ramaniton propagates in a waveguide it displays quantum oscillations between photon and phonon occupation, leading to resonant squeezed Stokes-antiStokes light when the phonon occupation becomes equal to zero without recurring back to the photon vacuum. This phenomenon is predicted to generate up to 28 dB of squeezed light even in standard silicon on insulator waveguides. Published by the American Physical Society 2024
The unusual two-photon emission by Bose-condensed excitons caused by simultaneous recombination of two excitons with opposite momenta leaving the occupation numbers of excitonic states with momenta $\mathbf{p}\ensuremath{\ne}0$ unchanged (below coherent two-exciton recombination) is investigated. Raman scattering accompanied by the analogous two-exciton recombination (or creation) is also analyzed. The excess momentum equal to the change of the electromagnetic field momentum in these processes can be transferred to phonons or impurities. The processes under consideration take place if there is Bose condensation in the interacting exciton system, and, therefore, can be used as a method to reveal exciton Bose condensation. If the frequency of the incident light $\ensuremath{\omega}<2\ensuremath{\Omega}$ $(\ensuremath{\Omega}$ is the frequency corresponding to the recombination of an exciton with p=0), the coherent two-exciton recombination with the excess momentum elastically transferred to impurities leads to the appearance of the spectral line $2\ensuremath{\Omega}\ensuremath{-}\ensuremath{\omega}$ corresponding to the induced two-photon emission. In this case the anti-Stokes line on frequency $\ensuremath{\omega}+2\ensuremath{\Omega}$ also appears in the Raman spectrum. If $\ensuremath{\omega}>2\ensuremath{\Omega},$ there are both Stokes and anti-Stokes lines on frequencies $\ensuremath{\omega}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\Omega}$ in the Raman spectrum. The induced two-photon emission is impossible in this case. The spectral lines mentioned above have phonon replicas on frequencies $|\ensuremath{\omega}\ifmmode\pm\else\textpm\fi{}(2\ensuremath{\Omega}\ensuremath{-}n{\ensuremath{\omega}}_{0}^{s})|$ corresponding to the transmission of the excess momentum (partially or as a whole) to optical phonons of frequency ${\ensuremath{\omega}}_{0}^{s}$ (n is an integer number). The quantitative estimation shows that the light corresponding to the coherent two-exciton recombination can be experimentally observed in Cu2O.
The correlated Raman scattering, referred to here as the SaS process, occurs with the annihilation, within a material, of two photons of an excitation laser and the creation of a quantum correlated Stokes (S) and anti-Soktes (aS) photon pair where the phonon created in the S process is annihilated in the aS scattering. We found that, in addition to real SaS process where the energy exchange coincides with the energy of a vibrational state of the material, there is also the virtual SaS process, whose the exchange of energy and momentum between the photons of the laser, generating the S-aS photon pair, is mediated by a virtual vibrational excitation, setting up a photon-photon interaction similar to the electron-electron attraction responsible for the creation of Cooper pairs of the BCS theory of superconductivity. We observed the SaS process in transparent media in general, by measuring non-classical values of the normalized second-order cross-correlation function of the Stokes and anti-Stokes fields, 2(0). In diamond, we characterize the intensity of the virtual SaS scattering ( ) as a function of the virtual phonon energy, proving that the SaS process occurs only when the photon-photon interaction is attractive, as in the BCS theory for the Cooper pairs. We show that photons S and aS from the SaS process are scattered predominantly in the same polarization as the excitation laser of the sample and, with this, we implemented the pump-probe technique to study the lifetime of the real phonon (obtained in the diamond order 2.8 ps ) and the lifetime of the virtual excitation, which proved to be inferior to the temporal resolution of the measurement’s, characterizing one of the main differences between the two processes. We also observed that, due to the relations of energy and momentum conservation, have the same spatial intensity profile of the non-interacting laser that crosses the sample, different from the behavior observed for uncorrelated Raman scattering which spreads photons in all directions. We observed that the efficiency of the SaS scattering is proportional to the Raman scattering cross-section when we compare the process in different hydrocarbons and we generalize the observations made in the diamond to the sample of liquid decane. In water, the values of 2(0), predicted by the theoretical description of the process, corroborate the experimental data, validating the BCS theory for virtual SaS scattering, setting the pair of Stokes and anti-Stokes photons as counterparts of the Cooper pairs.
A theoretical analysis is carried out for the recently developed three-pulse photon echo spectroscopy employing dual frequency combs (DFC) as the light sources. In this method, the molecular sample interacts with three pulse trains derived from the DFC, and the generated third-order signal is displayed as a two-dimensional (2D) spectrum that depends on the waiting time introduced by employing the asynchronous optical sampling method. Through the analysis of the heterodyne-detected signal interferogram using a local oscillator derived from one of the optical frequency combs, we show that the 2D spectrum closely matches the spectrum expected from a conventional approach with four pulses derived from a single femtosecond laser pulse, and the waiting time between the second and third field-matter interactions is given by the down-converted detection time of the interferogram. The theoretical result is applied to a two-level model system with solvation effect described by solvatochromic spectral density. The model 2D spectrum reproduces spectral features such as the loss of frequency correlation, dephasing, and spectral shift as a function of the population time. We anticipate that the present theory will be the general framework for quantitative descriptions of DFC-based nonlinear optical spectroscopy.