Stokes anti-Stokes Research Articles

Measurement-induced collective vibrational quantum coherence under spontaneous Raman scattering in a liquid

Spontaneous vibrational Raman scattering is a ubiquitous form of light–matter interaction whose description necessitates quantization of the electromagnetic field. It is usually considered as an incoherent process because the scattered field lacks any predictable phase relationship with the incoming field. When probing an ensemble of molecules, the question therefore arises: What quantum state should be used to describe the molecular ensemble following spontaneous Stokes scattering? We experimentally address this question by measuring time-resolved Stokes–anti-Stokes two-photon coincidences on a molecular liquid consisting of several sub-ensembles with slightly different vibrational frequencies. When spontaneously scattered Stokes photons and subsequent anti-Stokes photons are detected into a single spatiotemporal mode, the observed dynamics is inconsistent with a statistical mixture of individually excited molecules. Instead, we show that the data are reproduced if Stokes–anti-Stokes correlations are mediated by a collective vibrational quantum, i.e. a coherent superposition of all molecules interacting with light. Our results demonstrate that the degree of coherence in the vibrational state of the liquid is not an intrinsic property of the material system, but rather depends on the optical excitation and detection geometry.

Tip-Enhanced Stokes-Anti-Stokes Scattering from Carbyne.

Carbyne, a linear chain of carbon atoms, is the truly one-dimensional allotrope of carbon and the strongest known Raman scatterer. Here, we use tip-enhanced Raman scattering (TERS) to further enhance the Raman response of a single carbyne chain confined inside a double-walled carbon nanotube. We observe an increase of the anti-Stokes scattering by a factor of 3290 and a 22-fold enhancement of the anti-Stokes/Stokes ratio relative to far-field measurements. The power dependence of the anti-Stokes/Stokes ratio under TERS conditions is indicative of coherent Stokes–anti-Stokes scattering mediated by an excited phonon. The role of resonance effects and laser-induced heating are discussed and potential opportunities are outlined.

Terahertz cavity optomechanics using a topological nanophononic superlattice.

Cavity optomechanical systems operating at the quantum ground state provide a novel way for the ultrasensitive measurement of mass and displacement and provide a new toolbox for emerging quantum information technologies. The high-frequency optomechanical devices could reach the quantum ground state at a high temperature because the access to high frequency is favorable for the cavity optomechanical devices to decouple from the thermal environment. However, reaching ultra-high frequency (THz) is extremely difficult due to the structure of cavity optomechanical devices and properties of materials. In this paper, by introducing acoustic topological interface states, we designed a THz mechanical frequency semiconductor pillar microcavity optomechanical device based on a GaAs/AlAs nanophononic superlattice. In the optomechanical system, multi-optical cavity modes are obtained and the frequency separation between adjacent optical modes is equal to the frequency of the mechanical mode (optomechanical frequency matching). By detuning the laser pump to a lower (higher) energy-resolved sideband to make a spontaneously scattering photon doubly resonate with optical cavity modes at an anti-Stokes (Stokes) frequency and pump frequency, we can achieve an anti-Stokes (Stokes) scattering efficiency 2600 (1800) times larger than that of Stokes (anti-Stokes) scattering, which provides potential for laser cooling and low threshold phonon lasing in the optomechanical system.

Enhancement of Stokes–anti-Stokes correlations by the classical incoherent incident light

It is known that spontaneous Raman scattering is accompanied by the appearance of nonclassical cross correlations of photons at Stokes and anti-Stokes frequencies. Such correlations occur due to the internal nonlinear interaction between electronic and nuclear vibration degrees of freedom. Since the properties of a given media are unchangeable, the possibilities for controlling the cross correlations are limited. This, in turn, restricts the possible applications of the correlated light obtained during the spontaneous Raman scattering. In this work, we investigate the influence of statistical properties of an incident light on the cross correlations of Stokes and anti-Stokes light. We show that the incoherence of the incident light results not only in the incoherence of the scattered light but also in the enhancement of the interbeam coherence at different frequencies. We demonstrate that the cross correlations of Stokes and anti-Stokes light intensities are enhanced when the incident light with high second-order autocorrelation function is applied. Our results pave the way to control correlated light obtained in the process of spontaneous Raman scattering.

Stokes–anti-Stokes light-scattering process: A photon-wave-function approach

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 process of correlated Stokes--anti-Stokes 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 Stokes--anti-Sokes (SaS) photon pair. We arrive at an expression for the two-photon wave function of the scattered SaS photon pair, which is in agreement with a number of experimental results.

Quantum reversibility in cooperative interaction of the atom system with bi-modal cavity field in Raman conversion

The restoration of the initial state in the Raman interaction of the two atoms with the quantified pump and Stokes (anti-Stokes) cavity modes is analytically obtained. For this the su (2) symmetry representation of the bimodal field and a system of two atoms in scattering interaction is proposed for the simplification of the problem. Using the proprieties of the generators su (2) algebra the exact non-stationary solution of the system of two atoms in interaction with the bimodal field is found, taking into consideration the initial disentangled state between the atomic and field superposition. It is demonstrated that after this collapse and revivals of the inversion of flying atoms in the processes of absorption and emission of the photons from Stokes and pump modes the system atoms and field becomes entangled. The conditions of the restoration of the initial state of the atom-field system were established as a function of the flying time through the resonator possible. A set of discrete flying time intervals for the restoration of the initial disentangled state was found.

Study of the intensity asymmetry in Brillouin light scattering from magnons in FeNi thin films

The Stokes–anti-Stokes intensity asymmetry, observed by Brillouin light scattering from surface magnetic excitations in thin FeNi films, has been studied by replacing substrates with different dielectric constant as well as varying the applied magnetic field and the laser incident angle. The experimental results show that the Stokes–anti-Stokes intensity ratio depends upon the applied magnetic fields, the wave vectors and also the material of the substrates used to support the FeNi films. Most interesting is that for a fixed magnetic field and a fixed wave vector, the intensity ratio is much more significant for the FeNi film deposited on Nb-doped SrTiO3 substrate than that deposited on surface oxidized Si substrate. The phenomenon of the different asymmetry is depending on the dielectric constant of the substrates. The tendency is in agreement with the theory.

Quasidistribution of phases in Raman process with weak and strong pumps

Nonclassicality is quantified using a quasidistribution of phases for the Raman process under both weak and strong pump conditions. In the former case, the solution is applicable to both resonant and off-resonant Raman processes, while strong classical pump is assumed at resonance. Under weak pump conditions (i.e. in a complete quantum treatment), the phase difference of phases described by single nonclassical modes is required to be filtered to describe a regular distribution function, which is not the case with strong pump. Compound Stokes-phonon mode shows nonclassical features of phases in both weak and strong pumping, which effect is similar to that for compound pump-phonon (Stokes–anti-Stokes) mode with weak (strong) pump. While anti-Stokes-phonon mode is observed to be classical and coherence conserving in strong pump case, pump-Stokes mode shows similar behavior in a special case in quantum treatment.

Stokes–anti-Stokes correlated photon properties akin to photonic Cooper pairs

Photons interact with each other in condensed matter through the same mechanism that forms Cooper pairs in superconductors -- the exchange of virtual phonons [PRL 119, 193603 (2017)]. It is however unclear which consequences of this interaction will be observable and potentially lead to further analogy with superconductivity. We investigate the energy, momentum and production rate of correlate Stokes-anti-Stokes (SaS) photons in diamond and other transparent media, experiencing properties akin to those of electronic Cooper pairs. The rate of correlated SaS production depends on the energy shifts of the pair, which in the BCS theory determines whether there should be an attractive or repulsive interaction. With this view, we only observe correlated SaS in the case of attractive interactions. While traditional photon-phonon collisions scatter light in all directions, the correlated SaS photons follow the same path as the noninteracting laser. The observed correlated SaS photon pairs are rare, but our model indicates paths to achieve higher interaction energies.

Multiple transparency in a multimode quadratic coupling optomechanical system with an ensemble of three-level atoms

We theoretically investigate a multimode quadratic coupling optomechanical system (OMS) assisted with N cold Λ-type three-level atoms. The coupling interaction between two mechanical membranes (MR1 and MR2) and the cavity is quadratic. The three-level atoms interact with an external controlling field and an internal cavity field. The optical cavity is driven by a strong coupling field and a weak probe field. In the resolved sideband regime, four transparency windows are obtained due to the atomic coherence and quadratic coupling in the absorption spectrum for the suitable choice of the controlling parameters. We analyze how to vary the number of the transparency window dips and to adjust their mutual spacing by changing the controlling parameters such as strength of the quadratic coupling between MR1 (MR2) and the cavity, the collective coupling strength between the atomic ensemble and the cavity field, the Rabi frequency associated with the coupling interaction between the controlling field and the three-level atom, power of the coupling field, different frequencies and decay rates of MR1 (MR2), decay rate of the cavity field, and the environmental temperature. Further, we also demonstrate the normal-mode splitting in the generated Stokes and anti-Stokes field in the OMS, where the changing collective coupling strength affects the splitting width of the output field at the Stokes (anti-Stokes) frequency.

基于正交相干接收的布里渊斯托克斯与反斯托克斯散射光分离技术

基于正交相干接收的布里渊斯托克斯与反斯托克斯散射光分离技术

Quantum Optics Model of Surface-Enhanced Raman Spectroscopy for Arbitrarily Shaped Plasmonic Resonators

We present a self-consistent quantum optics approach to calculating the surface enhanced Raman spectrum of molecules coupled to arbitrarily shaped plasmonic systems. Our treatment is intuitive to use and provides fresh analytical insight into the physics of the Raman scattering near metallic surfaces and can be applied to a wide range of geometries including resonators, waveguides, as well as hybrid photonic-plasmonic systems. Our general theory demonstrates that the detected Raman spectrum originates from an interplay between nonlinear light generation and propagation. Counter intuitively, at the nonlinear generation stage, we show that the Stokes (anti-Stokes) signal at the molecule location depends on the plasmonic enhancements, through the local density of photon states (LDOS), at the anti-Stokes (Stokes) frequency. However, when propagating from the vibrating molecule to the far field, the Stokes (anti-Stokes) emission experiences a plasmonic enhancement at the Stokes (anti-Stokes) frequency, as expected. We identify the limits of the commonly known E^4 electric-field rule for Raman signal enhancement near plasmonic surfaces at low pump powers, as well as a different E^8 rule at high pump powers, and we clarify the role of the LDOS. Our theory uses a generalized quantum master equation where the plasmonic system is treated as an environmental bath that is described through the photonic Green function of the medium. Therefore, any electrodynamics related physics, such as quenching and propagation, are self-consistently included in the model. The presented formalism is also capable of spatially describing the full Raman response in a simple analytical way, which is typically not possible using simpler coupled mode theories, even if one adopts a quantum picture.

Linking classical and molecular optomechanics descriptions of SERS.

The surface-enhanced Raman scattering (SERS) of molecular species in plasmonic cavities can be described as an optomechanical process where plasmons constitute an optical cavity of reduced effective mode volume which effectively couples to the vibrations of the molecules. An optomechanical Hamiltonian can address the full quantum dynamics of the system, including the phonon population build-up, the vibrational pumping regime, and the Stokes-anti-Stokes correlations of the photons emitted. Here we describe in detail two different levels of approximation to the methodological solution of the optomechanical Hamiltonian of a generic SERS configuration, and compare the results of each model in light of recent experiments. Furthermore, a phenomenological semi-classical approach based on a rate equation of the phonon population is demonstrated to be formally equivalent to that obtained from the full quantum optomechanical approach. The evolution of the Raman signal with laser intensity (thermal, vibrational pumping and instability regimes) is accurately addressed when this phenomenological semi-classical approach is properly extended to account for the anti-Stokes process. The formal equivalence between semi-classical and molecular optomechanics descriptions allows us to describe the vibrational pumping regime of SERS through the classical cross sections which characterize a nanosystem, thus setting a roadmap to describing molecular optomechanical effects in a variety of experimental situations.

Spectral features of anti-Stokes and Stokes modes generated by stimulated Raman scattering in liquid toluene

Stimulated Raman scattering leading to the generation of four first-order Stokes modes at shifts of 862.9, 1035, 2967 and 3086 cm−1, one second-order Stokes mode at a shift of 2032.5 cm−1 and one first-order anti-Stokes mode at a shift of 946.3 cm−1 has been measured in an experiment using liquid toluene. The observed shifts are assigned to the earlier reported Raman shifts of toluene at 786, 1006, 2979, 3060 cm−1 due to ring-breathing mode, ring deformation mode, CH3 stretching mode and CH stretching mode, respectively. Simultaneous measurement of all the Raman modes, including the second-order Stokes and first-order anti-Stokes, and their correct assignment to the vibrational modes of toluene is not reported widely in earlier work. The Raman modes generated from toluene emerge as concentric rings of different diameters. The phase-matching angle for anti-Stokes generation is thus measured and compared with the expected value from calculation. The spectral broadening observed near two of the modes is explained with the help of Raman-active modes of toluene reported earlier by others. Raman shifts, threshold levels, gain and beam profile of all the modes, along with the phase matching of the anti-Stokes mode, are reported.

Combined spontaneous Stokes and coherent anti-Stokes Raman scattering spectroscopy

The simultaneous determination of multiple parameters is the key in the characterization of processes and materials that change with time. In combustion environments, the combined measurement of temperature and chemical composition is particularly desirable. In the present work, possible approaches for the simultaneous application of spontaneous Raman scattering (RS) and coherent anti-Stokes Raman scattering (CARS) spectroscopy are proposed and analyzed. While RS provides concentration information of all major species, vibrational CARS is a highly accurate thermometry tool at flame conditions. Five experimentally feasible CARS–RS schemes are identified and discussed with respect to signal intensity, measurement volume, and experimental complexity. From this analysis, one scheme was found to be the best option. It utilizes a broadband dye laser centered at 852 nm as a pump and the fundamental 1064-nm radiation of the Nd:YAG as Stokes laser. The third harmonic is used as CARS probe and RS laser. The experimentally most elegant scheme replaces the third harmonic in the above scheme by the second harmonic hence involving the smallest number of optical components in the setup.

Stokes–anti-Stokes correlation in the inelastic scattering of light by matter and generalization of the Bose-Einstein population function

The Stokes and anti-Stokes components in the inelastic scattering of light are related to phonon statistics and have been broadly used to measure temperature and phonon lifetimes in different materials. However, correlation between the components are expected to change the Stokes/anti-Stokes intensity ratio, imposing corrections to the broadly used Bose-Einstein statistics. Here the excitation power dependence of these scattering processes is theoretically described by an effective Hamiltonian that includes correlation between the Stokes and the anti-Stokes events. The model is used to fit available experimental results in three-dimensional diamond and two-dimensional graphene, showing that the phenomenon can significantly increase in the low-dimensional system under specific resonance conditions. By setting the scientific basis for the Stokes-anti-Stokes correlated phenomenon, the use of the Bose-Einstein population function for reasoning the inelastic scattering is generalized, providing a model to predict the conversion of optical phonons into heat or light, according to coupling constants and decay rates. The model applies to inelastic scattering in general.

Stokes and anti-Stokes Raman spectra of the high-energy C-C stretching modes in graphene and diamond

The Stokes and the anti-Stokes Raman spectra from the high energy carbon–carbon stretching modes in graphene and diamond are studied, with a focus on their intensity dependence on the excitation laser power. For diamond, the experiment was performed on a 50 μm slice of chemical vapour deposition grown single crystal using a 785 nm laser, in both the continuous wave (CW) and pulsed mode-locked (ML—130 fs pulses) excitation regimes. For graphene, the experiments were performed on suspended samples, including single layer, bilayer with AB-staking, twisted bi-layer and a sample with 4–6 layers, using λ = 532 and 633 nm CW lasers. The Stokes and anti-Stokes intensities vary largely from sample to sample, and the anti-Stokes/Stokes intensity ratio shows different excitation laser power behaviours. These differences can be explained on the basis of laser heating or correlated Stokes–anti-Stokes scattering phenomena.

Detailed investigation of intermodal four-wave mixing in SMF-28: blue-red generation from green.

A short piece of commercial-grade SMF-28 optical fiber is pumped with a 680 ps high-peak power green laser. Red Stokes and blue anti-Stokes beams are generated spontaneously from vacuum noise in different modes in the fiber via intermodal four-wave mixing. Detailed experimental and theoretical analyses are performed and are in reasonable agreement. The large spectral shifts from the pump protect the Stokes and anti-Stokes from contamination by spontaneous Raman scattering noise. This work highlights the predictive power and limitations of a theoretical model to explain the experimental results for a process that relies on the amplification of quantum vacuum energy over more than 11 orders of magnitude.

Stokes-anti-Stokes correlations in diamond.

We investigate the arrival statistics of Stokes (S) and anti-Stokes (aS) Raman photons generated in thin diamond crystals. Strong quantum correlations between the S and aS signals are observed, which implies that the two processes share the same phonon; that is, the phonon excited in the S process is consumed in the aS process. We show that the intensity cross-correlation g(S,aS)(2)(0), which describes the simultaneous detection of Stokes and anti-Stokes photons, increases steadily with decreasing laser power and saturates at very low pump powers, implying that the number of Stokes-induced aS photons is comparable to the number of spontaneously generated aS photons. Furthermore, the coincidence rate shows a quadratic plus cubic power dependence, indicating the generation of multiple S photons per pulse at high powers.

The focusing effect on the angular distribution of the Raman antiStokes branch emissions

The angular distributions of the 1st to 3rd antiStokes emissions produced by Nd:YAG pumping a H 2 high pressure Raman cell have been measured and explained as a consequence of the destructive interference of the Stokes–antiStokes interaction.