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Quantum Electronics and Laser Science Conference

Generation of coherent LO phonons by nonlinearly induced longitudinal light

Dirk Michaelis, Ulf Peschel, F. Lederer

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Summary form only given. If resonantly excited the effect of the longitudinal phonon mode is dominant resulting in an effective three-wave interaction. Photons are down converted between the optical waves while creating a coherent phonon emission via difference frequency mixing. If a phonon background is present and a single optical pulse is injected, a new down-shifted wave is generated. In any case a mutual locking of the two optical pulses can be observed although their group velocities are different. In the coherent case a subsequent up and down conversion occurs, where an equilibrium state of the field distribution is readily obtained for incoherent phonons. In the latter case the resulting rather stable bound state. The created pulses can be used to detect the density and spectral properties of the phonon background.

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Resonant and near-resonant two-photon excitations with ultrashort laser pulses of forbidden atomic transitions give access to a wide class of nonlinear-optical processes such as two-photon absorption, stimulated Raman scattering, four-wave sum- and difference-frequency mixing. The latter has proofed to be a powerful tool for efficient femtosecond pulse generation in the VUV-spectral range [1]. Nevertheless, up to now only few experimental results have been obtained which allow the direct observation of the coherent dynamics in two-photon induced radiation-matter interactions (see experimental papers [2-5] and monograph [6]).

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Coherent Phonon Generation and High Frequency Phonon Spectroscopy.

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Sensing coherent phonons with two-photon interference

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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.

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It is revealed that the generation of a coherent wave by frequency conversion of incoherent waves is a characteristic feature of three-wave interaction in a nonlinear medium when angular dispersion of input waves is properly chosen. In this case the combining action of the pairs of spectral components of incoherent waves may result in the cumulative driving of a single plane monochromatic wave in up-conversion and down-conversion processes. As a fundamental result we point out an enhancement of the spectral radiance of the generated wave in comparison with incoherent waves.

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Electron-phonon dynamics in optically excited quantum dots: Exact solution for multiple ultrashort laser pulses

Alexei Vagov, V. M. Axt, T. Kühn

A model of semiconductor quantum dots coupled to phonons and laser light, which is relevant in the limit of strong electronic confinement, is investigated. For an arbitrary sequence of excitations by ultrafast pulses, analytical solutions are obtained for all pertinent density-matrix elements. The results are nonperturbative with respect to the coupling to both phonons and laser light. The derivation depends neither on a particular choice of electronic wave functions nor on a particular wave-vector dependence of the phonon interaction or phonon dispersion. All components of the density matrix exhibit oscillatory dependences on the pulse areas of the exciting pulses analogously to the Rabi oscillations known from simple two-level systems. Three typical applications of the general results are worked out: (a) the influence of phonons on four-wave-mixing spectra, (b) the coherent control of electronic dot occupations in the presence of phonons, and (c) the dynamics of phonon correlations including the formation of a stable polaron spatially localized in the dot and the emission of a pulsed phonon wave packet that leaves the dot.

Physical review. B, Condensed matter•Oct 23, 2002•152 citations
Summary form only given. If resonantly excited the effect of the longitudinal phonon mode is dominant resulting in an effective three-wave interaction. Photons are down converted between the optical waves while creating a coherent phonon emission via difference frequency mixing. If a phonon background is present and a single optical pulse is injected, a new down-shifted wave is generated. In any case a mutual locking of the two optical pulses can be observed although their group velocities are different. In the coherent case a subsequent up and down conversion occurs, where an equilibrium state of the field distribution is readily obtained for incoherent phonons. In the latter case the resulting rather stable bound state. The created pulses can be used to detect the density and spectral properties of the phonon background.
Resonant and near-resonant two-photon excitations with ultrashort laser pulses of forbidden atomic transitions give access to a wide class of nonlinear-optical processes such as two-photon absorption, stimulated Raman scattering, four-wave sum- and difference-frequency mixing. The latter has proofed to be a powerful tool for efficient femtosecond pulse generation in the VUV-spectral range [1]. Nevertheless, up to now only few experimental results have been obtained which allow the direct observation of the coherent dynamics in two-photon induced radiation-matter interactions (see experimental papers [2-5] and monograph [6]).
A number of optical techniques have been developed in recent years which have been applied to study the dynamics of high frequency phonons. Monoenergetic phonons were generated by spin-lattice relaxation between two electronically excited states of an impurity ion. Resonant trapping provided the means to detect these phonons with good temporal resolution. VSPS was used to detect high frequency phonons over a wide frequency range with excellent temporal, spectral and spatial resolution. The life-time of a monoenergetic non-equilibrium distribution of phonons was determined by the observation of optical dephasing, using free induction decay(FID), which results from phonon induced coherence loss(PICOLO). Non-resonant fluorescence line narrowing(FLN) techniques provided a means to determine the spectral distribution of non-equilibrium phonons generated by spin lattice relaxation. Keywords: Phonons; Phonon decay; Coherent phonon generation; Phonon spectroscopy; High frequency phonons and Monoenergetic phonons.
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.
We present results for two coherent control schemes in semiconductor heterostructures obtained within Boltzmann- Bloch equations. The latter are obtained from Dyson's equation within the Keldysh nonequilibrium Green's function approach and allow a microscopic analysis of coherent control schemes in semiconductors. Here we focus on the coherent control of optical gain and longitudinal optical photon emission rates in intersubband transitions in a three-subband model of a biased asymmetric double well. We show that by coupling the two energetically close subbands with a coherent microwave field, we can induce coherence into the carriers in the double well, thus manipulating intersubband transitions. By adjusting the phase of the microwave field, we can achieve significant modification to the gain spectra for light pulses shorter than the period of the low frequency intersubband polarization. Similarly, LO- phonon induced intersubband transitions can be controlled due to quantum interference between electron-lattice and electron-light interactions.
It is revealed that the generation of a coherent wave by frequency conversion of incoherent waves is a characteristic feature of three-wave interaction in a nonlinear medium when angular dispersion of input waves is properly chosen. In this case the combining action of the pairs of spectral components of incoherent waves may result in the cumulative driving of a single plane monochromatic wave in up-conversion and down-conversion processes. As a fundamental result we point out an enhancement of the spectral radiance of the generated wave in comparison with incoherent waves.
A model of semiconductor quantum dots coupled to phonons and laser light, which is relevant in the limit of strong electronic confinement, is investigated. For an arbitrary sequence of excitations by ultrafast pulses, analytical solutions are obtained for all pertinent density-matrix elements. The results are nonperturbative with respect to the coupling to both phonons and laser light. The derivation depends neither on a particular choice of electronic wave functions nor on a particular wave-vector dependence of the phonon interaction or phonon dispersion. All components of the density matrix exhibit oscillatory dependences on the pulse areas of the exciting pulses analogously to the Rabi oscillations known from simple two-level systems. Three typical applications of the general results are worked out: (a) the influence of phonons on four-wave-mixing spectra, (b) the coherent control of electronic dot occupations in the presence of phonons, and (c) the dynamics of phonon correlations including the formation of a stable polaron spatially localized in the dot and the emission of a pulsed phonon wave packet that leaves the dot.