Coherent THz Phonons Driven by Light Pulses and the Sb Problem: What is the Mechanism?

Abstract

Femtosecond laser pulses generate in Sb coherent E g phonons at ഠ3.4 THz, in addition to oscillations of A 1g symmetry accounted for by the phenomenological displacive-excitation model. Experiments agree with theoretical calculations showing that the coherent driving force in absorbing materials like Sb is determined by Raman processes, as in transparent media. The Raman formalism provides a unifying approach for describing light-induced motion of atoms of both impulsive and displacive character. [S0031-9007(96)01455-X] PACS numbers: 78.47.+p, 63.20.Kr, Following recent advances in femtosecond laser technology, several groups demonstrated that the propagation of light pulses in solids is accompanied by intense lattice vibrations showing a high degree of spatial and temporal coherence [1][2][3][4][5][6][7][8][9]. The availability of coherent phonons at THz frequencies has led to a variety of suggestions for applications and experiments involving, in particular, time-domain spectroscopy of phonons using pumpprobe methods [1][2][3][4][5][6][7][8][9], conversion of mechanical into coherent electromagnetic energy [7], and intriguing proposals relying on photon control of the ionic motion [10,11]. While coherent vibrations have been produced in insulators, semiconductors, and metals using, basically, the same technique [1][2][3][4][5][6][7][8][9], the experiments reveal fundamental, but poorly understood differences between transparent and opaque materials [1,4]. This Letter presents a unifying mechanism for phonon generation that explains the differences.Phenomenologically, the lattice motion is described bywhere Q is a classical phonon field of frequency V, and F is the driving force [1]. In transparent media, it has been known for a long time that vibrational coherences rely on coherent (stimulated) Raman scattering (CRS) for which F P uy ͑x R uy E u E y ͒͞2. Here, E u denotes a component of the optical pump field, x R uy ഠ ≠x ͑1͒ uy ͞≠Q is the nonlinear Raman, and x ͑1͒ uy is the linear susceptibility [12]. When the pulse width t 0 is small compared with V 21 , F acts as an impulsive force giving Q~sin͑Vt͒. For absorbing substances, a unique process has so far not been identified [1]. The experimental evidence indicates that Raman selection rules are strictly obeyed (see, e.g., [3,5,7,13]). However, the oscillation phase varies from material to material, and relative intensities gained from time-domain measurements and spontaneous Raman scattering (RS) do not appear to correlate [4]. One of the leading proposals for explaining opaque systems is the mechanism known as displacive excitation of coherent phonons (DECP). The DECP model, accounting, in particular, for results on semimetals [4], provides a simple explanation for driving fully symmetric modes, seemingly unrelated to Raman scattering [4,14]. In the DECP picture, the equilibrium positions of the ions experience a sudden shift due to coupling with photoexcited carriers created by the optical pulse. Hence, F is steplike and, thus, Q~͓1 2 cos͑Vt͔͒. As discusse...

Control of Electron Coherences with Coherent Phonons

“…In this context, we recall that the spontaneous cross-section is proportional to |/?nv| 2 ; hence, ISRS and conventional Raman spectra are closely related. These considerations apply strictly to transparent substances but, as discussed in [29] and supported by our resonant impulsive results [23], they can be extended to cover opaque materials as well. The resonant work covers the E' 2 -resonance of antimony [23,33] and an investigation of GaSe using impulsive excitation resonant with the band gap [33].…”

“…These considerations apply strictly to transparent substances but, as discussed in [29] and supported by our resonant impulsive results [23], they can be extended to cover opaque materials as well. The resonant work covers the E' 2 -resonance of antimony [23,33] and an investigation of GaSe using impulsive excitation resonant with the band gap [33]. We also discuss squeezed phonons in KTa0 3 , representing quantum entanglement between states at ± k of the same branch [30], and (thermally-) entangled transverse optical-acoustical modes in SrTiC^ [34].…”

“…Hence the force is step-like and, thus, Q « cos(ßr). Our studies on antimony [23] contain theoretical and experimental results which question the validity of the DECP interpretation. The theoretical work shows that the DECP model can be obtained as a particular case of resonant coherent RS [23] and, therefore, that Raman scattering provides a unifying approach for describing light-induced motion of atoms of both impulsive and displacive character.…”

Materials Modification by Electronic Excitation

“…Another class of process exploits the coherent phonons produced by light pulses (e.g. [6]), perhaps so that phonon coherence is exploited to control the¯ow of vibrational energy usefully. There will be mixed cases, in which both photons and phonons have roles.…”

Resonant tunneling in a pulsed phonon field

“…Experimentally, this might be realized by subjecting the sample to suitable light pulses, the propagation of which is known to be accompanied by lattice vibrations. 9 It is well known, both experimentally 10 and theoretically, 11 that optical phonons lead to additional structure in the measured IV curve of resonant tunneling systems, i.e., secondary maxima at voltages determined by the LOphonon frequency. To investigate the time-dependent formation of these structures caused by pulsed phonon fields, we generalize the nonequilibrium linked-cluster expansion ͑NLCE͒ of Ref.…”