Optical control of the coherent dynamics of a bismuth lattice at liquid-helium temperature at low and high excitation levels

The fully symmetric A_1g phonons of bismuth have been investigated at liquid-helium temperature by the coherent control method for various crystal excitation levels. It has been found that large-amplitude coherent phonons exhibit the “rigidity” of the phase, which is absent at a small amplitude. The impossibility of changing the phase of phonon oscillations appears at the excitation levels at which their amplitude relaxation law changes from exponential to power. The modification of the phase properties and relaxation law of the excitations of the crystal lattice can be understood in terms of the concept of the condensation of phonons, which occurs with an increase in the crystal excitation level.     

Generation of coherent terahertz phonons by sharp focusing of a femtosecond laser beam in the bulk of crystalline insulators in a regime of plasma formation

The generation of coherent terahertz phonons in a regime of plasma formation by a femtosecond laser radiation with an intensity of 10¹³ W/cm² in the bulk of crystalline quartz has been detected by the method of probing by a probe pulse of the third harmonic. A smooth increase in the frequency of coherent terahertz phonons from 2.2 to 5.5 THz has been detected, along with its subsequent sharp decrease down to 2.2 THz due to an α-β phase transition in crystalline quartz. The generation of 1-THz coherent phonons has been detected in BaF₂ crystals. A smooth variation of the frequency of coherent phonons from 2 to 2.5 THz has been detected in leucosapphire. The generation of coherent phonons during local laser excitation in CaF₂ and LiF crystals develops at the frequencies of 2.3 and 0.1 THz, respectively.     

On the nature of coherent phonons generated by ultrashort laser pulses in single-crystal antimony

Reflectivity oscillations generated by A_1g coherent phonons in an antimony single crystal have been studied by a method involving pumping and probing by femtosecond laser pulses, which was complemented by spectral filtration of the signal. An analysis of the spectrally resolved signal showed that not only the integrated intensity but also the spectrum of the probe pulse are functions of the delay time between the pumping and probing and oscillate between the Stokes and anti-Stokes components at the optical-phonon frequency. A comparison of the integrated lattice excitation relaxation dynamics with the spectrally resolved lattice excitation relaxation dynamics revealed new facets in the nature and generation mechanism of coherent phonons.     

Generation of coherent phonons in bismuth by ultrashort laser pulses in the visible and NIR: Displacive versus impulsive excitation mechanism

We have applied femtosecond pump-probe technique with variable pump wavelength to study coherent lattice dynamics in Bi single crystal. Comparison of the coherent amplitude as a function of pump photon energy for two different in symmetry Eg and A1g phonon modes with respective spontaneous resonance Raman profiles reveals that their generation mechanisms are quite distinct. We show that displacive excitation, which is the main mechanism for the generation of coherent A1g phonons, cannot be reduced to the Raman scattering responsible for the generation of lower symmetry coherent lattice modes.     

Investigation of ultrafast processes in photoexcited bismuth by broadband probing in the wavelength range 0.4–0.9 μm

The decay of the photoexcited state of a bismuth single crystal is investigated in the wavelength range from 400 to 900 nm by means of femtosecond laser reflection spectroscopy. Oscillations produced by coherent fully symmetric A _1g phonons have been detected in the photoinduced response, along with a relaxation component. The dynamics of the electronic subsystem of the crystal is shown to be characterized by three values of the decay time: 1 ps, 7 ps, and ∼1 ns. The spectral dependence of the reflectivity oscillation amplitude has been measured; the possible cause of the shape of the derived curve is described.     

Pump pulse duration dependence of coherent phonon amplitudes in antimony

Coherent optical phonons of A_1k and E_k symmetry in antimony have been studied using the femtosecond pump–probe technique. By varying the pump-pulse duration and keeping the probe duration constant, it was shown that the amplitude of coherent phonons of both symmetries exponentially decreases with increasing pulse width. It was found that the amplitude decay rate for the fully symmetric phonons with larger frequency is greater than that of the doubly degenerate phonons, whereas the frequency and lifetime for coherent phonons of both symmetries do not depend on the pump-pulse duration. Based on this data, the possibility of separation between dynamic and kinematic contributions to the generation mechanism of coherent phonons is discussed.     

Period dependence of coherent oscillations in manganite superlattices

In three-component superlattices of [(NdMnO3)_n/(SrMnO3)_n/(LaMnO3)_n]_m consisting of nonferroelectric and antiferromagnetic layers, the generation of coherent phonons in the system is investigated by the relaxation process of the superlattice using a pump–probe technique. The coherent phonons are related to MnO₆ octahedra in the layers. While the frequency of the phonons is 49 GHz without regard to the period of each layer, the amplitude of the phonons is influenced by the period of the superlattices. The superlattices have the maximum amplitude of the acoustic phonons at a period of (5, 12) together with strong emergent interfacial effects such as ferromagnetism and ferroelectricity, which are not present in bulk materials. This implies a possible correlation of the lattice structure with interface-induced properties.     

Details of coherent phonon motion in tellurium

We study impulsively excited coherent phonons in tellurium at various lattice temperatures and excitation densities. From a comparison with temperature-dependent reflectivity and X-ray scattering data, we infer the direction and estimate the amplitude of the coherent ionic motion. In addition, we show quantitatively that electronic weakening of the crystal forms the dominant contribution to a density-dependent red-shift of the phonon frequency.     

Nonlinear lattice dynamics of bismuth as a means of clarifying the nature of coherent phonons

The nonlinear regime of generation of coherent phonons in bismuth single crystals irradiated by ultrashort high-energy laser pulses has been investigated. In this regime, autoecho phenomenon is implemented at a low (helium) crystal temperature, manifesting itself as a collapse and revival of reflection oscillations generated by coherent A _1g phonons. Different mechanisms of the observed phenomena are considered.     

Quantum dynamical study of the amplitude collapse and revival of coherent <Emphasis Type="Italic">A</Emphasis><Subscript>1g</Subscript> phonons in bismuth: a classical phenomenon?

We parameterize the potential energy surface of bismuth after intense laser excitation using accurate full-potential linearized augmented plane wave calculations. Anharmonic contributions up to the fifth power in the A _1g phonon coordinate are given as a function of the absorbed laser energy. Using a previously described model including effects of electron–phonon coupling and carrier diffusion due to Johnson et al., we obtain the time-dependent potential energy surface for any given laser pulse shape and duration. On the basis of this parameterization we perform quantum dynamical simulations to study the experimentally observed amplitude collapse and revival of coherent A _1g phonons in bismuth considering work of Misochko et al. Our results strongly indicate that the observed beatings are not related to quantum effects and are most probably of classical origin.     

Two-phonon bound states in imperfect crystals

The question of the occurrence of two-phonon bound states in imperfect crystals is investigated. It is shown that the anharmonicity mediated two-phonon bound state which is present in perfect crystals gets modified due to the presence of impurities. Moreover, the possibility of the occurrence of a purely impurity mediated two-phonon bound state is demonstrated. The bound state frequencies are calculated using the simple Einstein oscillator model for the host phonons. The two-phonon density of states for the imperfect crystal thus obtained has peaks at the combination and difference frequencies of two host phonons besides the peaks at the bound state frequencies. For a perfect crystal the theory predicts a single peak at the two-phonon bound state frequency in conformity with experimental observations and other theoretical calculations. Experimental data on the two-phonon infrared absorption and Raman scattering from mixed crystals of GA_1−c Al _c P and Ge_1−c Si _c are analysed to provide evidence in support of impurity-mediated two-phonon bound states. The relevance of the zero frequency (difference spectrum) peak to the central peak observed in structural phase transitions, is conjectured; This work is a part of the thesis to be submitted by one of the authors (SS) in partial fulfilment of the degree of Doctor of Philosophy to Utkal University, Bhubaneswar, India.     

Anomalous dephasing of bosonic excitons interacting with phonons in the vicinity of the Bose-Einstein condensation

The dephasing and relaxation kinetics of bosonic excitons interacting with a thermal bath of acoustic phonons is studied after coherent pulse excitation. The kinetics of the induced excitonic polarization is calculated within Markovian equations both for subcritical and supercritical excitation with respect to a Bose-Einstein condensation (BEC). For excited densities n below the critical density , an exponential polarization decay is obtained, which is characterized by a dephasing rate . This dephasing rate due to phonon scattering shows a pronounced exciton-density dependence in the vicinity of the phase transition. It is well described by the power law that can be understood by linearization of the equations around the equilibrium solution. Above the critical density we get a non-exponential relaxation to the final condensate value p⁰ with that holds for all densities. Furthermore we include the full self-consistent Hartree-Fock-Bogoliubov (HFB) terms due to the exciton-exciton interaction and the kinetics of the anomalous functions . The collision terms are analyzed and an approximation is used which is consistent with the existence of BEC. The inclusion of the coherent exciton-exciton interaction does not change the dephasing laws. The anomalous function F_k exhibits a clear threshold behaviour at the critical density. Received 13 December 1999     

Coherent phonon excitation in bismuth

Ultrafast time-resolved reflectivity of a bismuth thin film evaporated on a silicon substrate is measured to investigate coherent phonons in bismuth. The reflectivity result is analyzed by a linear chirp approximation to obtain the time dependent frequencies of coherent phonons. Not only the optical modes are detected, which are generated by a combination of impulsive stimulated Raman scattering and displacive excitation of coherent phonon, acoustic phonon modes are also observed, which are emitted by the A_1g optical phonon.     

Femtosecond reflectivity study of coherent phonons in doubly photoexcited bismuth

Ultrafast optical excitation generates coherent A_1g optical phonons in bismuth via the mechanism of displacive excitation of coherent phonons (DECP). Here, femtosecond pump-probe reflectivity spectroscopy examines the dynamics of coherent phonons in doubly photoexcited bismuth. Two successive pump pulses are employed to generate optic phonons and thus to investigate the phonon dynamics including bond softening and dephasing with variable pump fluence and inter-pump separation times. Combined with thermal analysis, it distinguishes thermal and nonthermal effects of photoexcitation on the phonon dynamics. It also reveals that photocarriers relax via electron-hole recombination and diffusion out of the optical penetration depth on ultrafast timescales of 10–20?ps.     

Observation of coherent phonon states in porous silicon films

The dynamics of differential transmission and reflectance spectra of porous silicon films was studied using the femtosecond excitation technique (τ≈50 fs, ?ω_pump=2.34 eV) with supercontinuum probing (?ω_probe=1.6–3.2 eV) and controlled time delay with a step of Δt=7 fs between the pump and probe pulses. A short-lived region of photoinduced bleaching was observed in the differential transmission spectra at wavelengths shorter than the pump wavelength. The excitation of coherent phonon states with a spectrum corresponding to nanocrystalline silicon with an admixture of a disordered phase was observed. The relaxation of electronic excitation was found to slow down in the spectral region where the amplitude of excited coherent vibrations was maximal.     

2 + 1 Flavors QCD Equation of State in NJL Model with Proper Time Regularization

Totally symmetric A_1g phonons are studied for the equilibrium and coherent states of a Bi₂Te₃ lattice. Equilibrium phonons were investigated in the frequency domain by the method of spontaneous Raman scattering, whereas coherent phonons were studied by the method of active femtosecond spectroscopy in the time domain. In the latter case, femtosecond laser pulses were used both for generating and detecting coherent A_1g phonons having a well-defined phase allowing the selective optical control of the lattice dynamics. A comparison of the results obtained in the frequency and time domains suggests that diagonal and nondiagonal elements of the density matrix of lattice excitations relax with the same characteristic time to the equilibrium and zero values, respectively.     

Dynamics of cooperative Jahn-TellerT-systems

We consider a cubic crystal with a triply degenerate electronic ground-state in each unit cell (T-state). A linear Jahn-Teller interaction with acoustic phonons is assumed (T-e coupling). Below a critical temperatureT _c a tetragonal cooperative ordering is established. If a static crystal field splits the electronic states, an anticrossing of the cooperative excitation branches and the phonons in the smallk-regime is found. The resulting mixed modes are calculated (RPA and isotropic Debye model). The dispersion curves are given for specifick-directions and the temperature dependence is discussed.Supported by a grant from the Deutsche Forschungsgemeinschaft     

Mode dependent scattering of phonons by domain walls in ferroelectric KDP

Thermal conductivity and ballistic phonon imaging measurements in KH₂PO₄ (KDP) at low temperature (T<3K) indicate that scattering from domain walls has a large effect on phonon transport. kDP has a ferroelectric phase transition from tetragonal to orthorhombic structure atT _c =122 K. BelowT _c domains of opposite electric polarization and crystal orientation form unless the sample is colled in an electric field. Thermal conductivity measured along the [100] (tetragonal) axis drops 30% when domain walls are present, which is independent of sample size and temperature. We attribute this decrease to phonon polarization-dependent scattering at the domain boundaries. This is verified by measurements of ballistic transport, using phonon imaging techniques, which reveal the phonon polarization and mode dependence of the scattering. The scattering is successfully modelled using continuum acoustics with simple acoustic mismatch at the domainwall. The interface scattering is found to be mode dependent: Caustic structures in the phonon images due to slow transverse phonons are most affected by the domain wall scattering, which channels these phonons along parallel planes by multiple reflections without mode conversion. Mode conversion scattering, though possible for a number of phonons, has little effect on the overall phonon transmission.     

Pseudospin solitons in the coherent stripe phase of a bilayer quantum Hall system

In the Hartree–Fock approximation and at total filling factor ν=4N+1, the ground state of the two-dimensional electron gas in a double quantum well system in a quantizing magnetic field is, in some range of interlayer distances, a coherent striped phase. This stripe phase has one-dimensional coherent channels that support charged excitations in the form of pseudospin solitons. In this work, we compute the transport gap of the coherent striped phase due to the creation of soliton–antisoliton pairs using a supercell microscopic unrestricted Hartree–Fock approach. We study the energy gap as a function of interlayer distance and tunneling amplitude. Our calculations confirm that the soliton–antisoliton excitation energy is lower than the corresponding Hartree–Fock electron–hole pair energy.