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Theoretical investigation of subpicosecond vibronic dynamics in alkali halides
JOURNAL OF
LUMINESCENCE EISEVIER
Journal
of Luminescence
72-74 (1997) 838-839
Theoretical investigation of subpicosecond vibronic dynamics in alkali halides R. Scholza,b,*, F. Bassanib, M. Schreiber” aInstitute fir Physik, TU Chemnitz, D-09107 Chemnitz, Germany b Scuola Normale Superiore, I-56126 Piss, Italy
Abstract We present a theoretical analysis of a recent femtosecond experiment on alkali halide F-centers [ 11. In the experiment, subpicosecond dynamics of an optically excited vibronic wave packet in alkali halide F-centers was investigated by a pumpprobe technique using femtosecond laser pulses. The temporal evolution of the wave packet leads to damped periodic oscillations of the sample transmission. These are interpreted as the A,.#:) breathing modes of the surrounding octahedron of cations associated with the electronic ground and excited states. It is shown that the vibrational modes of lower symmetry are responsible for the observed transient Jahn-Teller effect. Keywords: Color center; Ultrafast phenomena; Localized vibrations; Alkali halides
1. Experimental
The optical transition of the color center presents a large Stokes shift due to the strong coupling of the electronic states to the localized vibrations of the lattice surrounding the anion vacancy. An optical pump-probe technique based on femtosecond laser pulses allows to create a vibronic wavepacket with the pump pulse and to detect its subsequent dynamics with a time-delayed probe pulse. The experiment is performed with pulses of 10 fs duration and photon energy of 1.75 eV on thin KBr samples with a concentration of 3 x 1016 cme3 F-centers [I]. The probe transmission as a function of delay shows a clear beating pattern of two oscillations with A,, symmetry, interpreted as the breathing modes associated to the ground and excited *Correspondenceaddress: D-09107
Chemnitz,
Institut
fiir Physik, TU Chemnitz,
Germany.
0022-2313/97/$17.00 ~c 1997 Elsevier Science B.V. All rights reserved PII SOO22-23 13(97)00089-6
electronic states. At room temperature, their respective frequencies are found to be vg = 3.125 & 0.010 THz and v, = 3.435 f. 0.010 THz, slightly lower than observed in low-temperature Raman experiments [2]. The dephasing times are about 2 ps. Except for delays shorter than 200 fs there are no contributions of El, and TZg symmetries.
2. Density matrix calculation for A,, modes In order to include coherence and dephasing effects for the A,, vibrations we performed a density matrix calculation based on the oscillator Fock states associated with the electronic ground and excited states [3,4]. Calculating the nonlinear transmission with the third-order nonlinear polarization Pc3) cc E&E,, it is easily shown that the oscillatory parts of the signal are due to offdiagonal elements of the density matrix between
R. Scholz et al. / Journal of Luminescence
consecutive levels in the excited and in the groundstate potential. The absence of signal contributions of the lower symmetries El, and Tzs demonstrates that the initial orientation of the excited electronic p-state is lost on a time scale of about 100 fs. This leads to a reduction of the vibrational amplitude associated to the excited state by a factor of 3, a fact we used to assign the ground and excited state frequencies.
3. Reorientation
of p-state
In order to understand the ultrafast reorientation of the p-state, we performed a direct integration of the Schrodinger equation for initial states.
where the electronic part ip) is given by the orientation of the pump pulse and the second (third) part by the product of Fock states of El, (T,,) symmetry [3,4]. For the Hamiltonians of these symmetries in the excited state, we allowed for a shift along the oscillator coordinate, e.g.
for one of the Tzg modes, where the c and ct operators are annihilation and creation operators of p-states, a4 and LZ: annihilation and creation operators of the oscillator mode, and i the coupling
72- 74 (1997) 838-839
839
constant. Assuming degenerate El, and TZgmodes, her = k~r = 10 meV, we observe a cubic or isotropic reorientation pattern, depending on the ratio of the coupling coefficients for the El, and Tzg modes. With < = 10 meV, i.e. a shift of each upper state oscillator by one energy quantum, we observe a reorientation on a time scale of about 50 fs, in reasonable agreement with the experiment and with the coupling coefficients observed in stationary spectroscopy [Sj.
Acknowledgements
The authors thank M. Nisoli, S. de Silvestri and 0. Svelto for sharing unpublished experimental results.
References Cl1 M. Nisoli, S. De Silvestri, 0. Svelto, R. Scholz, R. Fanciulli, V. Pellegrini. F. Beltram and G.F. Bassani, Phys. Rev. Lett. ll(1996) 3463. PI D.S. Pan and F. Liity, in: 3rd Int. Conf. on Light Scattering in Solids, eds. by M. Balkanski, R.C.C. Leito, and S.P.S. Porto (Flammarion, Paris, 1975) p. 539. c31R. Scholz, F. Bassani and M. Schreiber, in: Excitonic Processes in Condensed Matter, ed. by M. Schreiber (Dresden University Press, Dresden, 1996) p. 211. M R. Scholz, M. Schreifer, F. Bassani, M. Nisoli, S. De Silvestoi and 0. Svelto, submitted to Phys. Rev. B. c51S.E. Schnatterly, Phys. Rev. A 140 (1965) 1364.
LUMINESCENCE EISEVIER
Journal
of Luminescence
72-74 (1997) 838-839
Theoretical investigation of subpicosecond vibronic dynamics in alkali halides R. Scholza,b,*, F. Bassanib, M. Schreiber” aInstitute fir Physik, TU Chemnitz, D-09107 Chemnitz, Germany b Scuola Normale Superiore, I-56126 Piss, Italy
Abstract We present a theoretical analysis of a recent femtosecond experiment on alkali halide F-centers [ 11. In the experiment, subpicosecond dynamics of an optically excited vibronic wave packet in alkali halide F-centers was investigated by a pumpprobe technique using femtosecond laser pulses. The temporal evolution of the wave packet leads to damped periodic oscillations of the sample transmission. These are interpreted as the A,.#:) breathing modes of the surrounding octahedron of cations associated with the electronic ground and excited states. It is shown that the vibrational modes of lower symmetry are responsible for the observed transient Jahn-Teller effect. Keywords: Color center; Ultrafast phenomena; Localized vibrations; Alkali halides
1. Experimental
The optical transition of the color center presents a large Stokes shift due to the strong coupling of the electronic states to the localized vibrations of the lattice surrounding the anion vacancy. An optical pump-probe technique based on femtosecond laser pulses allows to create a vibronic wavepacket with the pump pulse and to detect its subsequent dynamics with a time-delayed probe pulse. The experiment is performed with pulses of 10 fs duration and photon energy of 1.75 eV on thin KBr samples with a concentration of 3 x 1016 cme3 F-centers [I]. The probe transmission as a function of delay shows a clear beating pattern of two oscillations with A,, symmetry, interpreted as the breathing modes associated to the ground and excited *Correspondenceaddress: D-09107
Chemnitz,
Institut
fiir Physik, TU Chemnitz,
Germany.
0022-2313/97/$17.00 ~c 1997 Elsevier Science B.V. All rights reserved PII SOO22-23 13(97)00089-6
electronic states. At room temperature, their respective frequencies are found to be vg = 3.125 & 0.010 THz and v, = 3.435 f. 0.010 THz, slightly lower than observed in low-temperature Raman experiments [2]. The dephasing times are about 2 ps. Except for delays shorter than 200 fs there are no contributions of El, and TZg symmetries.
2. Density matrix calculation for A,, modes In order to include coherence and dephasing effects for the A,, vibrations we performed a density matrix calculation based on the oscillator Fock states associated with the electronic ground and excited states [3,4]. Calculating the nonlinear transmission with the third-order nonlinear polarization Pc3) cc E&E,, it is easily shown that the oscillatory parts of the signal are due to offdiagonal elements of the density matrix between
R. Scholz et al. / Journal of Luminescence
consecutive levels in the excited and in the groundstate potential. The absence of signal contributions of the lower symmetries El, and Tzs demonstrates that the initial orientation of the excited electronic p-state is lost on a time scale of about 100 fs. This leads to a reduction of the vibrational amplitude associated to the excited state by a factor of 3, a fact we used to assign the ground and excited state frequencies.
3. Reorientation
of p-state
In order to understand the ultrafast reorientation of the p-state, we performed a direct integration of the Schrodinger equation for initial states.
where the electronic part ip) is given by the orientation of the pump pulse and the second (third) part by the product of Fock states of El, (T,,) symmetry [3,4]. For the Hamiltonians of these symmetries in the excited state, we allowed for a shift along the oscillator coordinate, e.g.
for one of the Tzg modes, where the c and ct operators are annihilation and creation operators of p-states, a4 and LZ: annihilation and creation operators of the oscillator mode, and i the coupling
72- 74 (1997) 838-839
839
constant. Assuming degenerate El, and TZgmodes, her = k~r = 10 meV, we observe a cubic or isotropic reorientation pattern, depending on the ratio of the coupling coefficients for the El, and Tzg modes. With < = 10 meV, i.e. a shift of each upper state oscillator by one energy quantum, we observe a reorientation on a time scale of about 50 fs, in reasonable agreement with the experiment and with the coupling coefficients observed in stationary spectroscopy [Sj.
Acknowledgements
The authors thank M. Nisoli, S. de Silvestri and 0. Svelto for sharing unpublished experimental results.
References Cl1 M. Nisoli, S. De Silvestri, 0. Svelto, R. Scholz, R. Fanciulli, V. Pellegrini. F. Beltram and G.F. Bassani, Phys. Rev. Lett. ll(1996) 3463. PI D.S. Pan and F. Liity, in: 3rd Int. Conf. on Light Scattering in Solids, eds. by M. Balkanski, R.C.C. Leito, and S.P.S. Porto (Flammarion, Paris, 1975) p. 539. c31R. Scholz, F. Bassani and M. Schreiber, in: Excitonic Processes in Condensed Matter, ed. by M. Schreiber (Dresden University Press, Dresden, 1996) p. 211. M R. Scholz, M. Schreifer, F. Bassani, M. Nisoli, S. De Silvestoi and 0. Svelto, submitted to Phys. Rev. B. c51S.E. Schnatterly, Phys. Rev. A 140 (1965) 1364.