Ultrafast coherent vibronic dynamics in color centers

JOURNAL

OF

LUMINESCENCE Journal of Luminescence 76&77 (1998) 48-5 1

ELSEVIER

Ultrafast coherent vibronic dynamics in color centers R. Scholz”,

M. Schreiber

Institut,$ir Physik, Technische Unioersitiit, D-09107 Chemnitz Germanic

Abstract Recent femtosecond pumpprobe experiments on KBr F-centers are interpreted using a density matrix scheme for the breathing modes and a calculation of the time evolution of a wave packet for the local vibrations of lower symmetry. The elongations of all modes are derived from stationary absorption measurements, while the frequencies and dephasing times of the breathing modes are taken from the femtosecond pump-probe results. With a density matrix calculation for the breathing modes we achieve quantitative agreement with the oscillation pattern observed in the femtosecond experiments without free parameters. The time integration of an excited wave packet in the product space of the d-symmetric local vibrations and the excited p states gives insight into the observed ultrafast reorientation of the excited p state. lc 1998 Elsevier Science B.V. All rights reserved. Keywords:

Color center; Localized

vibration;

Vibronic

wave packet; Ultrafast -

1. Experimental The Stokes shift and the absorption line width of the optical transition of color centers show a dominant contribution of the breathing modes of the lattice around the defect [l], so that the creation of a vibronic wave packet of these modes must be possible with a short enough optical pulse. A pumpprobe set-up with 15 fs pulses at 1.75 eV has allowed for the first observation of such breathing-mode oscillations in real time around the KBr color center [2]. Later detailed symmetry assignments have confirmed that the oscillation pattern is, indeed, independent of pump and probe polarizations, namely Al, [3,4]. Experimental results at room temperature are presented in Fig. 1. In Fig. la, the probe transmission is shown as a function of time delay between the two pulses, the *Corresponding author. Fax: [email protected]. 0022-2313/98/$19.00 c PI1 SOO22-2313(97)00142-7

+ 493715313143;

e-mail:

1998 Elsevier Science B.V. All rights reserved.

optical measurement

maximum of the pump defining zero delay. For pump polarized along a cubic axis, the probe transmission averaged over different probe polarizations shows a clear beating pattern (A,,), while the difference of the probe transmission for polarization parallel and orthogonal to the pump (E,,) is close to zero and shows no oscillatory contribution. The absence of E,,-symmetric signals after about 200 fs indicates that the initial orientation of the excited electronic p state vanishes on an ultrafast time scale. The oscillatory part of the data is shown in Fig. lb, calculated from the measured signals by subtracting the exponentials fitted to the slow components. The A,, oscillation pattern shows no significant difference for pump along a cubic axis (lower curves) and at 45” to a cubic axis (upper curves). The superimposed two-oscillator fits show excellent agreement, both in the time domain in Fig. lb and in the Fourier spectra in Fig. lc. The room temperature frequencies of the breathing modes are found to be 1~~= 3.125 i 0.006THz

0.61.

0

8.

I.

8.

I.

I

1

2

3

4

’ 5

time delay (ps) FIN. I. (:I) Observed measured 45

A,,

at 45

change of probe transmission

dotted

to a cubic

for pump

as a function

polarized

polarized

along

in the electronic ground state and 17,= 3.435 k O.OlOTHz in the excited state. in good agreement with the temperature dependence observed in Raman experiments [S-7]. The assignment of the two frequencies to ground and excited electronic states follows from the model calculation explained below. The dephasing times are about 2 ps in both cases.

for Al, modes

The density matrix calculation for the breathing modes is based on the Hamiltonian

where s.s denote the electronic part of the basis states and i,,j the vibronic part. The eigenfrequencies have been abbreviated as (ogi = Es,4 + (i + i)co, and co,, = E,/h + (,j + $_oe. The coupling to the electric field R of the optical pulses is expressed by the dipole operator fi &,,(A,,)

= - cs’.,(r) I;x + (J’.z),

fiI = (1 1 (Ir,.j)(s, i.j

1

i( F,ji + (S, i)(.X,,jlFij),

2 3 frequency

4 (THz)

5

of time delay between pump and probe puke. (b) Oscillatory

and at 45

to an axis (upper). with two-oscillator

along a cubic axis). (c) Amplitude

axis. long dashes: for pump

2. Density matrix calculation

0

time delay (ps)

signals for pump along a cubic axis (lower)

polarization.

pump

0.0

(2) (3)

where d = (slsls) is the dipole matrix element between the electronic ground and excited states. and

Fourier

spectra of(b).

a cubic axis. dots: correspondmg

fits superimposed solid line: expcrlmental t\+o-oscillator

6

part of the (dashed for data for

lit.

Fji = (j,ji,) are the Franck- Condon factors between the oscillator eigenstates. In order to obtain the transient quantum dynamics resulting from the passage of the pump pulse, the above equations of motion are iterated up to second order in the pump field. Assuming an excitation density of 10% and a relation T1 = 2T, between thermalization time T, and dephasing time T2. we obtain the time-dependent occupation changes in Fig. 2a and Fig. 2b and the transient correlations between consecutive vibronic levels in Fig. 2c and Fig. 2d. The initial occupation changes and correlations of vibronic levels corresponding to the electronic excited state show a marked resonance, compare Fig. 2a and Fig. 2c. the non-equilibrium occupations relaxing subsequently to a thermalized distribution on a time scale of a few picoseconds. For the occupation changes and correlations of the vibronic levels related to the electronic ground state in Fig. 2b and Fig. 2d, the initial coupling strength results from a combination of the thermalized initial distribution and the resonance condition: The strongest coupling occurs for vibronic level 2 instead of the most occupied level 0 because the photon energy of 1.75eV is slightly below the absorption maximum. The saturation of the probe absorption is calculated as the linear response of the system to the probe field after being disturbed by the pump pulse. Assuming the orientation of the excited p state to be a good quantum number on the time scale of the experiment. we obtain the two upper curves in

50

R. Schok

M. Schreiher

i Journal

of’ Luminescence

76&77

(I 998) 48-51

I 0

2

4

6

8

-1

10

time (ps)

0

1

2

3

4

5

5

6

time delay (ps)

time (ps) 21

k

18 % 2 14

S 5 ‘G :: 8 2 T

18

(b)

10

T 15 k e 12 B g S ?! 6

-..

6 2 -2 22 -6 B -2

k

3 0

0

2

4

6

8

10

-1

0

time (ps)

1

2

3

4

5

time (ps)

0

1

2 3 4 frequency (THz)

Fig. 2. (a) Occupation change of vibronic levels j = 0,2,4,. of the electronic excited state (from bottom to top) and (b) of vibronic levels of the ground state. The time axis refers to the maximum of the pump intensity. (c) Real part of correlations between .-, consecutive levels j and .j + 1 of the excited electronic state, for j = 0,2,4.. (from bottom to top) and (d) likewise for the electronic ground state levels i = 0,1.2,. (e) Saturation of probe absorption as a function of time delay between pump and probe, for different geometries: parallel polarizations of the two pulses (II), orthogonal (I). assuming instantaneous reorientation of p states (“av”), and comparison (“exp”) of oscillatory part of the latter (solid line) to the observed oscillation pattern (dots). (r) Fourier spectra of(e). for parallel polarizations (long dashes), perpendicular polarizations (short dashes). and average (solid). The dotted curve superimposed on the latter is the two-oscillator fit of Fig. 1b and Fig. lc i=OlT .

Fig. 2e. For parallel polarizations, the wave packet oscillating in the vibronic potential of the excited state contributes to the Pauli blocking of the optical transition, leading to a characteristic beating of the signal. For perpendicular polarizations of the two pulses, no beating pattern occurs because this excited state wave packet is related to a p state corresponding to the pump polarization so that it cannot be observed with the probe polarization orthogonal to it. Therefore, only the ground state wave packet contributes to the absorption saturation in the latter case. Both the calculated curves for parallel and orthogonal polarizations do not correspond to the measured signals, which is seen clearly from the Fourier spectra of the oscillatory parts in Fig. 2f. We conclude that the p orientation vanishes on an ultrashort time scale. Assuming this reorientation rate to be infinite for simplicity, we can compute the probe signal by including only 4 of the signal resulting from the upper vibronic potential (“a? in

Fig. 2e). The oscillatory part of this signal coincides perfectly with the experimental trace, both in the time domain and in the Fourier spectra. From the comparison of the measured and calculated signals we conclude that the experimental excitation density is 6% [3].

3. Reorientation effect

of p state: Transient Jahn-Teller

In the previous Section, the ultrafast reorientation of the excited p state was introduced phenomenologically. Analyzing the influence of the El,- and T,,-symmetric Jahn-Teller modes on the excited p state, one finds that the fastest part of the reorientation can be understood as the reversible time evolution of the initial vibronic state on the potential surface of the excited p states. Details of this calculation have been given elsewhere [3,4].

The time evolution of a wave packet out of its initial state can be interpreted as a loss of coherence for the breathing modes. This limits the observability of the breathing-mode oscillations to a pulse duration of the order of the so-defined coherence time r,, which is about rC = 24 fs at T = 0 K and about 5, = 12 fs at room temperature [3].

for the observability tions.

of the breathing-mode

oscilla-

Acknowledgements The authors thank M. Nisoli. S. de Silvestri and Svelto for sharing unpublished experimental results and the DFG for financial support. 0.

4. Conclusions References With a density matrix calculation based on the breathing modes around the KBr color center, we obtained quantitative agreement with the oscillation patterns observed in pumpprobe spectroscopy without free parameters. The E,,- and T,,-symmetric modes lead to an ultrafast reorientation of the excited p states, which can be understood as a reversible evolution of the excited wave packet according to the Hamiltonians of the corresponding symmetries. This defines a maximum pulse length

111 SE. Schnatterly. Phys. Rev. A 140 (1965) 1364. PI M. Nisoli et al.. Phys. Rev. Lett. 77 (19961 3463. II31 R. Scholz et al.. Phys. Rev. B 56 (1997) I 179. c41 R. Scholz. F. Bassam. M. Schreiber. in: M. Schrciber (Ed.), Proc. 2nd Int. Conf. Excitonic Processes ITI Condensed Matter. Dresden University Press. Dresden. lY96. p. 21 I. R.C.C. Leltv. S.P.S. CSI D.S. Pan. F. Liity. in: M. Balkanski. Porte (Eds.). Proc. 3rd Int. Conf. Light Scattering in Solids. Hammarion, Paris. 1975, p. 539. [61 A.D.B. Woods et al.. Phys. Rel. 131 (1963) 1015. et al.. Phys. Rev. 131 (lY63) 1030. [71 R.A. Cwlcy