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Coherent transfer from fluorescence interference noise
JOURNALOF
LUMINESCENCE ELSEVIER
Journal of Luminescence
76&77
(199X) 115
I46
Abstract
The optical response of a finite-level system (FLS) to classical optical field having two subsequent &pulses was studied by applying the density operator formalism. The response of FLS has been developed for spontaneous fluorescence for the case where the population relaxation is much longer than the coherence relaxation. For a pair of time-dclaycd pulse5 with random relatke phase the variance of the noisy correlated fluorescence signal as a function of the pulse dciay allows direct access to (coherent and incoherent) energy transfer rates. We show that the prerlictrtl COIN signal of some bichromophoric molecules (a) has an undulatory pattern (direct evidence of intermoiety resonant transfer): (b) contains information on inter-site incoherent transfer. The COIN spectroscopy approach is a very stable and robust method which may provide a powerful diagnostic tool for ‘visualizing’ different transfer regimes present in FLS. ( I 99X Elscvier Science R.V. All rights reserved. /GY~w~.Y: Coherence:
Fluorescence
Excitation energy transfer is an important phenomenon in many areas of physics. Spatially restricted systems such as bichromophoric molecules [I] serve as a prototype system for experimental as well as theoretical investigation of excitation transfer dynamics in molecular systems. The importance of coherent (resonant) excitation energy transfer in these materials was manifested by femtosecond real-time optical measurements. Recent progress in intensity fluctuation spectroscopy showed that c~~he~~~rzce ohrrration by intrr,f~~wm~ noise (COIN) is an effective tool for the measurement of optical coherence [2]. In this method, a pair of pulses of sufficiently short duration (two &pulses) are used. The second &pulse shifted by time 5 and having a random relative
* C‘orrcsponding
0022-2313 P/I
9X $19.00
author.
(
s00~2-2.;I.i(!,7~00196-8
E-mail: szocs(~fns.uniba.sh
phase monitors the quantum amplitude of excited states prepared by the first pulse. Finally. the quantum interference fluctuations (noise) of the emission (fluorescence) are monitored. The variance of fluorescence intensity as a function of time delay T contains information about (coherent and dissipative) dynamics of FLS. Kinrot et al. [2] modeled the system (potassium doublet) by two equally populated and dgnamically independent TLS models. i.e. the resulting fluorescence signal is a sum of two TLS signals. For simulating the excitation dynamics of a coupled two-site system-like bichromophoric molecules [l], however, a TLS model is inadequate. In this case. the excited states are dynamically coupled and the evolution of the whole FLS has to be solved. We use the Liouville equation (LE) approach containing: (i) a resonant. Hamiltonian-like transfcl
1998 ElsevicrScience l3.V. All rights reserved
146
V. .Piics, H.F. E(a@mm~
/I Joumal
(ii) a dissipative relaxation channel including nonradiative depopulation of the excited electronic states as well as dephasing of the non-diagonal part of the electronic density matrix [3], (iii) an external field-induced transfer corresponding to the driving of the FLS by time-dependent Hamiltonian. As will be shown elsewhere [4], the LE with time-dependent Hamiltonian in the form of a sequence of delta pulses can be solved exactly. The energetic scheme of biaryls, in general, consists of a single ground state (1) and two excited states (2 and 3) which are energetically equivalent and are coherently (with transfer integral J) and incoherently (with rate 2~~) coupled Cl]. Higher states are, as usual, neglected. Using our approach [4], the orientational average of the fluorescence signal over all spatial orientations of the moiety dipole moments yields the result (in the rotating wave approximation)
+ cos * cos(wz - q) cos(Jz) x exp( - T/T:“‘)],
(1)
where l/T?’ = l/T; + ;‘i is the renormalized TLS pure dephasing time and $ is the angle between the polarization vectors of the two delta pulses. Further, (u is the carrier frequency, cp is the relative phase between pulses with time-delay s. As expected, the quantum interference term (the third term in Eq. (1)) carries information on the system dynamics (resonant as well as dissipative transfer) and decreases with increasing angle between polar-
o/‘Luminescencr
76~3 77 IIYYX)
145-146
ization vectors of the two pulses. Averaging the square of the fluorescence signal, Eq. (l), over random phase of the second external pulse cp results in the COIN signal (AQ2(r) = 4 1; cos2 $ cos2(Jz) exp( - 2r/T’;“).
(2)
The obtained result contains information on intersite resonant as well as incoherent transfer. Due to the symmetry, the COIN signal alone is not able to eliminate the characteristics of a TLS so one has to refer the two-site COIN signal to the fluctuation pattern of the single-site system. A simple comparison of the single-moiety (TLS) COIN signal to the 1 + 2 level model reveals that (AT)” (r)/(AT)&
(5) ac cos’(Jz) exp ( - 2;7,2),
i.e. provides direct evidence for coherent herent intermoiety transfer rates.
(3)
and inco-
The financial support from the Fonds zur Forderung der wissenschaftlichen Forschung, Wien (Project P 11344-CHE) and the Grant Agency of the Ministry of Education of the Slovak Republik is gratefully acknowledged.
References Cl1 F. Zhu, C. Galli. R.M. Hochstrasser.
.I. Chem. Phys. 9X (1993) 1042. 121 0. Kinrot, I.Sh. Averbukh, Y. Prior, Phys. Rev. Lett. 75 (1995) 3822. c31 V. &pek. V. Sziics, Phys. Stat. Sol. B 131 (1985) 667. r41 V. SzGcs, H.F. Kauffmann, to be published.
LUMINESCENCE ELSEVIER
Journal of Luminescence
76&77
(199X) 115
I46
Abstract
The optical response of a finite-level system (FLS) to classical optical field having two subsequent &pulses was studied by applying the density operator formalism. The response of FLS has been developed for spontaneous fluorescence for the case where the population relaxation is much longer than the coherence relaxation. For a pair of time-dclaycd pulse5 with random relatke phase the variance of the noisy correlated fluorescence signal as a function of the pulse dciay allows direct access to (coherent and incoherent) energy transfer rates. We show that the prerlictrtl COIN signal of some bichromophoric molecules (a) has an undulatory pattern (direct evidence of intermoiety resonant transfer): (b) contains information on inter-site incoherent transfer. The COIN spectroscopy approach is a very stable and robust method which may provide a powerful diagnostic tool for ‘visualizing’ different transfer regimes present in FLS. ( I 99X Elscvier Science R.V. All rights reserved. /GY~w~.Y: Coherence:
Fluorescence
Excitation energy transfer is an important phenomenon in many areas of physics. Spatially restricted systems such as bichromophoric molecules [I] serve as a prototype system for experimental as well as theoretical investigation of excitation transfer dynamics in molecular systems. The importance of coherent (resonant) excitation energy transfer in these materials was manifested by femtosecond real-time optical measurements. Recent progress in intensity fluctuation spectroscopy showed that c~~he~~~rzce ohrrration by intrr,f~~wm~ noise (COIN) is an effective tool for the measurement of optical coherence [2]. In this method, a pair of pulses of sufficiently short duration (two &pulses) are used. The second &pulse shifted by time 5 and having a random relative
* C‘orrcsponding
0022-2313 P/I
9X $19.00
author.
(
s00~2-2.;I.i(!,7~00196-8
E-mail: szocs(~fns.uniba.sh
phase monitors the quantum amplitude of excited states prepared by the first pulse. Finally. the quantum interference fluctuations (noise) of the emission (fluorescence) are monitored. The variance of fluorescence intensity as a function of time delay T contains information about (coherent and dissipative) dynamics of FLS. Kinrot et al. [2] modeled the system (potassium doublet) by two equally populated and dgnamically independent TLS models. i.e. the resulting fluorescence signal is a sum of two TLS signals. For simulating the excitation dynamics of a coupled two-site system-like bichromophoric molecules [l], however, a TLS model is inadequate. In this case. the excited states are dynamically coupled and the evolution of the whole FLS has to be solved. We use the Liouville equation (LE) approach containing: (i) a resonant. Hamiltonian-like transfcl
1998 ElsevicrScience l3.V. All rights reserved
146
V. .Piics, H.F. E(a@mm~
/I Joumal
(ii) a dissipative relaxation channel including nonradiative depopulation of the excited electronic states as well as dephasing of the non-diagonal part of the electronic density matrix [3], (iii) an external field-induced transfer corresponding to the driving of the FLS by time-dependent Hamiltonian. As will be shown elsewhere [4], the LE with time-dependent Hamiltonian in the form of a sequence of delta pulses can be solved exactly. The energetic scheme of biaryls, in general, consists of a single ground state (1) and two excited states (2 and 3) which are energetically equivalent and are coherently (with transfer integral J) and incoherently (with rate 2~~) coupled Cl]. Higher states are, as usual, neglected. Using our approach [4], the orientational average of the fluorescence signal over all spatial orientations of the moiety dipole moments yields the result (in the rotating wave approximation)
+ cos * cos(wz - q) cos(Jz) x exp( - T/T:“‘)],
(1)
where l/T?’ = l/T; + ;‘i is the renormalized TLS pure dephasing time and $ is the angle between the polarization vectors of the two delta pulses. Further, (u is the carrier frequency, cp is the relative phase between pulses with time-delay s. As expected, the quantum interference term (the third term in Eq. (1)) carries information on the system dynamics (resonant as well as dissipative transfer) and decreases with increasing angle between polar-
o/‘Luminescencr
76~3 77 IIYYX)
145-146
ization vectors of the two pulses. Averaging the square of the fluorescence signal, Eq. (l), over random phase of the second external pulse cp results in the COIN signal (AQ2(r) = 4 1; cos2 $ cos2(Jz) exp( - 2r/T’;“).
(2)
The obtained result contains information on intersite resonant as well as incoherent transfer. Due to the symmetry, the COIN signal alone is not able to eliminate the characteristics of a TLS so one has to refer the two-site COIN signal to the fluctuation pattern of the single-site system. A simple comparison of the single-moiety (TLS) COIN signal to the 1 + 2 level model reveals that (AT)” (r)/(AT)&
(5) ac cos’(Jz) exp ( - 2;7,2),
i.e. provides direct evidence for coherent herent intermoiety transfer rates.
(3)
and inco-
The financial support from the Fonds zur Forderung der wissenschaftlichen Forschung, Wien (Project P 11344-CHE) and the Grant Agency of the Ministry of Education of the Slovak Republik is gratefully acknowledged.
References Cl1 F. Zhu, C. Galli. R.M. Hochstrasser.
.I. Chem. Phys. 9X (1993) 1042. 121 0. Kinrot, I.Sh. Averbukh, Y. Prior, Phys. Rev. Lett. 75 (1995) 3822. c31 V. &pek. V. Sziics, Phys. Stat. Sol. B 131 (1985) 667. r41 V. SzGcs, H.F. Kauffmann, to be published.