Ultrafast energy processes in photosynthetic complexes
Ferretti, M.
2016
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Ferretti, M. (2016). Ultrafast energy processes in photosynthetic complexes.
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VRIJE UNIVERSITEIT
U
LTRAFAST ENERGY PROCESSES IN
PHOTOSYNTHETIC COMPLEXES
ACADEMISCH PROEFSCHRIFT
ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus
prof.dr. V. Subramaniam, in het openbaar te verdedigen ten overstaan van de promotiecommissie van de Faculteit der Exacte Wetenschappen
op vrijdag 14 oktober 2016 om 9.45 uur in de aula van de universiteit,
De Boelelaan 1105
C
ONTENTS
Introduction 1
References. . . 4
1 Ultrafast spectroscopy 7 1.1 Time resolved fluorescence. . . 7
1.2 Transient absorption . . . 9
1.3 Two-Dimensional Electronic Spectroscopy. . . 11
1.4 Global analysis . . . 14
References. . . 16
2 Two-dimensional electronic spectroscopy setup 19 2.1 The setup. . . 20 2.2 Wedges calibration . . . 22 2.3 Pulse auto-correlation . . . 23 2.4 Scattering subtraction . . . 24 2.5 Data acquisition . . . 25 2.6 Acknowledgements. . . 28 References. . . 29
3 The coherences in the B820 bacteriochlorophyll dimer revealed by two-dimensional electronic spectroscopy 31 3.1 Introduction . . . 32
3.2 Experimental results . . . 34
3.2.1 2D electronic spectra . . . 34
3.2.2 2D traces and quantum beats . . . 35
3.2.3 2D real rephasing frequency maps. . . 36
3.3 Modelling. . . 36
3.3.1 Exciton-vibrational Hamiltonian. . . 36
3.3.2 Exciton-vibrational structure of the absorption spectrum . . . . 38
3.3.3 Exciton and vibrational coherences . . . 41
3.3.4 Modeling of 2D frequency maps. . . 44
3.4 Discussion . . . 46
3.5 Conclusions. . . 47
3.6 Materials and methods . . . 48
3.7 Acknowledgements. . . 48
3.8 Appendix: beating frequencies . . . 49
References. . . 50
4 Ultrafast excited state processes in Roseobacter denitrificans antennae 55 4.1 Introduction . . . 56
4.2 Results . . . 57
4.2.1 Steady state absorption . . . 57
4.2.2 Time resolved spectroscopy . . . 58
4.3 Discussion . . . 63
4.4 Conclusions. . . 66
4.5 Materials and methods . . . 66
4.5.1 Sample. . . 66
4.5.2 Spectroscopy. . . 67
4.6 Acknowledgements. . . 67
References. . . 68
5 Dark States in the Light-Harvesting complex 2 Revealed by Two-dimensional Electronic Spectroscopy 73 5.1 Introduction . . . 74
5.2 Results . . . 75
5.2.1 Two-dimensional electronic spectra. . . 75
5.2.2 Time evolution of positive cross-diagonal peaks. . . 78
5.2.3 Model . . . 80
5.2.4 Frequency maps. . . 82
5.3 Discussion . . . 82
5.4 Materials and Methods . . . 84
5.4.1 Sample preparation . . . 84
5.4.2 Spectroscopy. . . 84
5.5 Acknowledgements. . . 85
References. . . 86
6 Ordered Structures in Phycocyanin Nanowires Revealed by Ultra-fast Spec-troscopy 91 6.1 Introduction . . . 92
6.2 Results . . . 93
6.3 Discussion . . . 97
6.4 Materials and Methods . . . 98
6.4.1 Sample. . . 98
6.4.2 Spectroscopy. . . 98
6.4.3 Global Analysis. . . 98
6.5 Acknowledgements. . . 98
CONTENTS v
Summary 103
Curriculum Vitæ 105
List of Publications 107
I
NTRODUCTION
Global energy demand is increasing at an incredibly high rate. Right now, most of the energy is produced by using fossil fuels. This is unsustainable. In fact, in addi-tion to the obvious environmental disadvantages of fossil fuels, the energy consump-tion growth rate is becoming bigger than the fossil fuel producconsump-tion rate. According to the energy consumption estimations (shown in Fig.1, as published in Letters to Nature[1]), in 2050 the annual power consumption that does not come from fossil fuels will be at least 20 TW. A possible source for the extra energy could be nuclear. However, considering a power production of 1 Giga-Watt per nuclear power plant, it would be necessary to build more than 20000 power stations before 2050. Moreover, it is proven that at 20 TW of production, the uranium will be exhausted in less than ten years. Another drawback of such massive use of nuclear energy would be the cost of the safe storage of nuclear waste for many thousands of years. Therefore the nuclear solution is obviously not feasible.
FIGURE1: Global power consumption estimation published in Letters to Nature[1]. It is clear that if all the energy produced by non-fossil fuels would come from a nuclear source, in 2050 we will need about 20 TW produced by nuclear energy. Assuming a production of 1 GW per nuclear power plant, this would require more than 20000 new plants, meaning that nuclear energy cannot be the answer to the energetic problem. The only way to satisfy the energy demand is thus to considerably increase the production of renewable energy.
The most abundant source of energy on Earth is the sun, which irradiates at a rate of about 120000 TW. This amount of energy is so large that in a few hours it could satisfy the global energy consumption of a whole year. There are two main approaches to exploit the sun-light energy: the photovoltaic, whose purpose is to convert the light energy into electricity, and the solar-fuel production, which aims
to convert the light energy into a fuel. The main drawback of both approaches is the low energy conversion efficiency. In fact, for example, the silicon photovoltaic has an energy conversion efficiency of about 20%. Although there are some non-commercial solar cells with an efficiency up to 46%, the production costs and the device stability are critical limiting factors.
A good inspiration to solve the energetic problem can come from the study of photosynthesis, which is the most efficient energy storage processes in Nature. In this biological process, the sun-light energy is collected by plants or bacteria, and converted into biochemical energy needed to power life. In particular, the first steps of photosynthesis have a quantum efficiency close to unity. These steps correspond to the sun-light harvesting and the energy transfer to the reaction centres, where the energy is chemically stored.
It is clear that we need a more radical approach in order to increase the efficiency of the current technologies. The energetic problem must be tackled applying funda-mental physics research in order to unravel the physical reasons behind such an high energy conversion efficiency of photosynthetic complexes. The first steps of pho-tosynthesis are extremely fast, within few femtoseconds up to few nano-seconds. The development of ultra-fast lasers sources has allowed the study of the energy transfer and charge separation processes in photosynthetic complexes. Rentzepis[2] showed in 1973 the first pioneer application of ultra-fast laser spectroscopy on the picosecond scale. Only two years later, in 1975, there has been the first application of the method developed by Rentzepis to the bacterial reaction center of
Rhodopseu-domonas sphaeroides (now called Rhodobacter sphaeroides)[3,4], which were
fol-lowed by many other works (among the others, see for instance Refs. [5–7]). These early experiments had a time resolution of a few picoseconds, which allowed the study of the charge separation steps happening in reaction centres after light excita-tion.
In the last forty years, the laser technology has improved, making possible a time resolution of few femtoseconds possible. This made feasible the study of exciton energy transfer within and between photosynthetic complexes. In particular, in the last decade, the development and use of coherent spectroscopic techniques, such as two-dimensional electronic spectroscopy[8–13], has given an insight into the exciton manifold of photosynthetic complexes.
trans-INTRODUCTION 3
fer dynamics in photosynthetic antennae, comparing isolated complexes with com-plexes embedded in the membrane environment, in order to study the effect of the native environment to the energy transfer efficiency. In particular, we show that the energy transfer between light-harvesting 2 and light-harvesting 1 complexes in the membrane has still an efficiency close to unity (95%).
R
EFERENCES
[1] M. I. Hoffert, K. Caldeira, A. K. Jain, E. F. Haites, H. L.D., S. D. Potter, M. E. Schlesinger, S. H. Schneider, R. G. Watts, T. M. Wigley, and D. Wuebbles, Energy
implications of future stabilization of atmospheric CO2 content,Nature 395, 881 (1998).
[2] G. E. Busch, R. P. Jones, and P. M. Rentzepis, Picosecond spectroscopy using a
picosecond continuum,Chem. Phys. Lett. 18, 178 (1973).
[3] M. G. Rockley, M. W. Windsor, R. J. Cogdell, and W. W. Parsont, Picosecond
de-tection of an intermediate in the photochemical reaction of bacterial photosyn-thesis,Proc. Natl. Acad. Sci. U. S. A. 72, 2251 (1975).
[4] P. L. Dutton, K. J. Kaufmann, B. Chance, and P. M. Rentzepiss, Picosecond
kinet-ics of the 1250 nm band of the Rps. sphaerozdes reaction center: the nature of the primary photochemical intermediate state.FEBS Lett. 60, 275 (1975).
[5] A. J. Campillo, R. C. Hyer, T. G. Monger, W. W. Parson, and S. L. Shapiro, Light
collection and harvesting processes in bacterial photosynthesis investigated on a picosecond time scale.Proc. Natl. Acad. Sci. U. S. A. 74, 1997 (1977).
[6] K. Peters, P. Avouris, and P. M. Rentzepis, Picosecond dynamics of primary
electron-transfer processes in bacterial photosynthesis.Biophys. J. 23, 207 (1978). [7] D. Holten, M. W. Windsor, W. W. Parson, and J. P. Thornber, Primary
photochem-ical processes in isolated reaction centers of Rhodopseudomonas viridis,BBA
-Bioenerg. 501, 112 (1978).
[8] G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, Evidence for wavelike energy transfer through
quantum coherence in photosynthetic systems.Nature 446, 782 (2007).
[9] E. Harel, A. F. Fidler, and G. S. Engel, Real-time mapping of electronic structure
with single-shot two-dimensional electronic spectroscopy.Proc. Natl. Acad. Sci. U. S. A. 107, 16444 (2010).
[10] K. L. M. Lewis and J. P. Ogilvie, Probing photosynthetic energy and charge transfer
with two-dimensional electronic spectroscopy,J. Phys. Chem. Lett. 3, 503 (2012). [11] A. F. Fidler, V. P. Singh, P. D. Long, P. D. Dahlberg, and G. S. Engel, Time scales
of coherent dynamics in the light-harvesting complex 2 (LH2) of Rhodobacter sphaeroides,J. Phys. Chem. Lett. 4, 1404 (2013).
[12] O. Rancova and D. Abramavicius, On the static and dynamic disorder in bacterial
light- harvesting complex LH2 : 2DES simulation study,J. Phys. Chem. B 118,
REFERENCES 5
[13] E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, Quantum coherence in photosynthesis for efficient
solar-energy conversion,Nat. Phys. 10 (2014).
[14] G. S. Beddard and G. Porter, Concentration quenching in chlorophyll,Nature
260, 366 (1976).
[15] E. E. Ostroumov, R. M. Mulvaney, R. J. Cogdell, and G. D. Scholes, Broadband 2D
electronic spectroscopy reveals a carotenoid dark state in purple bacteria,Science
1
U
LTRAFAST SPECTROSCOPY
I
NTRODUCTION
In photosynthetic complexes, electronic energy transfers (EET) processes, occur on a timescale of femtoseconds to picoseconds. Thus no electronic detection is fast enough to directly resolve in time EET dynamics. One possibility to have an exper-iment with time resolution in the femtosecond time scale is by using ultrafast laser beams. In most time-resolved laser spectroscopic experiments, the time resolution depends on the pulse duration, which can be of the order of 10-100 fs. There are sev-eral time-resolved spectroscopic techniques which have been successfully applied to photosynthetic complexes. This chapter introduces three techniques, with time res-olutions from a few picoseconds to a few femtoseconds: time resolved fluorescence, transient absorption and two-dimensional electronic spectroscopy.
1.1.
T
IME RESOLVED FLUORESCENCE
The aim of a time-resolved fluorescence experiment is to measure the spontaneous emission of a sample as a function of time. One very successful method is the time-correlated single photon timing (TCSPT), which has been used in photosynthesis research in the last decades[1]. However there are at least two limitations to this ap-proach. First the instrument response time is several tens of picoseconds. This is a major limitation if the subjects under study are individual pigment-protein com-plexes, where relevant processes occur on a sub-picosecond time scale. The second limitation is that only one detection wavelength is recorded at one time. Therefore multiple measurements at different wavelengths are required in order to record the spectral evolution of the fluorescence.
A synchroscan streak-camera system[2] (Fig.1.1a) affords the possibility to
1
come these limitations. The temporal instrument response of this system is few pi-coseconds, and with deconvolution (global analysis) it is possible to measure with atime resolution in the sub-picoseconds range.
FIGURE1.1: a Time resolved fluorescence setup scheme. An ultrafast laser beam, generated by an optical parametric amplifier (OPA), excites the sample (S). The spontaneous emission is measured by a detector consisting of a spectrograph, a streak camera and charge-coupled device (CCD). b Vibrational relaxation scheme. In this example two electronic states (ground state in blue and excited state in red) are coupled to a vibrational mode. The dashed lines rep-resents the spontaneous emission from the highest, in blue, and the lowest, in red, vibrational modes respectively. c Electronic scheme of two coupled complexes. Each complex is repre-sented as a two level system. Because of the coupling the electronic energy can be transferred from one complex to another. The dashed lines represent the spontaneous emission from the two complexes. d Streak camera image as a function of time (y-axis) and wavelength (x-axis). In color is represented the number of the CCD counts in arbitrary units.
In this setup, a mode-locked ultrafast laser beam and an optical parametric am-plifier (OPA) set the wavelength of the excitation beam, in the 400-850 nm range. The excitation beam is focused on the sample, then the spontaneous emission is mea-sured by the detector. The detector consists of a spectrograph, a streak camera and a charge-coupled device (CCD). The spectrograph disperses the wavelengths of the fluorescence along the horizontal axis. The streak camera is used to resolve in time, along the vertical axis, the detected fluorescence. In this way, with a CCD it is possi-ble to measure both kinetic and spectral information in one single measurement.
1.2.TRANSIENT ABSORPTION
1
9
(ground and excited states), which can be represented as the harmonic potential of Fig.1.1b. In this example, each of the electronic states is coupled to a single vibra-tional mode. After the system is excited, an electron is promoted from the ground state (in blue) to the excited state (in red). In the Condon approximation, the posi-tion of the nuclei does not change during excitaposi-tion. Thus the electron is promoted to one of the higher vibrational modes of the excited state, according to the Frank-Condon factor. Thus, after the system is excited, the electron relaxes to the lowest vibrational mode of the excited electronic state in a non-radiative way. The sponta-neous emission, caused by the relaxation to the electronic ground state, is the sum of two contributions: the emission from the higher vibrational modes and from the lowest one. As it is shown in Fig.1.1the two contributions (blue and red dashed lines) are at different wavelengths (or different energies). Therefore with a streak camera it is possible to resolve the vibrational relaxation of a system, if it occurs on a sub-picosecond time scale.
Another application of this method is to study the electronic energy transfer be-tween different molecules or complexes. The simplest example is shown in Fig.1.1c. This figure shows two coupled electronic states (|e1> and |e2>) with their respec-tive ground states (|g1> and |g2>). In this type of experiment, normally the elec-tronic state with higher energy is excited. Then the electron can either decay to the ground state or the energy can be transferred to the lowest electronic state |e2>. Thus the spontaneous emission can occur from |e1> (blue dashed line) or from |e2> (red dashed line). An example that can be described with this approximation is the LH2 antenna from purple bacteria. In this complex there are typically two electronic bands, the B800, absorbing at 800 nm and the B850 absorbing at 850 nm. If the B800 band is excited, the energy is transferred in 1-5 ps to the B850 band. This is shown in Fig1.1d, which represents a streak image of an LH2 from Rhodopseudomonas
palus-tris, excited at 790nm (B800 band). The spectra show that for few picoseconds after
the excitation, there is fluorescence emission from the B800 band at 800 nm. Then, because of energy transfer, the fluorescence from the B800 band disappears and the complex starts to emit from the B850 band at 850 nm.
1.2.
T
RANSIENT ABSORPTION
Transient absorption measures the changes in the absorbance at various times after sample excitation. Ultrafast transient absorption gives time resolutions from hun-dreds of femtoseconds to few nanoseconds. This is the perfect range to study EET in photosynthetic complexes[3–5].
1
FIGURE1.2: a Transient absorption setup scheme. The output of the laser is split in two by a beam splitter. The transmitted beam is used as pump. The central wavelength of the pump beam is set by an optical parametric amplifier (OPA) and is chopped by an optical chopper. A linear translational stage (Delay stage) sets the time delay between pump and probe. The probe beam, a broadband super-continuum of light, is obtained by focusing the component reflected by the beam splitter on a sapphire. The optical transmission spectrum is recorded by a detector, which consists of a spectrograph and a cool-coupled device (CCD) or a photodiode array for multi-wavelengths detection. b Electronic scheme explaining the three main contri-butions to the transient signal: ground state bleaching (GSB), stimulated emission (SE) and excited state absorption (ESA). In this scheme |g> is the ground state, |e1> the optically excited state, and |e2> represents an electronic state higher in energy. c Transient absorption image as a function of time (y-axis) and wavelength (x-axis). The transient signal∆A is represented by a colour map, which intensity is in mOD (1 mOD is the difference in absorption of about 1 over 1000 with respect to the steady state absorption, which is typically on the order of 1 OD.)
wavelength of the OPA output can be tuned between 400 nm and 850 nm, with a full width half maximum (FWHM) of 10 nm. The probe beam is obtained focusing the laser output on a sapphire crystal, and this produces a super-continuum from about 450 nm to 900 nm. The time difference between pump and probe is set by a trans-lational delay stage, with a precision of about 50 fs. The pump beam is chopped at a frequency which is half the repetition rate of the detector. In this way the pump beams are blocked for half of the number of acquisitions, therefore it is possible to measure the optical transmission with both the pump on (ION) and off (IOFF). The optical transmission spectra are recorded with a detector consisting of a spectro-graph and a photo-diode array or a CCD. The transient absorption,∆A is calculated:
1.3.TWO-DIMENSIONALELECTRONICSPECTROSCOPY
1
11
where AONand AOFFare the absorption with the pump on and off respectively. As compared to time-resolved fluorescence, transient absorption provides infor-mation on numerous photophysical quantum effects.The main contributions to a transient absorption signal are ground state bleaching (GSB), stimulated emission (SE) and excited state absorption (ESA), as shown in Fig.1.2b and explained below.
GSB: after an excitation, a fraction of the molecules have been promoted to the excited state (|e1> in Fig.1.2b), thus the number of molecules in the ground state has decreased. Therefore the ground state absorption in the excited sample is less than in the non-excited sample. This results in a negative signal in the∆A spectrum of eq.1.1in the ground state absorption region.
SE: When the excited molecules are probed, the electrons can relax back to the ground state via SE. This results in a higher optical transmission of the excited sam-ple, which corresponds to a negative signal in the∆A spectrum. The spectral profile of SE typically follows the fluorescence spectrum of the excited molecule, i.e., it is Stokes-shifted with respect to the ground state absorption.
ESA: The excited molecules can also be excited to higher electronic levels by the probe. This results in an increase of the excited sample absorption, and therefore corresponds to a positive signal in the∆A spectrum.
An example of transient absorption spectra, as a function of time and wavelength is shown in Fig.1.2c. Here the∆A in eq.1.1is shown with a colour plot. Colours from red to yellow correspond to positive values, whereas from green to blue to negative values. In this example, showing the transient absorption of LH2 complexes from
Roseobacter denitrificans, the GSB and SE are located in the 820 nm region, and the
ESA is located in the 790 nm region.
1.3.
T
WO
-D
IMENSIONAL
E
LECTRONIC
S
PECTROSCOPY
Two-dimensional electronic spectroscopy (2DES) aims at determining the third or-der optical response function S of a quantum-mechanical system made of interact-ing molecules, such as photosynthetic complexes. The sample is excited with a se-quence of three ultrashort laser pulses delayed in a controlled manner, as shown in Fig.1.3a. The three interactions perturb the optical polarization P of the sample on ultrafast time scales, causing the emission of a photon echo signal, the field of which is characterized in amplitude and phase.
The difference in time between pulses 1 and 2 is called coherence time,τ, the time difference between pulses 2 and 3 is called population time, T . The photon echo signal, ES(τ,T,ωt), is measured for differentτ and T , and it is related to the
third order polarization, P3(τ,T,ωt), by the relation[6]:
ES(τ,T,ωt) =
iωt
n(ωt)
P3(τ,T,ωt), (1.2)
1
FIGURE1.3: a Time sequence of the pulses in 2DES. The coherence timeτ is the time
be-tween pulses 1 and 2. The population time T is the time bebe-tween pulses 2-3. After a time t there is an emission of photon echo signal. The local oscillator (LO), is used for heterodine detection, as shown in chapter2. b Electronic level scheme of a two-level system. c Feynman diagram describing a diagonal peak of a correlation map S2D. d Correlation map expected
from a two-level system. e Electronic level scheme of an excitonic system composed of two two-level systems coupled together. This system is described by 4 states: ground state |g>, two single exciton states |e1> and |e2>, and one double exciton state |f>. f Feynman diagram describing an off-diagonal peak of the system in panel e. g Correlation map expected for an excitonic system
calculated performing a Fourier transformation alongτ:
S2D(ωτ, T,ωt) =
Z ∞ −∞
i P(3)(τ,T,ωt)exp(iωττ)dτ. (1.3)
For a fixed population time, S2D(ωτ,T,ωt)corresponds to a correlation map
be-tween excitation wavelengths,ωτand emission wavelengths,ωt.
1.3.TWO-DIMENSIONALELECTRONICSPECTROSCOPY
1
13
excited states is created. This is due to the ultra-fast excitation, which is broad in the frequency domain. It is difficult to describe such a superposition in the quantum states representation (|g>, |e>). Therefore it is convenient to introduce the density matrixρ: ρ = µ g,g g,e e,g e,e ¶ . (1.4)
In this representation the diagonal elements, (g,g) and (e,e), correspond to the populated quantum states |g> and |e> respectively. The off-diagonal elements rep-resent the superposition of these states. In a double side Feynman diagram, such as Fig.1.3c, two vertical lines represent the time evolution of the two density ma-trix elements. The interactions with the three laser pulses are shown with arrows; an arrow pointing to a vertical line means the absorption of a photon, whereas an ar-row coming out from a vertical line means the stimulated emission of a photon. The dashed line corresponds to the photon echo signal emitted from the system. In the example in Fig.1.3c, the first pulse sets a coherent superposition of states (g,e). This corresponds to the absorption of a photon with frequencyωe= ωτ. After a timeτ, the
interaction with the second pulse populates the excited state (e,e). The population of this state evolves during the population time T . After this time, the interaction with the third pulse creates another coherent state (e,g), with opposite phase evolution with respect to the first one (g,e). When re-phasing occurs, the system relaxes to the ground state, via the emission of a photon echo signal, at a frequencyωe= ωt. This
produces one point along the diagonal in the correlation map S2Din Fig.1.3d. The next step is to consider a system made of two two-level systems coupled together, shown in Fig.1.3e. In this case the quantum states are well described by 4 levels: a ground state, |g>, two single exciton states, |e1> and |e2>, and one double exciton state, |f>. In this case also off-diagonal peaks are possible. An example is shown with the Feynman diagram in Fig.1.3f, whereωτ= ωe1andωt= ωe2. This point appears off-diagonal in the corresponding correlation map shown in Fig.1.3g, which has in total two diagonal and two off-diagonal peaks.
1
lation of the states of the probed system. Thus 2DES, as transient absorption, canThe study of the dynamics of 2DES peaks reveals information about thepopu-be used to measure ultrafast energy transfer rates[11,15]. Furthermore 2DES spec-tra are also sensitive to coherent states of the system and therefore 2DES can also unravel the nature of the coupling in a complex system. This is described further in chapter3. 2DES is also sensitive to quantum states with a very low optical transition moment (dark states)[10], and can be used for detecting charge transfer states, as discussed in chapter5
The next chapter explains how to experimentally measure 2DES spectra, describ-ing in details the setup and how to calculate S2D(ωτ, T,ωt) from the measured photon
echo signal.
1.4.
G
LOBAL ANALYSIS
Global analysis consists in a simultaneous analysis of data across two parameters: wavelength (λ) and time (t). The main assumption of global analysis is that the time and wavelength properties are separable, which reflects the properties of spectra of being independent of time and the dynamics of spectra to be independent of the wavelength. Therefore the lifetimes are global parameters which are wavelength in-dependent. For this analysis a sequential model was used and the assumption of this model is that each state (or component which is a function of the wavelength) evolves into the next one with an increasing lifetime (or a decreasing k rate)[16–19]. Notice that because of the sequential model, each component does not necessarily represent one real state but may be a mix of different states (e.g. in the LH2 the mix between B800 and B850 bands).
A brief description of the mathematical model is as follows: According to linear system theory, when the impulse response of the system is an exponential decay, it has to be convolved with the instrument response function (IRF). Therefore a con-tribution of an exponentially decaying component can be described as:
CmP(t ) = Z ∞
−∞
IRF(τ,µ,∆)e−km(t −τ)dτ
where km= 1/τmis the decay rate and IRF(τ) is a gaussian function with
param-eters for its width (∆) and position (µ). In general, according to the superposition principle, the measured dataΨ(t,λ) can be expressed as a superposition of spectral properties²l(λ) of the components weighted by their concentration cl(t ):
Ψ(t,λ) =
ncomponents X
l =1
cl(t )²(λ)
fluo-1.4.GLOBAL ANALYSIS
1
15
rescence, where each concentration is a linear combination of exponential decays: Ψ(t,λ) = ncomponents X l =1 cl(t )²(λ) (1.5) cSl = l X j =1 bj lclS(kl) (1.6)
where the superscript S stands for sequential, respectively and the amplitudes bj l
are: bj l= l −1 Q m=1 km l Q n=1,6=j ¡kn− kj ¢ , for j É l
The case of transient difference absorption spectra can be described with the same formalism, with evolution associated difference spectra (EADS) instead of EAS:
Ψ(t,λ) =
ncomponents X
l =1
1
R
EFERENCES
[1] K. Sauer and M. Debreczeny, Fluorescence, in Adv. Photosynth. Respir. vol.3
(Springer, Dordrecht, 1996) Chap. 3, pp. 41–61.
[2] I. H. M. van Stokkum, B. V. Oort, and F. van Mourik, ( Sub )-picosecond spectral
evolution of fluorescence studied with a synchroscan streak-camera system, in
Adv. Photosynth. Respir., Vol. 26 (Springer, 2008) Chap. 12, pp. 223–240.
[3] R. Berera, R. van Grondelle, and J. T. M. Kennis, Ultrafast transient absorption
spectroscopy: principles and application to photosynthetic systems.Photosynth.
Res. 101, 105 (2009).
[4] V. Sundstrom, T. Pullerits, and R. van Grondelle, Photosynthetic
light-harvesting: reconciling dynamics and structure of purple bacterial LH2 reveals function of photosynthetic unit,J. Phys. Chem. B 103, 2327 (1999).
[5] R. van Grondelle, J. P. Dekker, T. Gillbro, and V. Sundström, Energy transfer and
trapping in photosynthesis,Biochim. Biophys. Acta - Bioenerg. 1187, 1 (1994). [6] T. Brixner, T. Mancal, I. V. Stiopkin, and G. R. Fleming, Phase-stabilized
two-dimensional electronic spectroscopy,J. Chem. Phys. 121, 4221 (2004).
[7] E. Harel, A. F. Fidler, and G. S. Engel, Real-time mapping of electronic structure
with single-shot two-dimensional electronic spectroscopy.Proc. Natl. Acad. Sci. U. S. A. 107, 16444 (2010).
[8] A. F. Fidler, V. P. Singh, P. D. Long, P. D. Dahlberg, and G. S. Engel, Time scales
of coherent dynamics in the light-harvesting complex 2 (LH2) of Rhodobacter sphaeroides,J. Phys. Chem. Lett. 4, 1404 (2013).
[9] O. Rancova and D. Abramavicius, On the static and dynamic disorder in bacterial
light- harvesting complex LH2 : 2DES simulation study,J. Phys. Chem. B 118,
7533 (2014).
[10] E. E. Ostroumov, R. M. Mulvaney, R. J. Cogdell, and G. D. Scholes, Broadband 2D
electronic spectroscopy reveals a carotenoid dark state in purple bacteria,Science
340, 52 (2013).
[11] E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, Quantum coherence in photosynthesis for efficient
solar-energy conversion,Nat. Phys. 10 (2014).
[12] G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, Evidence for wavelike energy transfer through
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[13] M. Ferretti, K. Duquesne, J. N. Sturgis, and R. van Grondelle, Ultrafast excited
state processes in Roseobacter denitrificans antennae: comparison of isolated
complexes and native membranes,Phys. Chem. Chem. Phys. 16, 26059 (2014).
[14] K. L. M. Lewis and J. P. Ogilvie, Probing photosynthetic energy and charge transfer
with two-dimensional electronic spectroscopy,J. Phys. Chem. Lett. 3, 503 (2012). [15] Y.-C. Cheng and G. R. Fleming, Coherence quantum beats in two-dimensional
electronic spectroscopy.J. Phys. Chem. A 112, 4254 (2008).
[16] I. H. M. van Stokkum, D. S. Larsen, and R. van Grondelle, Global and target
analysis of time-resolved spectra.Biochim. Biophys. Acta 1657, 82 (2004). [17] I. H. van Stokkum, D. S. Larsen, and R. van Grondelle, Erratum to “Global and
target analysis of time-resolved spectra” [Biochimica et Biophysica Acta 1658/2–3 (2004) 82–104],Biochim. Biophys. Acta - Bioenerg. 1658, 262 (2004).
[18] I. H. van Stokkum, B. van Oort, F. van Mourik, B. Gobets, and H. van Ameron-gen, Biophysical techniques in photosynthesis, inAdv. Photosynth. Respir. vol.2
(Springer, Dordrecht, 2008) pp. 223–240.
[19] J. J. Snellenburg, P. L. Seger, R. Serger, K. M. Mullen, and I. H. M. van Stokkum,
2
T
WO
-
DIMENSIONAL ELECTRONIC
SPECTROSCOPY SETUP
I
NTRODUCTION
In a two-dimensional electronic spectroscopy (2DES) experiment, three ultra-short and spectrally broad laser pulses, which are delayed relative to each other in a con-trolled manner, are used to excite a sample. After the excitation, the photon echo emitted by the complexes is recorded in the frequency domainωt as a function of
the coherence timeτ (the time difference between the first and second pulse) and the population time T (the time difference between the second and third pulse), as shown in Fig.1.3. Fourier transformation with respect toτ yields 2D spectra as a function of the excitation frequenciesωτfor each time T. In this chapter the 2DES setup is explained in detail, together with the calibration procedures and the data acquisition. The first section is about the optical setup: it describes how the ultra-fast excitation pulse is generated, split in 4 beams in a box-car configuration, and how the photon echo signal is measured. The second section discusses how the time delay between pulses 1 and 2 is set using two couples of glass wedges, and the cal-ibration procedures are showed in detail. In the third section the auto-correlation procedure, which is used for the pulse time compression, is presented. The fourth section is about the scattering subtraction, which is performed on a shot-to-shot ba-sis, and explains the electronic synchronization between the laser, the choppers and the detector. Finally the last section describes the data acquisition, showing how the photon echo signal is retrieved from the measured interferogram.
2
2.1.
T
HE SETUP
The 2DES setup consists of 4 main parts: the laser source, the non-collinear optical parametric amplifier (NOPA), the 2DES box-car generator and the detector, as it is shown in Fig.2.1.
The laser source is a PHAROS from Light Conversion; its output is an ultra-fast pulsed beam centered at 1028 nm and with a time duration of 200 fs. The repetition rate can be tuned from 100 Hz up to 200 kHz, with a maximum output power of about 6 W.
The NOPA is used to select the wavelength of the experiment and to compress the pulse in the time domain, in order to make it as short as possible. The home-built NOPA is shown in Fig.2.1a in the bottom-left. The output of the PHAROS is split into two beams by a beam splitter. The transmitted component is focused on a barium borate crystal (BBO) which doubles the frequency from 1028 to 514 nm. This component is used as the pump for the NOPA and after going through a delay stage is focused on a second BBO. The reflected component of the PHAROS is focused on a sapphire crystal to generate a super-continuum from about 500 to 1000 nm. The super-continuum is focused on the BBO and mixed with the pump in a non-collinear geometry. In this way it is possible to obtain a pulse with a central wavelength from about 600 nm up to almost 1000 nm, with a full width half maximum (FWHM) of 60-100 nm. After the central wavelength has been selected, the pulse is compressed in the time-domain by a set of two prisms which compensates for the linear dispersion in time (chirp). The output is a beam with a time duration of 20-10 fs, depending on the wavelength.
The 2DES box-car generation section[1], shown in Fig.2.1a at the bottom-right, is used to obtain 4 beams in a box-car geometry (Fig.2.1b) and to adjust the time delays between the four pulses. The output of the NOPA is split into two: the trans-mitted component is used for beams 1-2, whereas the reflected component is used for beams 3-4. The latter goes through a linear translational stage that sets the popu-lation time T, which corresponds to the time difference between pulse 2 and pulse 3. Both reflected and transmitted components are focused on a diffractive grating (DG) and the first orders of diffraction of both beams yield the four beams used for the experiment[2–6]. Before the beams are focused on the sample, beam 1 and beam 2 go through two couples of wedges which are mounted on a linear translational stage. This makes it possible to set the time delay between pulse 1 and pulse 2 (the coher-ence timeτ) with femtosecond precision.
2.1.THE SETUP
2
21
FIGURE2.1: a 2DES set-up scheme. The set-up consists of 4 parts: laser source top left, NOPA bottom left, box-car generator in the bottom right and detector top right. The colours corre-spond to the different wavelengths: purple 1028 nm, green 514 nm, yellow is the super con-tinuum (white light) and red is the excitation pulse (for instance, for the B820 and LH2 com-plexes measurements it corresponds to 820 nm, as will be discussed in the next chapters of this thesis). The NOPA is used for selecting the central wavelength of the laser pulse used for the experiment. A barium borate crystal (BBO) is used for amplifying a selected wavelength in the 640-900 nm range. In the 2DES box-car generation section the output of the NOPA is split in 4 beams by a beam splitter (dashed-lines) and a diffractive grating (DG). The population time
T is set by a delay stage, whereas the coherence timeτ is set by two couples of wedges (W1
2
enabling shot-to-shot measurements with a laser repetition rate up to 1 kHz.
2.2.
W
EDGES CALIBRATION
The time delayτ between pulses 1 and 2 is set by the glass wedges, and can be fine tuned with a femtosecond precision[1]. One wedge is mounted on a translational stage, which can increase or decrease the optical path inside the glass by moving it, in this way varying the time delay between pulses 1 and 2. For the calibration, the sample is replaced by a DG, leading to diffraction of beams 1 and 2 into a common direction. The corresponding spectral interferograms are recorded by moving the translational stage in steps of 10µm, as shown in Fig.2.2.
FIGURE2.2: Spectral interferogram of beams 1-2, obtained by focusing them onto a diffractive grating and collecting the output beams along the common direction. The y axis is the wave-length, while the x axis is the wedge position, which sets the time delay between beams 1 and 2. The colour-scale corresponds to the number of counts on the CCD, in arbitrary units. The hor-izontal oscillation period depends on the wavelength, whereas the vertical ellipse corresponds to zero time delay between beams 1 and 2.
Each horizontal line oscillates at a different frequencyΩ, that depends on the wavelengthλ in the following way:
Ω = 1/T = c/λ,
2.3.PULSE AUTO-CORRELATION
2
23
to define a time delayτ as τ =k1x, where x is the movement of the translational stage
and k is the calibration factor. An example of a trace as a function of the wedge spatial position is shown in blue in Fig.2.3a. Applying a Fourier transformation (Fig.2.3b), it is possible to measure the spatial period of oscillation L, which is also equal to:
L = kT = kλ
c.
Therefore, from the result of the Fourier transformation, the calibration factor k is calculated. For aλ = 820 nm, this is equal to 0.0375 mm/fs.
The spatial position corresponding to zero time delay between pulses 1 and 2 is found as follows: at time zero all the different wavelengths of the pulse are interfering constructively, leading to the vertical ellipse of Fig.2.2. On the other hand, at differ-ent positions the ellipses are tilted, because the oscillation frequencies depend on the wavelength. In order to find the position corresponding to time zero, the inter-ferogram map of Fig.2.2is integrated along the vertical (wavelengths) axis, as shown in red in Fig.2.3a. The maximum of the integrated interferogram corresponds to the time zero position.
FIGURE2.3: a In blue, interferogram trace corresponding to an horizontal line of Fig.2.2. The interferogram integrated along the vertical axis is shown in red. The maximum of the red curve corresponds to the zero time delay between beams 1 and 2. b Fast Fourier transformation of the blue curve of panel a. From the peak position it is possible to calculate the wedge calibration factor.
Once the two couples of wedges are calibrated, the W1 couple (Fig.2.1) is used to acquire rephasing data (positive coherence timeτ), while the W2 couple is used to acquire non-rephasing data (negative coherence timeτ).
2.3.
P
ULSE AUTO
-
CORRELATION
2
doubles the frequency of the incoming beams 1-2. This resultant autocorrelation signal is well separated from the fundamental of beams 1 and 2 due to the non-collinear alignment of the BBO. The autocorrelation signal can be measured with the spectrograph-CCD, both as a function of the wavelength (y-axis in Fig.2.4a) and as function of the time delay (x-axis). The time delay is set by scanning the wedge pair W1. The trace corresponding to the central wavelength is shown in Fig.2.4b. The full width half maximum (FWHM) of a Gaussian fit of the same, corresponds to time duration of the excitation beam. In the case shown in Fig.2.4b, this is 13 fs.
FIGURE2.4: a Autocorrelation map of beams 1-2. The time delay is on the x-axis, whereas the corresponding wavelength is on the y-axis. The colour map corresponds to the number of counts on the CCD camera, in arbitrary units. b Horizontal trace of the map of panel a, as a function of the delay time (dots). The red line corresponds to the Gaussian fit. From the FWHM it is possible to calculate the time duration of the pulse, which, in the presented case, is 13 fs.
2.4.
S
CATTERING SUBTRACTION
Once everything is calibrated, it is possible to measure the interferogram I between pulse 4 and the signal for specific coherence and population timesτ and T by:
I = |E4+ ES|2,
where E4is electric field corresponding to beam 4 (local oscillator) and ESis the elec-tric field corresponding to the photon echo signal. The scattering of beams 3, 1 and 2 contributes to the measured interferogram[1]. This can be mitigated by measuring:
I = I1234− I124− I34+ I4, (2.1)
where I1234is the signal recorded with all four beams hitting the sample, I124with only beams 1, 2 and 4, I34with only beams 3 and 4, and I4with only beam 4.
2.5.DATA ACQUISITION
2
25
the scattering. Herein, that method is modified by modulating beams 1-2 (CH1 in Fig.2.1) as well, in order to measure I34for each signal I1234, thus removing the scat-tering more efficiently. The two independent choppers must be synchronised with the CCD detector. The scheme of the electronic synchronization between choppers and CCD is shown in Fig.2.5.
FIGURE2.5: Electronic synchronization scheme: the laser triggers a synchronization box that is connected to: chopper 1 (CH1), which chops beams 1 and 2, chopper 2 (CH2), which chops beam 3 and the CCD detector.
The laser triggers a synchronization box that produces 3 outputs. One output, with half of the frequency of the laser, triggers the chopper 2, which modulates beam number 3. Another output, with one quarter of the frequency of the laser, triggers the chopper 1, which modulates beams 1 and 2. And finally a special output, with the same frequency of the laser, triggers the CCD acquisition. This last output produces a finite number (4N) of pulses, where N is the number of acquisitions. This output is generated only after a rise of the chopper 1 output (the slowest output), so that the first acquisition always corresponds to I1234. Thus by modulating both beams 1-2 and beam 3 using two independent choppers, all of the terms of eq.2.1are measured on a shot-to-shot basis.
2.5.
D
ATA ACQUISITION
Once the sample is excited by pulses 1, 2 and 3, the photon echo signal is measured with a heterodyne detection method. [7–10]. This method is used in electronic mea-surements as well, and it consists of mixing a low intensity periodic signal with a known reference signal, producing an interference which for easier detection ampli-fies the low intensity signal.
2
3). Thus, for a fixed population time, the coherence time is scanned for positive (rephasing frequencies) and negative (non-rephasing frequencies) values[1,11,12]. Notice that for positiveτ pulse 1 arrives before pulse 2, whereas for negative τ, pulse 1 arrives after pulse 2. The experiment is repeated for different population times. Fig.2.6a shows a 2D plot representing the measured interferogram as a function of detected wavelengths (λt) on the y-axis and positive coherence time (τ) on the x-axis.
A vertical cut of the 2D plot represents the interference I (ωt) between the local
oscillator and the photon echo signal at fixed coherence time:
I (ωt) = ¯ ¯ES(ωt) + E4(ωt)exp[iωttLO] ¯ ¯ 2 , (2.2)
where ESis the photon echo signal, E4is the local oscillator (pulse 4) and tLOis the
time delay between pulses 3 and 4. Fig.2.6b shows an example corresponding to
τ=0 (blue curve). As can be seen from eq.2.2, the interferogram oscilates with a
frequency equal to tLO. Therefore a fast Fourier transformation (FFT) applied to the
blue curve in Fig.2.6b, reveals two peaks: one at zero, corresponding to the non oscillating terms of eq.2.2, and one at tLO. An example FFT is shown in Fig. 2.6c.
A peak is evident at t =1.22 ps=tLO, as expected. The next step of the data analysis
is to isolate the peak at 1.22 ps with a windowing function (e.g. a step function or a gaussian function centered at 1.22 ps) and to apply a fast Fourier transformation in order to go back to the frequency domain (ωt), isolating in this way the oscillating
components of eq. 2.2. The result of such operation is presented in Fig.2.6b in red. This oscillating component corresponds to:
IOSC= p
IS(ωt)ILO(ωt)exp [i (ΦS(ωt) − ΦLO(ωt) − ωttLO)] . (2.3)
As explained in section2.4, for each photon echo shot the corresponding local oscillator (ILO) is measured. Thus IOSCcan be normalized to ILO, obtaining in this
way the amplitude of the signal (IS). Then an FFT is applied along the coherence time axis in order to get a map (S2D(ωτ, T,ωt)) that correlates absorbed frequencies
(ωτ) with detected frequencies (ωt).
The final step of the data acquisition is to retrieve the phase of the signal (ΦS). For this purpose the projection-slice theorem is used[13,14]. According to this theorem, the projection of the real part of the 2D spectra is equal to the transient absorption signal. In order to apply the projection-slice theorem, the transient absorption signal is measured using beam 2 as pump and beam 4 as probe. The transient absorption is shown in Fig.2.6d in blue. The transient signal is alternatively obtained by integrat-ing the 2D spectra:
A2D(T,ωt) = Re ½ ω t n(ωt) Z∞ −∞ S2D(ωτ, T,ωt) × exp[i Φc+ i ωttc]dωτ ¾ , (2.4) whereΦcand tcare phase parameters used to retrieve the signal phaseΦS. ThusΦc
2.5.DATA ACQUISITION
2
27
FIGURE2.6: a Measured interferogram as a function of detected wavelengths (ωt) and
coher-ence time (τ). b In blue, vertical cut of panel a, and in red isolated oscillating signal. c Fast Fourier transformation of the interferogram of panel b. d Transient signal used for the phas-ing procedure. Independent measurement in blue, and signal obtained from the 2D spectrum in red. e Real part of the 2D spectrum corresponding to T =60 fs. f Absolute part of the 2D spectrum at T =60 fs.
2
2.6.
A
CKNOWLEDGEMENTS
REFERENCES
2
29
R
EFERENCES
[1] T. Brixner, T. Mancal, I. V. Stiopkin, and G. R. Fleming, Phase-stabilized
two-dimensional electronic spectroscopy,J. Chem. Phys. 121, 4221 (2004).
[2] A. A. Maznev, K. A. Nelson, and J. A. Rogers, Optical heterodyne detection of
laser-induced gratings.Opt. Lett. 23, 1319 (1998).
[3] G. D. Goodno, G. Dadusc, and R. J. D. Miller, Ultrafast heterodyne-detected
transient-grating spectroscopy using diffractive optics,J. Opt. Soc. Am. B 15, 1791 (1998).
[4] G. D. Goodno, V. Astinov, and R. J. D. Miller, Diffractive optics-based
heterodyne-detected grating spectroscopy: Application to ultrafast protein dynamics,J. Phys. Chem. B 103, 603 (1999).
[5] M. Khalil, N. Demirdöven, O. Golonzka, C. J. Fecko, and A. Tokmakoff, A
phase-sensitive detection method using diffractive optics for polarization-selective fs Raman spec,J. Phys. Chem. A 104, 5211 (2000).
[6] Q.-H. Xu, Y.-Z. Ma, I. V. Stiopkin, and G. R. Fleming, Wavelength-dependent
reso-nant homodyne and heterodyne transient grating spectroscopy with a diffractive optics method: Solvent effect on the third-order signal,J. Chem. Phys. 116, 9333 (2002).
[7] L. Lepetit and M. Joffre, Two-dimensional nonlinear optics using
Fourier-transform spectral interferometry.Opt. Lett. 21, 564 (1996).
[8] J. P. Likforman, M. Joffre, and V. Thierry-Mieg, Measurement of photon echoes by
use of femtosecond Fourier-transform spectral interferometry.Opt. Lett. 22, 1104 (1997).
[9] N. Belabas and M. Joffre, Visible-infrared two-dimensional Fourier-transform
spectroscopy.Opt. Lett. 27, 2043 (2002).
[10] M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. a. Wiersma, Spectral
in-terferometry as an alternative to time-domain heterodyning.Opt. Lett. 22, 1338
(1997).
[11] S. M. Gallagher, A. W. Albrecht, J. D. Hybl, B. L. Landin, B. Rajaram, and D. M. Jonas, Heterodyne detection of the complete electric field of femtosecond
four-wave mixing signals,J. Opt. Soc. Am. B 15, 2338 (1998).
[12] L. Lepetit, G. Chériaux, and M. Joffre, Linear techniques of phase measurement
2
[13] J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, Two-dimensional Fourier
trans-form electronic spectroscopy,J. Chem. Phys. 115, 6606 (2001).
3
T
HE COHERENCES IN THE
B820
BACTERIOCHLOROPHYLL DIMER
REVEALED BY TWO
-
DIMENSIONAL
ELECTRONIC SPECTROSCOPY
Light-harvesting in photosynthesis is determined by the excitonic interactions in dis-ordered antennae and the coupling of collective electronic excitations to fast nuclear motions, producing efficient energy transfer with a complicated interplay between ex-citon and vibrational coherences. In this chapter we apply 2DES to an exex-citonically coupled bacteriochlorophyll dimer, the B820 subunit of the light harvesting complex 1 (LH1-RC) of R. rubrum G9. Fourier analysis of the measured kinetics and modeling of the spectral responses in a complete basis of electronic and vibrational states allow us to distinguish between pure vibrational, mixed exciton-vibrational (vibronic), and predominantly exciton coherences. Although the B820 dimer is a model system, the approach presented here represents a basis for further analyses of more complicated systems, providing a tool for studying the interplay between electronic and vibrational coherences in disordered photosynthetic antennae and reaction centres.
Parts of this chapter have been published as: M. Ferretti, V. I. Novoderezhkin, E. Romero, R. Augulis, A. Pandit, D. Zigmantas and R. van Grondelle, Physical Chemistry Chemical Physics 16, 9930 (2014) [1]
3
3.1.
I
NTRODUCTION
The success of natural photosynthesis is based on two ultrafast processes: excitation energy transfer after light absorption by the photosynthetic light harvesting antenna followed by transmembrane charge separation in the photosynthetic reaction cen-tre [2–4]. Both processes occur with a quantum efficiency approaching unity in spite of the highly disordered nature of these biological systems. In recent years, the role of quantum mechanics, disorder and coherence [5–8] has been proposed to explain the high energy conversion efficiency of the primary steps of photosynthesis.
Two-dimensional electronic spectroscopy (2DES) is a tool to study the presence and the role of quantum coherences in biological complexes [9–11]. In this tech-nique three spectrally broad and ultra-short laser pulses are used to set and detect the coherent superposition of quantum states in the complex. The three pulses are time delayed, and fast Fourier transformation (FFT) with respect to the coherence
timeτ (the time between the first and the second pulse) and with respect to the
rephasing time t (the time between the third pulse and the emitted signal) results in 2D spectra which correlate the absorbed frequencyωτwith the emitted frequencyωt
for a fixed population time T (the time between the second and the third pulse). The population time dynamics is related to the evolution of quantum coherence between quantum states and to energy transfer. The coherence appears as peak amplitude oscillations during T, whereas energy transfer appears as non-oscillating crosspeaks. Although originally off-diagonal amplitude oscillations were associated with exciton coherence [11] and diagonal amplitude oscillations with vibrational coherences, re-cently, electronic-vibrational (vibronic) models, with both diagonal and off-diagonal contributions to the oscillations, have been proposed[12–16]. Within the proposed mechanism, vibronic coherences appear when the exciton splitting energy is reso-nant with vibrational modes, and this resonance is potentially able to sustain, regen-erate, or even (re-)create coherences between electronic states during the time scale of energy and electron transfer [12,13,15,17–19] . However, due to the complexity of the exciton manifold of most of the photosynthetic complexes, the nature of the observed coherences has not been unambiguously determined yet.
split-3.1.INTRODUCTION
3
33
ting energy of the B820 dimer (400–500 cm−1) is comparable to the frequencies of the most dominant intramolecular BChl vibrational modes (as observed in a transient absorption experiment on mutants of the bacterial reaction center[24]). Moreover, the absorption intensity of the higher energy exciton component is of the same order of magnitude as the intensities of the vibrational satellites in the blue wing of the ab-sorption in this complex. Thus, the B820 is an excellent model system to investigate the interplay between exciton and vibrational coherences. The energetic disorder in B820, caused by slow protein motions (with respect to the ultrafast dynamics probed by 2DES), is large enough[25–27] to create a spread of the apparent exciton splitting from 400 to 800 cm−1, which can become resonant with the most intense vibrational modes.
FIGURE3.1: Top left frame: expected pigment–protein arrangement of the B820 sub-unit adapted from the crystal structure of the reaction center light-harvesting complex 1 of
Rhodopseudomonas palustris [24]. Top right frame: the B820 exciton energy level scheme with-out vibrational coupling. Bottom frame: in red, the B820 room temperature steady-state ab-sorption spectrum and in black, the laser spectral profile.
3
applied a model based on a two-pigment Hamiltonian in the complete diabatic basis of electronic and vibrational states to calculate the linear and non-linear (2D) spec-tral responses. The model enables us to explore the interplay between exciton and vibrational coherences for a single realization of the disorder, and to reproduce the experimentally obtained disorder-averaged 2D frequency maps. We find the simul-taneous presence of exciton and vibrational coherence and estimate the degree of exciton-vibrational mixing.
3.2.
E
XPERIMENTAL RESULTS
3.2.1.
2D
ELECTRONIC SPECTRAThe 2D real rephasing spectra, for T equal to 20, 100, 220 and 500 fs, are shown in Fig.3.2. The signal along the diagonal is dominated by a positive band at 815 nm which corresponds to the contributions of ground state bleach (GSB) and stimulated emission (SE) from the 820 nm super-radiant state. The almost-dark state at 795 nm is undistinguishable in the 2D spectra in agreement with its low amplitude in the steady state absorption spectrum shown in Fig.3.1. The off-diagonal peaks are both negative and correspond to the intrinsic lineshape of the rephrasing 2D spectrum and to the excited state absorption (ESA).
λτ(nm) λt (nm) T = 20 fs 760 800 840 880 760 800 840 880 λ τ(nm) λt (nm) T = 100 fs 760 800 840 880 760 800 840 880 λ τ(nm) λt (nm) T = 220 fs 760 800 840 880 760 800 840 880 λ τ(nm) λt (nm) T = 500 fs 760 800 840 880 760 800 840 880 −0.02 0 0.02 0.04 0.06 −0.05 0 0.05 0.1 −0.04 −0.02 0 0.02 0.04 0.06 0.08 −0.02 0 0.02 0.04 0.06
FIGURE3.2: 2D real rephasing spectra at population time ( T ) equal to 20, 100, 220 and 500 fs at room temperature.
The (superposition) states created by the three laser pulses and their rephasing can be described by double-sided Feynman diagrams. These diagrams allow us to as-sign certain processes to specific locations (λτ,λt) in the 2D spectra. With the
3.2.EXPERIMENTAL RESULTS
3
35
nm corresponds to the excitation from the one-exciton 820 nm state to the double-exciton f state (where both monomers are excited), whereas the peak at (804,845) nm corresponds to an excitation from the 795 nm state to the f state (see SUPPLE-MENTARY for 2D total real spectrum).
3.2.2.
2D
TRACES AND QUANTUM BEATSThe 2D traces (Fig.3.3, top-left frame), the real rephasing amplitude as a function of population time T, are analyzed in order to study the dynamic evolution of the spec-tra. The traces show a bi-exponential decay modulated by oscillations. The origin of the multi-exponential decay is due to several relaxation processes, which occur on different time scales, e.g. excitonic relaxation in hundreds of femtoseconds and vibrational relaxation in a few picoseconds [28]. The presence of amplitude oscilla-tions, the so called quantum beats, is a signature of quantum coherence.
FIGURE3.3: Top-left frame: population time (T ) dynamics of representative 2D real rephasing peaks. Top-right frame: quantum beats obtained after subtraction of the bi-exponential decay from the traces shown in the top frame. Some of the traces have been vertically translated for better visualization. Bottom frame: Power spectral density of the quantum beats indicating the different oscillation frequencies of the system. For a list of the most prominent frequencies see Table3.1
3
residues in order to evaluate the oscillation frequencies contained in the quantum beats. The power spectral density (PSD) of the FFT is shown in Fig.3.3bottom, and the corresponding frequencies are reported in Table3.1. For the interpretation of the frequencies and the nature of the coherences see the modelling of 2D frequency maps section below.
3.2.3.
2D
REAL REPHASING FREQUENCY MAPSThe analysis of the 2D traces presented in the previous section is applied to the whole 2D spectrum, i.e., to all the different (λτ,λt) combinations. The result is represented
by 2D frequency maps, each of them corresponding to different oT frequencies, in-stead of being associated with different time T (as is the case for the 2D spectra). These maps show only the state super-positions which oscillate with a certain fre-quencyωT during T. Four maps corresponding to oT equal to 345, 416, 546 and 735
cm−1are shown in Fig.3.4. Note that theωT resolution is about 90 cm−1.
The low frequency map at 345 cm−1shows an intense diagonal peak at 820 nm and two weaker off-diagonal peaks at (830, 810) nm and at (810, 830) nm. In the maps corresponding to frequencies near the exciton splitting (400–550 cm−1) the below-diagonal peaks at (800, 830) nm becomes dominant. At higher frequencies, such as 735 cm−1, the amplitudes of both diagonal and off-diagonal peaks are comparable, and the off-diagonal peaks show complicated structures. Even though the 735 cm−1 frequency exceeds the expected exciton splitting energy, exciton coherence can still appear in realizations of the disorder with significant asymmetry between the two BChl molecules, for instance, realizations with an energy difference of 200 cm−1 be-tween the two site energies. In this way the disorder can produce a mixed exciton-vibrational or predominantly exciton coherence at any frequency. To understand the origin of the coherences, we model the third-order response of the system in the basis of electron-vibrational eigenstates, taking into account the disorder in the site energies and the coupling of single vibrational modes to the exciton manifold of the system.
3.3.
M
ODELLING
3.3.1.
E
XCITON-
VIBRATIONALH
AMILTONIAN3.3.MODELLING
3
37 Hex−vi b = Hg+ He+ Hf Hg = |g > " Ω X s=x,y · 1 2 ³ ∆s g ´2 + µ β† sβs+ 1 2 ¶ −p1 2∆ s g ³ βs+ β†s ´¸ # < g | He = X n=1,2 |n > " ωn0+ Ω X s=x,y · 1 2 ¡ ∆s n ¢2 + µ β† sβs+ 1 2 ¶ −p1 2∆ s n ³ βs+ β†s ´¸ # < n| + X n6=m |n > Mnm< m| Hf = | f > " ω10+ ω20+ Ω X s=x,y · 1 2 ³ ∆s f ´2 + µ β† sβs+ 1 2 ¶ −p1 2∆ s f ³ βs+ β†s ´¸ # < f | where Hg, Heand Hf represent the Hamiltonian for none, one or both monomersexcited, respectively.
The basic states are given by a direct product of the electro- nic wavefunctions (ground |g >, one-exciton |n >, two-exciton | f >) and vibrational wavefunctions |as > depending on the effective nuclear coordinates s = x, y. Note that x and y
do not represent spatial coordinates, but the displacement in two independent di-rections. The basis wavefunctions |as> are unshifted, i.e., have zero displacement
along the x− and y− coordinates. The creation and annihilation phonon operators
β†
s andβs work on this unshifted basis. The displacements of the electronic
sur-faces along the s-coordinates (∆sg,∆sn,∆sf) are accounted for by the shifting operators Ω∆s
³
βs+ β†s
´
/p2, whereΩ is the vibrational frequency. Excitation of the diabatic state n corresponds to the g → n transition with the electronic transition dipole dn
and zero-phonon transition energyωn0. The interaction between the diabatic states
is given by the energy M12that is supposed to be independent of the vibrational co-ordinates. The two-exciton manifold consists of a single state corresponding to ex-citation of the two sites, i.e., | f >= |1,2 >. Diagonalization of the Hamiltonian gives the exciton-vibrational (vibronic) eigenstates:
HgCg = CgEg; |c >= X a Cacg |g , a >; Eg cc0= δcc0ωc HeCe = CeEe; |b >= X n,a Cen,ab|n, a >; Ebbe 0= δbb0ωb HfCf = CfEf; |r >= X a Carf | f , a >; Ef r r0= δr r0ωr
where |a >= |ax, ay> is the product of the vibrational wavefunctions corresponding
3
dbc = X n,a Cen,abdnCacg dr b = X n6=m Carf ³ dmCn,abe dnCem,ab ´ .Note that a similar approach has been previously employed to model electron transfer coupled to a coherent vibrational motion along two nuclear coordinates in the bacterial reaction centre[29], and recently the same Hamiltonian was used to ex-plore the structure of the electronic and vibrational coherences in the 2D spectral responses of a molecular dimer [16,30]. In the present modelling we use displace-ments∆xg,∆yg = ∆/2−1, −1 for the ground state |g >; ∆x1,∆y1= ∆/21, −1 and ∆x2,∆2y= ∆/2−1,1 for the excited states |1 > and |2 >; and ∆x
f,∆ y
f = ∆/21, 1 for the two-exciton
state | f >= |1,2 >. Note that the relative displacements for the |1 >→ |1,2 > and |2 >→ |1, 2 > transitions are the same as for the |g >→ |2 > and |g >→ |1 > transi-tions, respectively. The minima of the potential surfaces of the diabatic states 1 and 2 are displaced (with respect to each other) along the x-y direction. Therefore, the nuclear motion along this direction is affected by the mixing between the diabatic states. Note that the dynamics along the x-y direction corresponds to anticorrelated nuclear motion within the states 1 and 2.
3.3.2.
E
XCITON-
VIBRATIONAL STRUCTURE OF THE ABSORPTION SPEC-TRUM
3.3.MODELLING
3
39
FIGURE3.4: B820 2D frequency maps atωT= 345, 416, 546, and 735 cm−1; experimental (left
frame) and calculated (right frame) maps. The calculation is performed at room temperature, averaging over disorder (σ = 650 cm−1), withα = 251 cm−1and M
12= -270 cm−1. The excited
states are coupled to a single vibrational mode, taken from a specific manifold as discussed in the text. In the calculated maps the energy is counted from the unperturbed zero-phonon energiesω10=ω20, which correspond to the electronic excitation of a BChl monomer from the
lowest vibrational level of the ground state to the lowest vibrational level of the excited state (without disorder).
