ARTICLE
Received 21 Jan 2015 | Accepted 4 Jun 2015 | Published 9 Jul 2015
James Lim1,*, David Paleek2,3,*, Felipe Caycedo-Soler1, Craig N. Lincoln4, Javier Prior5, Hans von Berlepsch6, Susana F. Huelga1, Martin B. Plenio1, Donatas Zigmantas2 & Jrgen Hauer4
Natural and articial light-harvesting processes have recently gained new interest. Signatures of long-lasting coherence in spectroscopic signals of biological systems have been repeatedly observed, albeit their origin is a matter of ongoing debate, as it is unclear how the loss of coherence due to interaction with the noisy environments in such systems is averted. Here we report experimental and theoretical verication of coherent excitonvibrational (vibronic) coupling as the origin of long-lasting coherence in an articial light harvester, a molecular J-aggregate. In this macroscopically aligned tubular system, polarization-controlled 2D spectroscopy delivers an uncongested and specic optical response as an ideal foundation for an in-depth theoretical description. We derive analytical expressions that show under which general conditions vibronic coupling leads to prolonged excited-state coherence.
DOI: 10.1038/ncomms8755 OPEN
Vibronic origin of long-lived coherence in an articial molecular light harvester
1 Institut fr Theoretische Physik, Universitat Ulm, Albert-Einstein Allee 11, 89069 Ulm, Germany. 2 Department of Chemical Physics, Lund University, PO Box 124, SE-22100 Lund, Sweden. 3 Department of Chemical Physics, Charles University in Prague, Ke Karlovu 3, 121 16 Praha 2, Czech Republic. 4 Photonics Institute, Vienna University of Technology, Gusshausstrasse 27, 1040 Vienna, Austria. 5 Departamento de Fsica Aplicada, Universidad Politcnica de Cartagena, Cartagena 30202, Spain. 6 Forschungszentrum fr Elektronenmikroskopie, Institut fr Chemie und Biochemie, Freie Universitat Berlin, Fabeckstrabe 36a, D-14195 Berlin, Germany. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to J.H. (email: mailto:[email protected]
Web End [email protected] ).
NATURE COMMUNICATIONS | 6:7755 | DOI: 10.1038/ncomms8755 | http://www.nature.com/naturecommunications
Web End =www.nature.com/naturecommunications 1
& 2015 Macmillan Publishers Limited. All rights reserved.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8755
The remarkably high efciency in photosynthesis, where nine out of ten absorbed photons reach the reaction centre, is a fascinating eld of modern research. In such
photosynthetic complexes, structure, dynamics and function are inextricably linked. A conserved building block comprises strongly absorbing pigments arranged in close proximity to one another supported by the surrounding protein scaffold1,2. Typical inter-pigment distances are of order of 10 and photon absorption leads to the formation of delocalized excited electronic states (excitons) shared by two or more pigment molecules. Exciton creation, migration and trapping are central to the functionality of a photosynthetic apparatus. The controlled and adjustable arrangement of the pigments tunes the electronic network and the properties of its interaction with the vibrational environment that is associated with either the pigments or the protein. The detailed balance of these properties determines the efciency of light-harvesting systems3,4.
Exciton dynamics can be efciently probed by two-dimensional (2D) electronic spectroscopy5. This technique revealed oscillatory signals in the spectral response of a wide variety of photosynthetic aggregates6,7. Initially ascribed to excitonic beatings, oscillations have been found to persist up to several hundreds of femtoseconds at room temperature810. This timescale exceeds typical dephasing rates in the condensed phase and becomes comparable to exciton transfer times1, thus posing the question of the nature and functional relevance of these coherences4. Unfortunately, the complex structure of 2D signals makes the unambiguous identication of the underlying mechanisms that support such long-lived coherences a challenging task and several hypotheses to explain them have been formulated1121. The different approaches can be classied into theories including coherent interaction of excitons with intra-pigment vibrations1115 and theories focusing on incoherent excitonprotein interaction such as correlated uctuations1618. It is possible that some of these mechanisms may coexist on certain timescales and that one or another may become dominant depending on the system under consideration.
In this work, we show that the relatively simple excitonic structure of a molecular J-aggregate provides an ideal test case to identify the microscopic mechanism behind long-lived oscillations in electronic 2D signals. The investigated J-aggregate is tubular and aligns along the samples ow direction when in solution. In addition, the J-aggregate exhibits excitonic bands with roughly orthogonal transition dipole moments. It is this combination of perpendicular excitonic transitions and macroscopic alignment that makes electronic 2D spectroscopy with polarization-controlled excitation pulses an ideal tool to study coherence effects between the excitonic bands. This approach signicantly reduces the complexity of retrieved 2D signals, leading to only two peaks with oscillatory components in specic regions of the 2D maps, that is, one on the diagonal and one as a cross-peak for non-rephasing and rephasing signal components, respectively. Employing a vibronic model, we derive analytical expressions that show how system parameters such as electronic decoherence rates and excitonvibrational resonance determine the amplitude and lifetime of oscillatory signals. Fitting the analytical expressions to measured data, the vibronic model achieves quantitative agreement with experimental observations. Concerning potential functional relevance of the observed oscillations, we show that the long-lived oscillatory signals in our system are dominated by excited-state coherence rather than ground-state coherence.
ResultsThe system. J-aggregates of cyanine dyes are promising candidates for articial antenna systems2226. They are chemically
versatile and self-assemble into various extended supramolecular structures in aqueous solution27. Here a system that can be considered a macroscopically aligned synthetic light harvester was studied, namely a molecular J-aggregate of C8O3-monomers whose aggregation behaviour is well known28,29. As revealed by cryogenic transmission electron microscopy30, the aggregate structure is best described as a double-layered nanotube with outer diameter B11 nm and lamellar spacing of B2.2 nm between the chromophore layers. In addition, superhelical bundles of these tubes can also form though the addition of polyvinyl alcohol inhibits this process and thereby avoids single-layered tube formation24 and maintains a stable solution over several weeks31. A drawing of the J-aggregate under investigation, from here on referred to as C8O3, is shown in Fig. 1a. The bilayer conguration of C8O3 allows the effect of different decoherence rates to be studied as the outer solvent-exposed layer shows faster decoherence than the inner protected layer.
The structural properties of the aggregate are remarkable: the 11-nm outer diameter is contrasted by a length of several micrometres. Circulating solvated C8O3 with a wire-guided jet (Fig. 1a) leads to a macroscopic orientation of the tubes because
2 1
a b
1.0
1 2
Parallel Perp.
Abs. (a.u.)
0.5
0.0
1.0
0.5
0.0
3
3
16 17 18
Energy (1,000 cm1)
Energy (cm1)
c
Aggregate Monomer
[afii9840]1
Norm. int. (a.u.)
[afii9840]2
400 600 800
d
k2 (0)
LO (0)
k1 (90)
k3 (90)
ks= k1 + k2 + k3
[afii9853]3
Figure 1 | C8O3 and polarization-controlled 2D spectroscopy. (a) Wire-guided window-free jet used for sample circulation, along with a schematic of the double-layered structure of the C8O3 aggregate. The aggregates align along the ow direction (white arrow). The transition dipole directions of bands 13 are displayed by arrows, which are mainly polarized along the tube axis (bands 1 and 2 shown in blue) or perpendicular to the axis (band 3 shown in orange). (b) Absorption spectra in arbitrary units, Abs. (a. u.), with light polarized parallel (blue) and perpendicular (perp.; orange) to the ow direction. (c) Non-resonant Raman spectra of the C8O3 monomer (black line) and aggregate (grey area). The vibrational frequencies n1 and n2 are close to the exciton energy splitting between bands 1 and 3 and bands 2 and 3, respectively. (d) Polarization-controlled 2D spectroscopy with three excitation pulses (k1 to k3) and a local oscillator (LO) for heterodyne detection of the signal eld, depicted as an oscillating line. Polarization orientation (0 or 90) is given with respect to the longitudinal axis of aligned C8O3.
2 NATURE COMMUNICATIONS | 6:7755 | DOI: 10.1038/ncomms8755 | http://www.nature.com/naturecommunications
Web End =www.nature.com/naturecommunications
& 2015 Macmillan Publishers Limited. All rights reserved.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8755 ARTICLE
the longitudinal axis preferentially aligns along the ow direction. This creates anisotropy for linearly polarized light, as shown in Fig. 1b. Linear dichroism measurements31 and redox-chemistry studies32 assign bands 1 and 2 to longitudinal transitions localized on the inner and outer cylinders, respectively (Fig. 1a). Transitions to band 3 are preferentially polarized perpendicular to the long axis of C8O3 and are shared by both layers. A detailed description of sample-preparation methods and band assignments is given in the Supplementary Notes 1 and 2.
Fitting the well-dened absorption peaks of C8O3 with Lorentzian functions (see Supplementary Note 2) reveals an exciton energy difference between bands 1 and 3 of DO31E690 cm 1 and DO32E460 cm 1 for bands 2 and 3. Both exciton energy splittings are close to vibrational frequencies n1E668 cm 1 and n2E470 cm 1 observed in non-resonant Raman spectra33 (Fig. 1c). These vibrational frequencies are measured in both the monomer and aggregate Raman spectra, that is, they are not aggregation-induced Raman bands. Strongly enhanced modes at similar energies were observed in resonant Raman spectra of a related cyanine dye, and can be assigned to out-of-plane vibrations34. Such out-of-plane vibrations were shown to couple strongly to excitons35. The quasi-resonance between the vibrational frequencies n1 and n2 and exciton energy splittings DO31 and DO32 provides us with an interesting scenario of possible coherent interaction between bands (excitons) and vibrations11,13,14,21,36. Such excitonvibrational coupling induces vibronic12 and vibrational coherences15, which can both lead to long-lived beating signals in 2D spectra. Here we emphasize that coherence in the electronic excited-state manifold is referred to as vibronic and in the ground-state manifold as vibrational. Identifying the dominant contribution is of fundamental importance because only vibronic coherence, which manifests in excited-state dynamics, can enhance exciton transport and thus support light-harvesting function3739.
Experimental results. The absorption spectrum of a light-harvesting system may be heavily congested because of overlapping excitonic bands and the resulting 2D signal would exhibit signicant overlap between diagonal and cross-peaks, thereby impeding further analysis. It has been suggested to employ laser pulses of different relative polarization to selectively address relevant excitation pathways to obtain a clearer 2D signal40. However, the advantage of polarization-controlled 2D spectroscopy has been limited by the isotropic nature of the investigated samples (an ensemble). In the experiment presented here, these problems are circumvented by the measurement of the macroscopically aligned C8O3. The transition dipole moments of bands 1 and 2 are preferentially parallel to the longitudinal axis while band 3 is orthogonal, thus allowing for optimal polarization selectivity. This combination reduces the obtained 2D maps to only two relevant peaks with negligible overlap and an up to 30 times stronger signal intensity as compared with the isotropic case41.
The ideal pulse sequence to isolate beating signals between states with orthogonal transition dipole moments, that is, bands 1 and 3 in the present case, is depicted in Fig. 1d, where the phase-matched direction for measuring rephasing spectra is displayed: non-rephasing spectra can be measured along the same phase-matched signal direction by changing the order of the rst two pulses (see Methods). After subtraction of the non-oscillatory background, we performed a Fourier transformation along waiting time t2 for all points on the 2D (o1, o3) map. The resulting o2 plots allow the lineshape of beating signal with frequency o2 to be visualized as a function of position in (o1, o3) space. The slice at the exciton energy splitting between bands 1
and 3 (o2 70520 cm 1 with the experimental resolution of
20 cm 1) reveals a non-rephasing diagonal peak N11 and a rephasing cross-peak R31 as shown in Fig. 2a,b, respectively. N11 is centred at (o1, o3) (O1, O1) with exciton energy
O1E16,405 cm 1 of band 1 and a symmetric linewidth 2Gg1E130 cm 1 along both o1 and o3 axes (Fig. 2a). The centre of R31 is located at (o1, o3) (O3, O1) with exciton energy
O3E17,125 cm 1 of band 3 and asymmetric linewidths 2Gg3E300 cm 1 and 2Gg1E130 cm 1 along o1 and o3 axes, respectively (Fig. 2b). In peak amplitude, R31 is B30% of N11.
Relative FT-amplitude ([afii9853]2) (a.u.)
0 0.5 1
0 0
0.4
0
0.3
0.2
17.5
705 cm1, non-reph. experiment
705 cm1, reph. experiment
1 )
[afii9853] 3( 1,000 cm
[afii9853] 3( 1,000 cm
17.0
N11
R31
16.5
17.5
a
b
16.5 16.5
17.0 17.0
17.5 17.5
1 (1,000 cm1)
0.5 1
705 cm1, non-reph. theory
705 cm1, reph. theory
1 )
[afii9853] 3( 1,000 cm
17.0
16.5
17.5
17.0
c
d
16.5
17.0
17.5
16.5
17.0
17.5
0
462 cm1, non-reph. experiment
0
0.05
17.0
1 )
N22
16.8
16.5
16.6
16.6
f
e
16.8
17.0
16.5
17.0
17.5
Figure 2 | Experimental and theoretical 2D spectra. (a,b) The Fourier-transform (FT) amplitude maps of non-rephasing (non-reph.) and rephasing (reph.) spectra at o2 70520 cm 1, which reveal the
presence of a non-rephasing diagonal peak N11 and a rephasing cross-peak R31. These peaks stem from the coherent interaction of bands 1 and 3 with the quasi-resonant vibrational mode with frequency n1E668 cm 1. The amplitude of N11 is about three times larger than R31. The lineshape of N11 is symmetric along both o1 and o3 axes, while that of R31 is elongated along o1 axis. (c,d) The simulated spectra at o2 705 cm 1 with N11 and
R31. (e) The FT amplitude map at o2 46220 cm 1 reveals coherent
interaction of bands 2 and 3 with the quasi-resonant vibrational mode with frequency n2E470 cm 1. However, as depicted in (f) the associated nonrephasing peak N22 at o1,3E16,670 cm 1 is weak and only amounts to 5%
of N11 at o2 70520 cm 1 (see a). The diagonal peak at
o1,3E16,400 cm 1 in e stems from N11, with a peak centred at o2
70520 cm 1, but broad enough to appear at o2 46220 cm 1.
All measurements were carried out at room temperature.
NATURE COMMUNICATIONS | 6:7755 | DOI: 10.1038/ncomms8755 | http://www.nature.com/naturecommunications
Web End =www.nature.com/naturecommunications 3
& 2015 Macmillan Publishers Limited. All rights reserved.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8755
a
Turning to the o2 slice corresponding to the energy splitting between bands 2 and 3 (o2 46220 cm 1), Fig. 2e,f
reveal a diagonal non-rephasing peak N22, which is centred at (o1, o3) (O2, O2) with the exciton energy O2E16,672 cm 1 of
band 2 and a symmetric linewidth 2Gg2E225 cm 1 along o1 and o3 axes. The amplitude of N22 is only 5% of N11.
Theoretical model. To describe the long-lived oscillations in N11 and R31, a vibronic model is employed that describes the coupling of bands 1 and 3 to a quasi-resonant vibrational mode with frequency n1. Consider a system with electronic ground state |gki and excited states for bands 1 and 3, denoted by |1ki and
|3ki, respectively, where k 0 and 1 denote the vibrational
ground and excited states, respectively (Fig. 3a). The vibronic coupling between the quasi-resonant states |30i and |11i leads
to unnormalized vibronic eigenstates ~30
30
30
[afii9840]1
30 11
10
[afii9829][afii9853]
[afii9829][afii9853]
[afii9840]1
11
3 1
g1
g0
[afii9840]1
h j E 11
h j and
h
~11 j 11
h j E 30
h j. Here E represents the degree of vibronic
mixing dened by
E in1
S1
b
2
N11 Theory N11 Experiment
R31 Theory R31 Experiment
p iDn1 G13 1; 1
where Dn1 (O3 O1) n1 denotes the detuning between |30i
and |11i, that is, between the exciton energy splitting and
vibrational frequency, and S1 denotes the HuangRhys factor of the vibrational mode, which in turn quanties the strength of the vibronic coupling (see Supplementary Note 2 for details of the derivation). The electronic decoherence rate Ggk describes the exponential decay rate of the coherence between electronic ground state and band k, while G13 represents the overall exponential decay rate of the inter-exciton coherence between bands 1 and 3. In our model, we do not consider inhomogeneous broadening, which is justied by the observation that the experimentally measured absorption spectrum is well matched to a sum of Lorentzian functions with the linewidths 2Ggk (see
Supplementary Note 2). This is valid when homogeneous broadening dominates the linewidths and the HuangRhys factors are sufciently small, as is the case here. In addition, the lineshape of N11 (Fig. 2a) is not elongated along the diagonal o1
o3, implying our 2D signal is dominated by homogeneous
broadening. The same conclusion is reached from analysing 2D
correlation spectra33.
In nonlinear spectroscopy, the molecular response to laser excitation is described by response functions42. According to the vibronic model described above, the response function for the oscillatory signals in N11 reads
RN11
0
Norm. int. (a.u.)
2
c
1
1
0
0
200 600
400 800 Waiting time t2 (fs)
Figure 3 | Vibronic model. (a) We consider a vibronic model for bands 1 and 3 coupled to a vibrational mode with frequency n1E668 cm 1 (see
Supplementary Note 2). The vibronic states |k0i and |k1i denote the
vibrational ground and rst excited states of an electronic state |ki,
respectively, with the single index states |gi, |1i and |3i denoting the
electronic ground state and bands 1 and 3, respectively. The exciton energy splitting DO31 O3 O1 between bands 1 and 3 is quasi-resonant with the
vibrational frequency n1, where the detuning is denoted by Dn1 DO31 n1.
The excitonvibrational coupling between uncoupled states |30i and |11i
leads to vibronic eigenstates ~
30
and ~11
,
each of which is a superposition of |30i and |11i, leading to an energy-level shifting by do. (b) The time trace
of N11 in normalized intensity (Norm. Int.) against waiting time t2, where the experimental results are shown as light red circles and the theoretical simulation is shown as a full red line. (c) The time trace of R31 where the experimental results are shown as light blue circles and the simulated data are depicted as a full blue line. The root mean squared deviation between the experimental results and theoretical simulation in b and c is 0.92 and0.59, respectively.
; 2
with m1 and m3 denoting the transition dipole moment of bands 1 and 3, respectively. The prefactor Gg1 2 stems from the lineshape of N11, gv denotes the dissipation rate of the vibrations and do stands for the frequency shift of the vibronic eigenstates30 j and
11 j relative to the uncoupled states h30| and h11| due to the
vibronic coupling (see Fig. 3a and Supplementary Note 2 for further details). The coupling was found to be sufciently strong to induce non-negligible vibronic mixing E
j j2 0:03,
which leads to a long-lived beating signal in N11 up to t2E800 fs, as shown in Fig. 3b. These results imply that the initial excitonic part of 10
j i30 j decays rapidly with 1/e decay time of G13 1E66 fs,
while the vibronic coherence 10
j ih
~11 j explains a long-lived
oscillatory signal in N11: here 10
m21m23G 2g1 e i DO31 do G13 t2 e i n1 do gv t2E2
The response function for the oscillatory contributions to R31 is given by
RR31 m21m23G 1g3G 1g1
e i DO31 do G13 t2 e i n1 do g
3
where G 1g3G 1g1 derives from the asymmetric lineshape of R31 (see Fig. 2b,d). Here Ze and Zg represent the contribution of excited-state vibronic coherence 10
j i
~11
v
;
represents
coherence between two vibronic states |10i and ~30
(|10i and
j i ~30
10
j i ~11
and ground-state vibrational coherence |g0ihg1|, respectively, to the long-lived
beating signal in R31 (see Supplementary Note 2). The vibrational coherence in the electronic ground-state manifold does not play a role in exciton transfer dynamics, but nonetheless modulates the
~11
),
respectively.
4 NATURE COMMUNICATIONS | 6:7755 | DOI: 10.1038/ncomms8755 | http://www.nature.com/naturecommunications
Web End =www.nature.com/naturecommunications
& 2015 Macmillan Publishers Limited. All rights reserved.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8755 ARTICLE
2D spectra. A t of model parameters to experimental results (Fig. 3c) shows that |Ze|E2.5|Zg|. This means the long-lived beating signal in R31 is dominated by the excited-state coherence 10
j ih
~11 j. The short-lived beating signal in R31 is induced
by 10
j ih
~30 j, as is the case for N11. We note that the signal at
N11, with approximately three times the amplitude of R31, is exclusively determined by excited-state contributions. Details of this vibronic model and the corresponding Feynman diagrams for the spectral components N11 and R31 are discussed in the Supplementary Note 2.
These results demonstrate how an excitonic system within a noisy environment can exhibit long-lasting coherent features: the observed long-lived oscillations are the result of coherent interaction of excitonic bands with an underdamped, quasi-resonant vibration. This vibronic mechanism requires the vibrational dissipation rate gv to be much slower than the electronic decoherence rate G13, which is the case for C8O3, where gvt 1 ps
1 and G13E(66 fs) 1. The difference in
electronic and vibrational decoherence rates can be rationalized from the fact that excitons and vibrations are related to the motion of electrons and nuclei, respectively. The lower mass of electrons as compared with nuclei makes excitons more mobile and therefore more sensitive to environmental uctuations, such as local electric elds, than vibrations. We note that the vibronic mixing leading to long-lived beating signals in 2D electronic spectra is described by a vibronic coupling that induces coherent energy exchange between excitons and quasi-resonant vibrations (see Supplementary Note 2 for further details):
He v n1
S1
p 30
j i 11
h j 11
j i 30
h j
: 4 This implies that the vibronic coupling not only induces long-lasting electronic excited-state coherences but also can mediate population transfer between excitonic bands. In a combination with thermal relaxation of exciton populations, the vibronic coupling may further enhance exciton population transfer and as a result could, in principle, have functional relevance in exciton transport14,38,4345.
Interestingly, the different decoherence rates Gg3E2Gg1 of
bands 1 and 3 lead to different amplitudes of the short-lived beating signals in N11 and R31 (Fig. 3b,c), which are determined by the prefactors G 2g1 and G 1g3G 1g1, respectively. The lower decoherence rate of band 1 can be explained by band 1 being localized on the inner layer, while band 3 is delocalized over both the inner and outer layers46. As shown by the response functions for N11 and R31, the overall strength of the beating signals is proportional to the inverse of the electronic decoherence rates. It is therefore expected that the beating signal amplitude would diminish with an increase of the decoherence rate. This is the case for N22, where the physical situation in terms of exciton vibrational resonance (DO32En2E470 cm 1) is equivalent to
N11 (DO31En1E668 cm 1). The crucial difference is that band 2 has a higher decoherence rate than band 1, as band 2 is localized on the outer layer exposed to solvent46. This explains the broader linewidth of band 2 in absorption and 2D spectra. Using an estimated value of Gg2E(47 fs) 1, the presented theory predicts the strength of N22 to be 5% of N11 (see Supplementary Note 2), which is in line with the experimental observations (Fig. 2f). These results indicate that the experimentally observed long-lived beating signals, induced by vibronic mixing, require adequately low electronic decoherence rates, highlighting that resonance between exciton energy splitting and vibrational frequency alone is not sufcient47.
The presented vibronic model achieves quantitative agreement with the experimental observations. Crucially, the constraints imposed by the observed asymmetric decoherence rates Gg3E2Gg1 and fast relaxation of exciton population in C8O3
on sub-picosecond timescales33 rule out incoherent models, where long-lived oscillations are sustained by Markovian correlated uctuations (see Supplementary Note 3 for a detailed analysis). This further supports our conclusion that the observed experimental data provide evidence for vibronic mixing being the mechanism at play in our system.
We note that our results do not imply that correlated uctuations can be universally ruled out, as this mechanism could be in place in certain pigmentprotein complexes. The notion of correlated uctuations has been developed for photosynthetic complexes where pigments are embedded in a protein scaffold. The protein has been considered as the potential source of correlated uctuations in natural light harvesters16,17. For C8O3, a structural frame such as a protein scaffold is absent and therefore correlated uctuations are unlikely to induce long-lived oscillatory 2D signals, which is in line with our observations.
DiscussionWe have veried, theoretically and experimentally, that coherent vibronic coupling in the electronic excited-state manifold is responsible for the long-lived beating signals observed in 2D spectra of an articial light harvester. The relatively simple electronic and vibrational structure of the investigated molecular aggregate along with its macroscopic alignment allowed us to rule out the presence of correlated uctuations. The specic geometry of our system allowed us to gain further insights by illustrating the conditions under which intra-pigment vibrations can prolong electronic coherent effects. The moderately low decoherence rate of band 1, localized on the inner layer and protected from solvent, is the basis for excitonvibrational coupling as the source of long-lived beating signals. The outer band 2, even though resonantly coupled to a vibration, exhibits a higher decoherence rate and therefore fails to produce observable oscillations. We conclude that the mere resonance between excitons and vibrations does not sufce to explain long-lived beating signals. An adequately low electronic decoherence rate, determined by the interaction between system and bath, is an equally important prerequisite.
The inuence of vibronic coupling on energy transport in molecular aggregates has been extensively studied in the past, as recently reviewed44. The vibronic coupling has recently gained new interest (see ref. 48 for a recent tutorial overview), as it was suggested as a feasible mechanism to explain long-lived oscillations in the 2D spectra of several natural light-harvesting complexes and a photosynthetic reaction centre9,10. The requirement of excitonvibrational resonance is readily satised in such systems, given their numerous excitonic bands and rich vibrational structures. Incoherent models based on correlated uctuations were not ruled out though. Our work provides a quantum mechanical foundation for enhanced energy transfer based on vibronic coupling. As recently demonstrated, this mechanism is not limited to natural light harvesting, vibronic coupling is also of key importance in photovoltaic devices49.
Methods
Polarization-controlled 2D electronic spectroscopy. In 2D electronic spectroscopy, three ultrashort laser pulses generate an optical response of a molecular ensemble, which is spectrally resolved along both absorption (o1) and detection (o3) frequencies within the laser pulse spectrum. The absorption frequency o1 is obtained by precise scanning of the time delay between the rst two pulses and subsequent Fourier transformation (t1-o1). In detection, the signal is spectrally dispersed, leading directly to the detection frequency o3. Varying time delay t2 between pulses 2 and 3 provides information about evolution of the system on a femtosecond timescale5052. To retrieve the purely absorptive part, the signal induced by pulses 13 is detected in a heterodyned fashion by interfering it with a phase-stable local oscillator pulse. Polarization control is achieved by the combination of l/4 wave plates and wire grid polarizers for each of the laser beams to select the desired polarization with high accuracy. Polarization-resolved 2D experiments change the relative contributions of distinct pathways depending on
NATURE COMMUNICATIONS | 6:7755 | DOI: 10.1038/ncomms8755 | http://www.nature.com/naturecommunications
Web End =www.nature.com/naturecommunications 5
& 2015 Macmillan Publishers Limited. All rights reserved.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8755
the polarization of the laser pulses, orientation of the transition dipole moments and isotropy of the sample40. Rephasing spectra were acquired with a polarization sequence of (90, 0, 90, 0) for pulses (1, 2, 3, local oscillator), in contrast to nonrephasing spectra, where the time ordering of the rst two pulses is reversed, leading to a polarization sequence of (0, 90, 90, 0). The polarization scheme used for rephasing spectra (Fig. 1d) shows 0 was dened to be parallel to the sample ow direction, depicted as a white arrow in Fig. 1a. For a macroscopically aligned sample, this particular polarization sequence selects pathways stemming from interband coherences and vibronic mixing12,15, discussed throughout the paper, while pathways with all-parallel transition dipole moments such as ground-state bleach, stimulated emission, excited-state absorption and also vibrational wave packet excitation are suppressed. For the details regarding the experimental methods, see Supplementary Note 1. To subtract the non-oscillatory signals from 2D spectra, we employed a decay-associated spectra analysis33, where the population decays were tted by a sum of three 2D spectra with individual decay constants. The o2 maps in Fig. 2 were obtained using Fourier transformation (t2-o2) with zero-padding up to 27 data points. All measurements were carried out at room temperature.
References
1. van Amerongen, H., Valkunas, L. & van Grondelle, R. Photosynthetic Excitons (World Scientic, 2000).
2. Blankenship, R. E. Molecular Mechanisms of Photosynthesis (Blackwell Science, 2002).
3. Renger, T., May, V. & Khn, O. Ultrafast excitation energy transfer dynamics in photosynthetic pigment-protein complexes. Phys. Rep. 343, 137254 (2001).
4. Huelga, S. F. & Plenio, M. B. Vibrations, quanta and biology. Contemp. Phys.
54, 181207 (2013).
5. Jonas, D. M. Two-dimensional femtosecond spectroscopy. Annu. Rev. Phys. Chem. 54, 425463 (2003).
6. Engel, G. S. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782786 (2007).
7. Dostl, J., Manal, T., Vcha, F., Penk, J. & Zigmantas, D. Unraveling the nature of coherent beatings in chlorosomes. J. Chem. Phys. 140, 115103 (2014).
8. Collini, E. et al. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644647 (2010).
9. Romero, E. et al. Quantum coherence in photosynthesis for efcient solar-energy conversion. Nat. Phys. 10, 676682 (2014).
10. Fuller, F. D. et al. Vibronic coherence in oxygenic photosynthesis. Nat. Chem. 6, 706711 (2014).
11. Chin, A. W. et al. The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes. Nat. Phys. 9, 113118 (2013).
12. Plenio, M. B., Almeida, J. & Huelga, S. F. Origin of long-lived oscillations in 2D-spectra of a quantum vibronic model: electronic versus vibrational coherence. J. Chem. Phys. 139, 235102 (2013).
13. Chin, A. W., Huelga, S. F. & Plenio, M. B. Coherence and decoherence in biological system: principles of noise assisted transport and the origin of long-lived coherences. Phil. Trans. R. Soc. A 370, 36383657 (2012).
14. Kolli, A., OReilly, E. J., Scholes, G. D. & Olaya-Castro, A. The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae.J. Chem. Phys. 137, 174109 (2012).15. Tiwari, V., Peters, W. K. & Jonas, D. M. Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework. Proc. Natl Acad. Sci. USA 110, 12031208 (2013).
16. Lee, H., Cheng, Y.-C. & Fleming, G. R. Coherence dynamics in photosynthesis: protein protection of excitonic coherence. Science 316, 14621465 (2007).17. Ishizaki, A., Calhoun, T. R., Schlau-Cohen, G. S. & Fleming, G. R. Quantum coherence and its interplay with protein environments in photosynthetic electronic energy transfer. Phys. Chem. Chem. Phys. 12, 73197337 (2010).
18. Hayes, D., Grifn, G. B. & Engel, G. S. Engineering coherence among excited states in synthetic heterodimer systems. Science 340, 14311434 (2013).
19. Christensson, N. et al. High frequency vibrational modulations in two-dimensional electronic spectra and their resemblance to electronic coherence signatures. J. Phys. Chem. B 115, 53835391 (2011).
20. Caycedo-Soler, F., Chin, A. W., Almeida, J., Huelga, S. F. & Plenio, M. B. The nature of the low energy band of the Fenna-Matthews-Olson complex: vibronic signatures. J. Chem. Phys. 136, 155102 (2012).
21. Christensson, N., Kauffmann, H. F., Pullerits, T. & Manal, T. Origin of long-lived coherences in light-harvesting complexes. J. Phys. Chem. B 116, 74497454 (2012).
22. Heijs, D.-J., Dijkstra, A. G. & Knoester, J. Ultrafast pump-probe spectroscopy of linear molecular aggregates: effects of exciton coherence and thermal dephasing. Chem. Phys. 341, 230239 (2007).
23. Wrthner, F., Kaiser, T. E. & Saha-Mller, C. R. J-aggregates: from serendipitous discovery to supramolecular engineering of functional dye materials. Angew. Chem. Int. Ed. 50, 33763410 (2011).
24. Eisele, D. M. et al. Robust excitons inhabit soft supramolecular nanotubes. Proc. Natl Acad. Sci. USA 111, E3367E3375 (2014).
25. Yuen-Zhou, J. et al. Coherent exciton dynamics in supramolecular light-harvesting nanotubes revealed by ultrafast quantum process tomography. ACS Nano 8, 55275534 (2014).
26. Qiao, Y. et al. Nanotubular J-aggregates and quantum dots coupled for efcient resonance excitation energy transfer. ACS Nano 9, 15521560 (2015).
27. von Berlepsch, H. & Bttcher, C. in J-Aggregates Vol. 2 (ed. Kobayashi, T.) Ch. 4 119153 (World Scientic, 2012).
28. von Berlepsch, H., Kirstein, S. & Bttcher, C. Effect of alcohols on J-aggregation of a carbocyanine dye. Langmuir 18, 76997705 (2002).
29. von Berlepsch, H., Kirstein, S. & Bttcher, C. Controlling the helicity of tubular J-aggregates by chiral alcohols. J. Phys. Chem. B 107, 96469654 (2003).
30. von Berlepsch, H. et al. Supramolecular structures of J-aggregates of carbocyanine dyes in solution. J. Phys. Chem. B 104, 52555262 (2000).
31. von Berlepsch, H. et al. Stabilization of individual tubular J-aggregates by poly(vinyl alcohol). J. Phys. Chem. B 107, 1417614184 (2003).
32. Eisele, D. M. et al. Utilizing redox-chemistry to elucidate the nature of exciton transitions in supramolecular dye nanotubes. Nat. Chem. 4, 655662 (2012).
33. Milota, F. et al. Vibronic and vibrational coherences in two-dimensional electronic spectra of supramolecular J-aggregates. J. Phys. Chem. A 117, 60076014 (2013).
34. Aydin, M., Dede,. & Akins, D. L. Density functional theory and Raman spectroscopy applied to structure and vibrational mode analysis of 1,1,3,3-tetraethyl-5,5,6,6-tetrachloro-benzimidazolocarbocyanine iodide and its aggregate. J. Chem. Phys. 134, 064325 (2011).
35. Rich, C. C. & McHale, J. L. Resonance Raman spectra of individual excitonically coupled chromophore aggregates. J. Phys. Chem. C 117, 1085610865 (2013).
36. Butkus, V., Zigmantas, D., Abramavicius, D. & Valkunas, L. Distinctive character of electronic and vibrational coherences in disordered molecular aggregates. Chem. Phys. Lett. 587, 9398 (2013).
37. Womick, J. M. & Moran, A. M. Exciton coherence and energy transport in the light-harvesting dimers of allophycocyanin. J. Phys. Chem. B 113, 1574715759 (2009).
38. Womick, J. M. & Moran, A. M. Vibronic enhancement of exciton sizes and energy transport in photosynthetic complexes. J. Phys. Chem. B 115, 13471356 (2011).
39. Del Rey, M., Chin, A. W., Huelga, S. F. & Plenio, M. B. Exploiting structured environments for efcient energy transfer: the phonon antenna mechanism.J. Phys. Chem. Lett. 4, 903907 (2013).40. Hochstrasser, R. M. Two-dimensional IR-spectroscopy: polarization anisotropy effects. Chem. Phys. 266, 273284 (2001).
41. Read, E. L. et al. Cross-peak-specic two-dimensional electronic spectroscopy. Proc. Natl Acad. Sci.USA 104, 1420314208 (2007).
42. Mukamel, S. Principles of Nonlinear Optical Spectroscopy (Oxford University Press, 1995).
43. Perlk, V. et al. Vibronic coupling explains the ultrafast carotenoid-tobacteriochlorophyll energy transfer in natural and articial light harvesters.J. Chem. Phys. 142, 212434 (2015).44. Schrter, M. et al. Exciton-vibrational coupling in the dynamics and spectroscopy of Frenkel excitons in molecular aggregates. Phys. Rep. 567, 178 (2015).
45. Killoran, N., Huelga, S. F. & Plenio, M. B. Enhancing light-harvesting power with coherent vibrational interactions: a quantum heat engine picture. Preprint at http://arxiv.org/abs/1412.4136
Web End =http://arxiv.org/abs/1412.4136 (2015).
46. Didraga, C. et al. Structure, spectroscopy, and microscopic model of tubular carbocyanine dye aggregates. J. Phys. Chem. B 108, 1497614985 (2004).
47. Halpin, A. et al. Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences. Nat. Chem. 6, 196201 (2014).
48. Chenu, A. & Scholes, G. D. Coherence in energy transfer and photosynthesis. Annu. Rev. Phys. Chem. 66, 6996 (2015).
49. Falke, S. M. et al. Coherent ultrafast charge transfer in an organic photovoltaic blend. Science 344, 10011005 (2014).
50. Brixner, T., Manal, T., Stiopkin, I. V. & Fleming, G. R. Phase-stabilized two-dimensional electronic spectroscopy. J. Chem. Phys. 121, 42214236 (2004).
51. Augulis, R. & Zigmantas, D. Two-dimensional electronic spectroscopy with double modulation lock-in detection: enhancement of sensitivity and noise resistance. Opt. Express 19, 1312613133 (2011).
52. Augulis, R. & Zigmantas, D. Detector and dispersive delay calibration issues in broadband 2D electronic spectroscopy. J. Opt. Soc. Am. B 30, 17701774 (2013).
Acknowledgements
We thank Valentyn I. Prokhorenko for help in 2D-DAS analysis. C.N.L. and J.H. acknowledge funding by the Austrian Science Fund (FWF): START project Y 631-N27 and by COST Action CM1202PERSPECT-H2O. J.L., F.C.-S., S.F.H. and M.B.P. acknowledge funding by the EU STREP PAPETS and QUCHIP, the ERC Synergy Grant BioQ, the Deutsche Forschungsgemeinschaft (DFG) within the SFB/TRR21 and an
6 NATURE COMMUNICATIONS | 6:7755 | DOI: 10.1038/ncomms8755 | http://www.nature.com/naturecommunications
Web End =www.nature.com/naturecommunications
& 2015 Macmillan Publishers Limited. All rights reserved.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8755 ARTICLE
Alexander von Humboldt Professorship. J.P. acknowledges funding by the Spanish Ministerio de Economa y Competitividad under Project No. FIS2012-30625. D.P. and D.Z. acknowledge funding by the Swedish Research Council and Knut and Alice Wallenberg Foundation.
Author contributions
D.P., D.Z. and J.H. designed and conducted experiments; H.v.B. was responsible for sample preparation, structural characterization and Raman measurements; J.L., F.C.-S., C.N.L., D.P., J.P. and J.H. analysed the data; J.L., F.C.-S., S.F.H., J.H. and M.B.P. developed theory; all authors discussed the results and wrote the manuscript.
Additional information
Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications
Web End =http://www.nature.com/ http://www.nature.com/naturecommunications
Web End =naturecommunications
Competing nancial interests: The authors declare no competing nancial interests.
Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/
Web End =http://npg.nature.com/ http://npg.nature.com/reprintsandpermissions/
Web End =reprintsandpermissions/
How to cite this article: Lim, J. et al. Vibronic origin of long-lived coherence in an articial molecular light harvester. Nat. Commun. 6:7755 doi: 10.1038/ncomms8755 (2015).
This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the articles Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
Web End =http://creativecommons.org/licenses/by/4.0/
NATURE COMMUNICATIONS | 6:7755 | DOI: 10.1038/ncomms8755 | http://www.nature.com/naturecommunications
Web End =www.nature.com/naturecommunications 7
& 2015 Macmillan Publishers Limited. All rights reserved.
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer
Copyright Nature Publishing Group Jul 2015
Abstract
Natural and artificial light-harvesting processes have recently gained new interest. Signatures of long-lasting coherence in spectroscopic signals of biological systems have been repeatedly observed, albeit their origin is a matter of ongoing debate, as it is unclear how the loss of coherence due to interaction with the noisy environments in such systems is averted. Here we report experimental and theoretical verification of coherent exciton-vibrational (vibronic) coupling as the origin of long-lasting coherence in an artificial light harvester, a molecular J-aggregate. In this macroscopically aligned tubular system, polarization-controlled 2D spectroscopy delivers an uncongested and specific optical response as an ideal foundation for an in-depth theoretical description. We derive analytical expressions that show under which general conditions vibronic coupling leads to prolonged excited-state coherence.
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer