Effect of Pulse Shaping on Observing Coherent Energy Transfer in

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The Effect of Pulse Shaping on Observing Coherent Energy Transfer in Single Light Harvesting Complexes Kai Song, Shuming Bai, and Qiang Shi J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b07025 • Publication Date (Web): 17 Oct 2016 Downloaded from http://pubs.acs.org on October 26, 2016

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The Journal of Physical Chemistry

The Effect of Pulse Shaping on Observing Coherent Energy Transfer in Single Light Harvesting Complexes Kai Song, Shuming Bai, and Qiang Shi∗ Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China, and University of Chinese Academy of Sciences, Beijing 100049, China E-mail: [email protected]

∗

To whom correspondence should be addressed

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Abstract Recent experimental and theoretical studies have revealed that quantum coherence plays an important role in the excitation energy transfer in photosynthetic light harvesting complexes. Inspired by the recent single molecule two-color double-pump experiment, we investigate theoretically the effect of pulse shaping on observing coherent energy transfer in the single bacterial light harvesting 2 (LH2) complex. It is found that, quantum coherent energy transfer can be observed when the time delay and phase difference between the two laser pulses are controlled independently. However, when the two-color pulses are generated using the the pulse shaping method, how the laser pulses are prepared is crucial to the observation of quantum coherent energy transfer in single photosynthetic complexes.


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1

Introduction

Highly efficient excitation energy transfer (EET) between pigment molecules in photosynthetic light harvesting complexes is crucial to achieve the near unity quantum efficiency of initial charge separation, 1,2 and its mechanism at the molecular level has become an important topic of both experimental and theoretical studies over the past decades. 2–6 Especially, recent observations of quantum coherence in the two-dimensional (2D) spectra of photosynthetic complexes 7–9 have raised an important and not yet well understood question regarding the possible role of quantum coherence in biological photosynthesis. The origin of long time coherence observed in the 2D spectra is still an issue of debate. 10–13,13–17 A main reason is due to the fact that, EET dynamics in photosynthetic light harvesting complexes is often influenced by strong static disorder caused by structure inhomogeneities and dynamic disorder due to interactions with the protein environment. As a result, electronic coherence in photosynthetic light harvesting complexes can only survive up to a few hundred femtoseconds (fs), although vibrational coherence can last longer for several picoseconds. However, single molecule spectroscopy, combined with ultrafast technique, is capable to study EET dynamics beyond ensemble averages. A recent important progress in this field is the observation of quantum coherent energy transfer in single bacterial light harvesting 2 (LH2) complex, 18 where a large portion of the static disorder can be removed. The observed quantum beats indicate that quantum coherence can persist over 400 fs at room temperature. The single molecule experiment has also lead to new findings that would otherwise be hidden in ensemble experiments, such as distinct EET pathways in different light harvesting complexes, and their variations caused by sudden change of the local electronic structure. Stimulated by these works, more complex experimental techniques such as the single molecule 2D coherent spectroscopy are also under development. 19 The single molecule experiment in Ref. 18 employed a double-pump scheme, where two laser pulses with time delay Δt and phase difference Δφ interact with the LH2 complex 3 ACS Paragon Plus Environment


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sequentially, and the molecular fluorescence is used as the probe. The wavepacket created by the first laser pulse is subject to dephasing due to couplings to the protein environment. If the dephasing process is not fast enough to destroy the initial phase information, excitation caused by the second laser pulse will interfere with the initially created wavepacket and quantum coherence can be observed in the fluorescence signal. To study specifically the interference between the B850 wavepacket generated by energy transfer from the B800 excited state, and the wavepacket excited to the B850 states directly from the ground state by the second pulse, the pulse shaping method 20 is employed to generate a pair of two-color laser pulses that are resonant with the B800 and B850 transitions, respectively. 18 In the pulse shaping method, Δt and Δφ are no longer independent. But since Δφ changes very rapidly, fluorescence changes with respect to Δt and Δφ can still be monitored. 18 It can thus be expected that, the frequency and time domain relations between the two laser pulses generated by the pulse shaping method will greatly affect the observed quantum beat signal in the single molecule double-pump experiment, which is the main focus of this work. More specifically, simulations of the double-pump process are performed to investigate the effect of pulse shaping on observing quantum coherent EET in single LH2 complex, and to identify the optimal experimental schemes to observe the quantum beat signals. We will show that, although quantum coherence in EET can be observed when Δt and Δφ are controlled independently, the specific pulse shaping scheme is crucial to observe quantum coherences. The remainder of this paper is arranged as follows. The model Hamiltonian and theoretical methods to calculate the EET dynamics are presented in section 2. Simulation results are shown in section 3. Finally, conclusions and discussions are made in section 4.


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2

Theory

2.1

The Frenkel exciton model

To model the single molecule double-pump experiment of the LH2 complex, we employ the following total Hamiltonian that describes a molecular system coupled to an electromagnetic field: H(t) = Hmol − µ · E(t) ,

(1)

where Hmol is the Hamiltonian of the molecular system, E(t) is the electric field, and µ is the dipole operator. For the molecular Hamiltonian, we consider a Frenkel exciton model coupled to a phonon bath: 1,2,6 Hmol = He + Hph + He−ph . Here, the excitonic Hamiltonian He describes the electronic degrees of freedom, which is written as

He =

N

m a†m am +

m=1

N

Jmn (a†m an + a†n am ) ,

(2)

m=1 n 70 fs). Such changes in I(ω) lead to different excited state population with respect to Δt and Δφ as shown in Fig. 3, and thus oscillations in the fluorescence signal. However, in the second scheme to generate the twocolor pulse pairs using the pulse shaping method with the phase ramp, I(ω) does not change since variation of the phase profile does not alter the laser power spectrum. According to Eq. (11), the total excited state population should not be changed as shown in Fig. 5, and no oscillations in the fluorescence signal could be observed. In the third scheme we proposed, both the amplitude and phase profiles are modified as shown in Eqs. (8) and (9). I(ω) is thus modified when varying Δt and Δφ. Quantum beats can thus be observed again, as shown in Figs. 6 and 7.



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4

Conclusions and discussions

In summary, based on the above simulations and analysis, the way how the two-color laser pulse pairs are generated in the single molecule double-pump experiment is very important in observing quantum coherence in EET of the single LH2 complex. More specifically, it is shown that, to observe quantum beats in the fluorescence signal, the laser power spectrum must be altered as a function of Δt and Δφ. We first demonstrated this using two independent Gaussian pulses. It is then shown that, the pulse shaping method that only modifies the phase profile is not an appropriate way to observe quantum coherence, because the laser power spectrum is not altered in this setup when only the phase profile is varied. Finally, it is shown that, when both the amplitude and phase profiles are modulated in the pulse shaping method, quantum beats can be observed again. The simulations also show some discrepancies with the experimental results presented in Ref., 18 especially in the amplitude of quantum beats, which is much smaller than that observed experimentally. We also note that the current simulation and discussions have employed rather simple schemes to generate the two color pulses. More advanced pulse shaping techniques such as the feedback optimized control schemes 40,41 may also be used to further increase the sensitivity in observing the quantum beats in photosynthetic light harvesting complexes. Recently, the pulse shaping method has been applied in 2D spectroscopic studies using the pump-probe configuration and phase cycling methods, 42–44 where the amplitude of the laser spectrum is also modified. It is thus expected that, similar approaches to generate appropriate two-color pulses could be useful for further experimental studies of coherent EET in single photosynthetic light harvesting complexes. As stated in section 1, a significant debate in the field of quantum coherence in photosynthetic complexes is that whether the experimentally observed quantum beats are due to electronic coherence or vibrational coherence. 7–13,13–17 New experimental advances that aim at extending the single molecule techniques to study third order optical responses 19 might help to resolve this problem. 12 ACS Paragon Plus Environment

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Acknowledgement This work is supported by NSFC (Grant No. 21290194), the 973 program (Grant No. 2013CB933501), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB12020300).

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2

1.5

Abs (a.u.)

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Simulation Expt.

1

0.5

0 750

800

λ (nm)

850

900

Figure 1: Absorption spectrum of the LH2 complex. Black (dotted) line corresponds to the experimental result 33 and red (solid) line is the simulated result.



0.025

B800 B850

0.02

Population

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0.015 0.01 0.005 0 0

100

200

300

t (fs) Figure 2: Population dynamics of the B800 and B850 states in the case of two independent laser pulses. The time delay is Δt = 109 fs between the pulse centers, and the phase difference is Δφ = 0.


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0.031 0.0305

Population

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0.03

0.03

0.0295

0.029

0.029 0.028 0

100 200 300 400

0

Δt (fs)

0.5

1

Δφ/π

1.5

2

Figure 3: (a) Total population of the B800 and B850 states as a function of time delay Δt with the phase difference fixed at Δφ = 0. (b) Total population of the B800 and B850 states as a function of phase difference Δφ with the time delay fixed at Δt = 95 fs. Two independent Gaussian laser pulses are used in this simulation.



Amplitude

0.2

Amplitude (a.u.)

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0.1

phase profile

5 0

12000 14000 -1 ω (cm )

0

-0.1 0

1000

500

t (fs) Figure 4: Amplitude of the electric field of the two-color laser pulse pair generated using the pulse-shaping method which only modifies the phase profile, with Δt = 221.5 fs. The inset shows the laser power spectra, and the phase profile used for pulse-shaping. A phase ramp is applied for laser wavelength longer than 820 nm (12195 cm−1 ).


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0.032

0.031

0.03

Population

0.03

Population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Δt=44.3 fs Δt=132.9 fs Δt=221.5 fs

0.02 0.01 0 0

500

1000 t (fs)

1500

0.029

0.028 0

50

100

Δt (fs)

150

200

Figure 5: Total population of the B800 and B850 states as a function of time delay Δt for the laser pulse pair generated using the pulse-shaping method which modulates only the phase profile. The inset shows time evolution of the total population for Δt = 44.3, 132.9, and 221.5 fs.



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Figure 6: Total population of the B800 and B850 states as a function of time delay Δt for the laser pulse pair generated using the pulse-shaping method where both the amplitude and phase profiles are modulated.


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0.025

Population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.024 0.023 0.022 0.021 0

1

0.5

Δ φ/π

1.5

2

Figure 7: Total population of the B800 and B850 states as a function of phase difference Δφ for the laser pulse pair generated using the pulse-shaping method where both the amplitude and phase profiles are modulated. The time delay is Δt = 110.7 fs.



0.0305

Integrated from Eq. (11) HEOM Population

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0.03

0.0295

0.029 0

1

0.5

Δφ/π

1.5

2

Figure 8: Total population of the B800 and B850 states as a function of phase difference Δφ calculated using Eq. (11) and the real time HEOM method. The parameters are the same as those in Fig. 3(b).


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Toc Graphic


Effect of Pulse Shaping on Observing Coherent Energy Transfer in

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