On the mechanism of weak-field coherent control of retinal isomerization in bacteriorhodopsin

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Comparative Femtosecond Spectroscopy of Primary Photoreactions of Exiguobacterium sibiricum Rhodopsin and Halobacterium salinarum Bacteriorhodopsin

The primary stages of the Exiguobacterium sibiricum rhodopsin (ESR) photocycle were investigated by femtosecond absorption laser spectroscopy in the spectral range of 400-900 nm with a time resolution of 25 fs. The dynamics of the ESR photoreaction were compared with the reactions of bacteriorhodopsin (bR) in purple membranes (bR_PM) and in recombinant form (bR_rec). The primary intermediates of the ESR photocycle were similar to intermediates I, J, and K in bacteriorhodopsin photoconversion. The CONTIN program was applied to analyze the characteristic times of the observed processes and to clarify the reaction scheme. A similar photoreaction pattern was observed for all studied retinal proteins, including two consecutive dynamic Stokes shift phases lasting ∼0.05 and ∼0.15 ps. The excited state decays through a femtosecond reactive pathway, leading to retinal isomerization and formation of product J, and a picosecond nonreactive pathway that leads only to the initial state. Retinal photoisomerization in ESR takes 0.69 ps, compared with 0.48 ps in bR_PM and 0.74 ps in bR_rec. The nonreactive excited state decay takes 5 ps in ESR and ∼3 ps in bR. We discuss the similarity of the primary reactions of ESR and other retinal proteins.

Coherent control of an opsin in living brain tissue

Retinal-based opsins are light-sensitive proteins. The photoisomerization reaction of these proteins has been studied outside cellular environments using ultrashort tailored light pulses^1-5. However, how living cell functions can be modulated via opsins by modifying fundamental nonlinear optical properties of light interacting with the retinal chromophore has remained largely unexplored. We report the use of chirped ultrashort near-infrared pulses to modulate light-evoked ionic current from Channelrhodopsin-2 (ChR2) in brain tissue, and consequently the firing pattern of neurons, by manipulating the phase of the spectral components of the light. These results confirm that quantum coherence of the retinal-based protein system, even in a living neuron, can influence its current output, and open up the possibilities of using designer-tailored pulses for controlling molecular dynamics of opsins in living tissue to selectively enhance or suppress neuronal function for adaptive feedback-loop applications in the future.

Interfering resonance as an underlying mechanism in the adaptive feedback control of radiationless transitions: Retinal isomerization

Control of molecular processes via adaptive feedback often yields highly structured laser pulses that have eluded physical explanation. By contrast, coherent control approaches propose physically transparent mechanisms but are not readily visible in experimental results. Here, an analysis of a condensed phase adaptive feedback control experiment on retinal isomerization shows that it manifests a quantum interference based coherent control mechanism: control via interfering resonances. The result promises deep insight into the physical basis for the adaptive feedback control of a broad class of bound state processes.

Communication: Analytical optimal pulse shapes obtained with the aid of genetic algorithms: Controlling the photoisomerization yield of retinal

We recently proposed a Quantum Optimal Control (QOC) method constrained to build pulses from analytical pulse shapes [R. D. Guerrero et al., J. Chem. Phys. 143(12), 124108 (2015)]. This approach was applied to control the dissociation channel yields of the diatomic molecule KH, considering three potential energy curves and one degree of freedom. In this work, we utilized this methodology to study the strong field control of the cis-trans photoisomerization of 11-cis retinal. This more complex system was modeled with a Hamiltonian comprising two potential energy surfaces and two degrees of freedom. The resulting optimal pulse, made of 6 linearly chirped pulses, was capable of controlling the population of the trans isomer on the ground electronic surface for nearly 200 fs. The simplicity of the pulse generated with our QOC approach offers two clear advantages: a direct analysis of the sequence of events occurring during the driven dynamics, and its reproducibility in the laboratory with current laser technologies.

Shaped and Feedback-Controlled Excitation of Single Molecules in the Weak-Field Limit

Coherent control uses tailored femtosecond pulse shapes to influence quantum pathways and drive a light-induced process toward a specific outcome. There has been a long-standing debate whether the absorption properties or the probability for population to remain in an excited state of a molecule can be influenced by the pulse shape, even if only a single photon is absorbed. Most such experiments are performed on many molecules simultaneously, so that ensemble averaging reduces the access to quantum effects. Here, we demonstrate systematic coherent control experiments on the fluorescence intensity of a single molecule in the weak-field limit. We demonstrate that a delay scan of interfering pulses reproduces the excitation spectrum of the molecule upon Fourier transformation, but that the spectral phase of a pulse sequence does not affect the transition probability. We generalize this result to arbitrary pulse shapes by performing the first closed-loop coherent control experiments on a single molecule.

Coherent Control of Photofragment Distributions Using Laser Phase Modulation in the Weak-Field Limit

The possibility of quantum interference control of the final state distributions of photodissociation fragments by means of pure phase modulation of the pump laser pulse in the weak-field regime is demonstrated theoretically for the first time. The specific application involves realistic wave packet calculations of the transient vibrational populations of the Br2(B, v(f)) fragment produced upon predissociation of the Ne-Br2(B) complex, which is excited to a superposition of resonance states using pulses with different linear chirps. Transient phase effects on the fragment populations are found to persist for long times (about 200 ps) after the pulse is over due to interference between overlapping resonances in Ne-Br2(B).

Pulse-train control of photofragmentation at constant field energy

We consider a phaselocked two-pulse sequence applied to photofragmentation in the weak-field limit. The two pulses are not overlapping in time, i.e., the energy of the pulse-train is constant for all time delays. It is shown that the relative yield of excited Br (*) in the nonadiabatic process: I + Br* ← IBr → I + Br, changes as a function of time delay when the two excited wave packets interfere. The underlying mechanisms are analyzed and the change in the branching ratio as a function of time delay is only a reflection of a changing frequency distribution of the pulse train; the branching ratio does not depend on the detailed pulse shape.

The photocycle and ultrafast vibrational dynamics of bacteriorhodopsin in lipid nanodiscs

The photocycle and vibrational dynamics of bacteriorhodopsin in a lipid nanodisc microenvironment have been studied by steady-state and time-resolved spectroscopies. Linear absorption and circular dichroism indicate that the nanodiscs do not perturb the structure of the retinal binding pocket, while transient absorption and flash photolysis measurements show that the photocycle which underlies proton pumping is unchanged from that in the native purple membranes. Vibrational dynamics during the initial photointermediate formation are subsequently studied by ultrafast broadband transient absorption spectroscopy, where the low scattering afforded by the lipid nanodisc microenvironment allows for unambiguous assignment of ground and excited state nuclear dynamics through Fourier filtering of frequency regions of interest and subsequent time domain analysis of the retrieved vibrational dynamics. Canonical ground state oscillations corresponding to high frequency ethylenic and C-C stretches, methyl rocks, and hydrogen out-of-plane wags are retrieved, while large amplitude, short dephasing time vibrations are recovered predominantly in the frequency region associated with out-of-plane dynamics and low frequency torsional modes implicated in isomerization.

Solvation Stokes-Shift Dynamics Studied by Chirped Femtosecond Laser Pulses

The early optical dynamic response, resulting population, and electronic coherence are investigated experimentally and modeled theoretically for IR144 in solution. The fluorescence and stimulated emission response are studied systematically as a function of chirp. The magnitude of the chirp effect on fluorescence and stimulated emission is found to depend quadratically on pulse energy, even where excitation probabilities range from 0.02 to 5%, in the so-called "linear excitation regime". Interestingly, the shape of the chirp dependence on fluorescence and stimulated emission is found to be independent of pulse energy. The chirp dependence reveals dynamics related to solvent rearrangement following excitation and also depends on electronic relaxation of the chromophore. The experimental results are successfully simulated using a four-level model in the presence of inhomogeneous broadening of the electronic transitions.

Exploring the role of phase modulation on photoluminescence yield

We report an investigation to elucidate the mechanisms of control in phase-sensitive experiments in two molecular systems. A first inspection of optimization procedures yields the same experimental result: increase in the emission efficiency upon excitation by a phase modulated pulse in a two-photon transition. More detailed studies, which include power dependence, spectral response, one and two color pump-probe and pump-pump experiments show that while for one chromophore phase modulation leads to spectral matching between the two-photon cross section and the second order power spectrum for the other it provides a tool to manipulate the wavepacket dynamics in the excited state.

Quantum control experiment reveals solvation-induced decoherence

Coherent control holds the promise of becoming a powerful spectroscopic tool for the study of complex molecular systems. Achieving control requires coherence in the quantum system under study. In the condensed phase, coherence is typically lost rapidly because of fluctuating interactions between the solvated molecule and its surrounding environment. We investigate the degree of attainable control on a dye molecule when the fluctuations of its environment are systematically varied. A single successful learning curve for optimizing stimulated emission from the dye in solution is reapplied for a range of solvents with varying viscosity, revealing a striking trend that is correlated directly with the dephasing time. Our results provide clear evidence that the environment limits the leverage of control on the molecular system. This insight can be used to enhance the yield of control experiments greatly.