Excited-state Coherence Research Articles

Theoretical model of femtosecond coherence spectroscopy of vibronic excitons in molecular aggregates.

When used as pump pulses in transient absorption spectroscopy measurements, femtosecond laser pulses can produce oscillatory signals known as quantum beats. The quantum beats arise from coherent superpositions of the states of the sample and are best studied in the Fourier domain using Femtosecond Coherence Spectroscopy (FCS), which consists of one-dimensional amplitude and phase plots of a specified oscillation frequency as a function of the detection frequency. Prior works have shown ubiquitous amplitude nodes and π phase shifts in FCS from excited-state vibrational wavepackets in monomer samples. However, the FCS arising from vibronic-exciton states in molecular aggregates have not been studied theoretically. Here, we use a model of vibronic-exciton states in molecular dimers based on displaced harmonic oscillators to simulate FCS for dimers in two important cases. Simulations reveal distinct spectral signatures of excited-state vibronic-exciton coherences in molecular dimers that may be used to distinguish them from monomer vibrational coherences. A salient result is that, for certain relative orientations of the transition dipoles, the key resonance condition between the electronic coupling and the frequency of the vibrational mode may yield strong enhancement of the quantum-beat amplitude and, perhaps, also cause a significant decrease of the oscillation frequency to a value far lower than the vibrational frequency. Future studies using these results will lead to new insights into the excited-state coherences generated in photosynthetic pigment-protein complexes.

Two-dimensional coherent electronic spectrometer with switchable multi-color configurations.

Broadband implementation of two-dimensional electronic spectroscopy (2DES) is a desirable goal for numerous research groups, yet achieving it presents considerable challenges. An effective strategy to mitigate these challenges is the utilization of two-color approaches, effectively broadening the spectral bandwidth accessible with 2DES. Here, we present a simple approach to include multi-color configurations based on adjustable mirror mounts. This enables seamless toggling between single-color, two-color, and transient 2DES within the same spectroscopic apparatus, which is benchmarked on two common laser dyes, Rhodamine 6G and Nile blue. Upon mixing the dyes, single-color 2DES shows overlapping signals, whereas a high selectivity toward Nile blue responses is maintained in two-color and transient 2DES, owing to the fully resonant excitation that is spectrally shifted relative to the detection window. This method is readily implemented in other setups with similar experimental layouts and can be used as a simple solution to overcome existing bandwidth limitations. With the inclusion of transient 2DES, additional insights into excited-state processes can be gained due to its increased sensitivity toward excited-state coherences.

Magnetic field modulation of polaron relaxation coherence effects in III-V semiconductor Gaussian quantum wells

We have theoretically investigated the effects of the cyclotron frequency of magnetic field, the initial depth and the range of the asymmetrical Gaussian confinement potential on the vibrational frequency, ground state energy, excited state energy and coherence time of polaron in III-V semiconductors by using a linear combination operator and unitary transformations methods. Through numerical calculations, we find some interesting phenomena that the polaron decreases the energy level and releases the energy of a phonon to jump. From the point of view of the energy level of the polaron, which is αℏωLO energy lower than that of the electron, and the transition of the polaron to the ground state will have a change in lattice position, and the lattice relaxation phenomenon will appear. The theoretical study of the quantum coherence effect of polaron energy levels will provide guidance for the development of optoelectronic devices and the transmission of quantum information.

Magnetic-field-induced Wigner crystallization of charged interlayer excitons in van der Waals heterostructures

Ever since its inception, coherent excited states of semiconductors have been the focus of semiconductor materials research to evolve into a vibrant field of low-dimensional solid-state physics. The field is gaining new momentum these days due to emerging transdimensional semiconductors such as van der Waals bound layers of transition metal dichalcogenides (TMDs) of controlled thickness. Here, we develop the theory of magnetic-field-induced Wigner crystallization for charged interlayer excitons (CIE) discovered recently in TMD heterobilayers. We derive the ratio of the potential interaction energy to the kinetic energy for the many-particle CIE system in the perpendicular magnetostatic field of an arbitrary strength and predict the crystallization effect in the strong field regime. We show that magnetic-field-induced Wigner crystallization and melting of CIEs can be observed in magneto-photoluminescence experiments with TMD bilayers of systematically varied electron-hole doping concentrations. Our results advance the capabilities of this new generation of transdimensional quantum materials.

Quantum error correction in the noisy intermediate-scale quantum regime for sequential quantum computing

We use density-matrix simulations to study the performance of three distance three quantum error correction (QEC) codes in the context of the rare-earth (RE) ion-doped crystal platform for quantum computing. We analyze pseudothresholds for these codes when parallel operations are not available, and examine the behavior both with and without resting errors. In RE systems, resting errors can be mitigated by extending the system's ground-state coherence time. For the codes we study, we find that if the ground-state coherence time is roughly 100 times larger than the excited-state coherence time, resting errors become small enough to be negligible compared to other error sources. This leads us to the conclusion that beneficial QEC could be achieved in the RE system with the expected gate fidelities available in the noisy intermediate-scale quantum regime. However, for codes using more qubits and operations, a factor of more than 100 would be required. Furthermore, we investigate how often QEC should be performed in a circuit. We find that for early experiments in RE systems, the minimal $[[5,1,3]]$ would be most suitable as it has a high threshold error and uses few qubits. However, when more qubits are available the $[[9,1,3]]$ surface code might be a better option due to its higher circuit performance. Our findings are important for steering experiments to an efficient path for realizing beneficial quantum error correcting codes in early RE systems where resources are limited.

Coherent contributions to population dynamics in a semiconductor microcavity

Multidimensional coherent spectroscopy (MDCS) is used to separate coherent and incoherent nonlinear contributions to the population-time dynamics in a GaAs-based semiconductor microcavity encapsulating a single InGaAs quantum well. In a three-pulse four-wave-mixing scheme, the second delay time is the population time that in MDCS probes excited-state coherences and population dynamics. Nonlinear optical interactions can mix these contributions, which are isolated here for the lower- and upper-exciton polariton through the self- and mutual-interaction features. Results show fast decays and oscillations arising from the coherent response, including a broad stripe along the absorption energy axis, and longer time mutual-interaction features that do not obey a simple population decay model. These results are qualitatively replicated by Bloch equation simulations for the $1s$ exciton strongly coupled to the intracavity field. The simulations allow for separation of coherent and incoherent Pauli-blocking and Coulomb interaction terms within the ${\ensuremath{\chi}}^{(3)}$-limit, and a direct comparison of each feature in one-quantum rephasing and zero-quantum spectra.

Redox conditions correlated with vibronic coupling modulate quantum beats in photosynthetic pigment–protein complexes

Quantum coherences, observed as time-dependent beats in ultrafast spectroscopic experiments, arise when light-matter interactions prepare systems in superpositions of states with differing energy and fixed phase across the ensemble. Such coherences have been observed in photosynthetic systems following ultrafast laser excitation, but what these coherences imply about the underlying energy transfer dynamics remains subject to debate. Recent work showed that redox conditions tune vibronic coupling in the Fenna-Matthews-Olson (FMO) pigment-protein complex in green sulfur bacteria, raising the question of whether redox conditions may also affect the long-lived (>100 fs) quantum coherences observed in this complex. In this work, we perform ultrafast two-dimensional electronic spectroscopy measurements on the FMO complex under both oxidizing and reducing conditions. We observe that many excited-state coherences are exclusively present in reducing conditions and are absent or attenuated in oxidizing conditions. Reducing conditions mimic the natural conditions of the complex more closely. Further, the presence of these coherences correlates with the vibronic coupling that produces faster, more efficient energy transfer through the complex under reducing conditions. The growth of coherences across the waiting time and the number of beating frequencies across hundreds of wavenumbers in the power spectra suggest that the beats are excited-state coherences with a mostly vibrational character whose phase relationship is maintained through the energy transfer process. Our results suggest that excitonic energy transfer proceeds through a coherent mechanism in this complex and that the coherences may provide a tool to disentangle coherent relaxation from energy transfer driven by stochastic environmental fluctuations.

Nonadiabatic quantum dynamics of the coherent excited state intramolecular proton transfer of 10-hydroxybenzo[h]quinoline

The photoinduced nonadiabatic dynamics of the enol-keto isomerization of 10-hydroxybenzo[h]quinoline (HBQ) are studied computationally using high-dimensional quantum dynamics. The simulations are based on a diabatic vibronic coupling Hamiltonian, which includes the two lowest pi pi ^* excited states and a npi ^* state, which has high energy in the Franck–Condon zone, but significantly stabilizes upon excited state intramolecular proton transfer. A procedure, applicable to large classes of excited state proton transfer reactions, is presented to parametrize this model using potential energies, forces and force constants, which, in this case, are obtained by time-dependent density functional theory. The wave packet calculations predict a time scale of 10–15 fs for the photoreaction, and reproduce the time constants and the coherent oscillations observed in time-resolved spectroscopic studies performed on HBQ. In contrast to the interpretation given to the most recent experiments, it is found that the reaction initiated by 1pi pi ^* longleftarrow S_0 photoexcitation proceeds essentially on a single potential energy surface, and the observed coherences bear signatures of Duschinsky mode-mixing along the reaction path. The dynamics after the 2pi pi ^* longleftarrow S_0 excitation are instead nonadiabatic, and the npi ^* state plays a major role in the relaxation process. The simulations suggest a mainly active role of the proton in the isomerization, rather than a passive migration assisted by the vibrations of the benzoquinoline backbone.Graphic

Nonresonant coherent two-dimensional spectroscopy

Coherent electronic two-dimensional spectroscopy is nowadays a matured experimental technique that monitors the time evolution of the studied sample after its resonant optical excitation. However, the experimental experience shows that even nonresonant interactions can provide detectable spectral contributions. These are often present as a weak parasitic signals originating in the solvent and/or cuvette walls underlying the resonant spectrum of the actual sample and as such they are usually discarded from the analysis. In this work, we adapt the formalism of double-sided Feynman diagrams for the needs of coherent two-dimensional spectroscopy in the nonresonant regime. We analytically calculate the third-order polarization of a two-level and several variants of three-level systems. As a result, we demonstrate the typical appearance of the optical Kerr-effect, cross-phase modulation, excited-state coherence, two-photon absorption and stimulated Raman scattering in the 2D spectrum. This provides a framework for studying these effects by means of coherent two-dimensional spectroscopy.

Линейный дихроизм и двулучепреломление зондирующего излучения в спектроскопии накачка-зондирование в многоатомных молекулах

Probe beam dichroism and birefringency occurring in the excited states of polyatomic molecules under excitation with two femtosecond laser pulses have been theoreticaly studied as a function of delay between the pulses. General expressions describing the change of intensity and polarization of the probe laser pulse passed through the solution of arbitrary polyatomic molecules at any initital polarization of the laser pulses have been derived using the spherical tensor approach. The expressions take into account the coherence in excited molecule vibrational states and decay of these states due to vibrational relaxation, rotational diffusion, and radiative transitions. The expressions describe the effects of probe beam linear dichroism and birefringency occurring in molecular excited states. As shown, under certain conditions both effects can be observed simultaneously. It has been concluded that within the geometry of almost collinear propagation of the pump and probe laser pulses through the molecular sample the contributions from linear dichroism and birefringency can be completely separated from each other by an appropriate choice of the polarization analyzer placed in front of the photodetector. The obtained expressions were applied for description of the signals that can be recorded experimentally by means of the polarization-modulation scheme developed in the recent author's publication (Gorbunova et al,Phys. Chem. Chem. Phys. 2020, Vol. 22, 18155−18168). The theory predicts that the modulated signals of dichroism and birefringency appear in quadrature with respect to the double frequency reference modulation signal.

Non-Uniform Excited State Electronic-Vibrational Coupling of Pigment-Protein Complexes.

Photosynthetic organisms exploit interacting quantum degrees of freedom, namely intrapigment electron-vibrational (vibronic) and interpigment dipolar couplings (J-coupling), to rapidly and efficiently convert light into chemical energy. These interactions result in wave function configurations that delocalize excitation between pigments and pigment vibrations. Our study uses multidimensional spectroscopy to compare two model photosynthetic proteins, the Fenna-Matthews Olson (FMO) complex and light harvesting 2 (LH2), and confirm that long-lived excited state coherences originate from the vibrational modes of the pigment. Within this framework, the J-coupling of vibronic pigments should have a cascading effect in modifying the structured spectral density of excitonic states. We show that FMO effectively couples all of its excitations to a uniform set of vibrations while in LH2, its two chromophore rings each couple to a unique vibrational environment. We simulate energy transfer in a simple model system with non-uniform vibrational coupling to demonstrate how modification of the vibronic coupling strength can modulate energy transfer. Because increasing vibronic coupling increases internal relaxation, strongly coupled vibronic states can act as an energy funnel, which can potentially benefit energy transport.

Leveraging excited-state coherence for synthetic control of ultrafast dynamics.

Design-specific control over excited-state dynamics is necessary for any application seeking to convert light into chemical potential. Such control is especially desirable in iron(II)-based chromophores, which are an Earth-abundant option for a wide range of photo-induced electron-transfer applications including solar energy conversion1 and catalysis2. However, the sub-200-femtosecond lifetimes of the redox-active metal-to-ligand charge transfer (MLCT) excited states typically encountered in these compounds have largely precluded their widespread use3. Here we show that the MLCT lifetime of an iron(II) complex can be manipulated using information from excited-state quantum coherences as a guide to implementing synthetic modifications that can disrupt the reaction coordinate associated with MLCT decay. We developed a structurally tunable molecular platform in which vibronic coherences-that is, coherences reflecting a coupling of vibrational and electronic degrees of freedom-were observed in ultrafast time-resolved absorption measurements after MLCT excitation of the molecule. Following visualization of the vibrational modes associated with these coherences, we synthetically modified an iron(II) chromophore to interfere with these specific atomic motions. The redesigned compound exhibits a MLCT lifetime that is more than a factor of 20 longer than that of the parent compound, indicating that the structural modification at least partially decoupled these degrees of freedom from the population dynamics associated with the electronic-state evolution of the system. These results demonstrate that using excited-state coherence data may be used to tailor ultrafast excited-state dynamics through targeted synthetic design.

Coherence effects of the strongly-coupled optical polaron-level qubit in a quantum well with asymmetrical semi-exponential potential

Abstract A theoretically investigation of the effects of barrier height of an asymmetrical semi-exponential confinement potential (ASECP) quantum well (QW) and the range of the ASECP on vibration frequency, first excited state (FES) energy, excitation energy and coherence time in the ASECP QW is performed. In order to determine the relationship between these factors, the linear combination operator, twice unitary transformations and Fermi Golden Rule methods are used. The vibration frequency, FES energy and excitation energy of the strong-coupled polaron are derived, as well as the qubit coherence time in the ASECP QW when the barrier height of the QW and the ASECP range are varied. It is found that these physical quantities are increasing functions of the barrier height, whereas they are decaying functions of the range. Furthermore, the coherence time is a decaying function with increased barrier height and an increasing function with enhanced range.

Quantum Coherence and Its Signatures in Extended Quantum Systems.

Quantum coherence controls almost every aspect of static and dynamic response of a strongly correlated quantum system, although details of this control have not been elucidated in many cases. We find that, in the presence of a significant static off-diagonal coupling, quantum coherence can survive much longer than the bath correlation time in a noisy environment. In the presence of time correlated noise (non-Markovian limit), coherence could propagate through the excited bath states, and this plays a nontrivial role in giving rise to a noncanonical temperature dependence of population distribution in an extended conjugated polymer-like system. The quantum coherence through the excited bath states vanishes in the high temperature limit, giving rise to the equilibrium Boltzmann distribution. Second, we discuss a role of quantum coherence in exciton localization that bears resemblance to Anderson localization. Calculations have been carried out not only with a chain of conjugated polymer but also with dimer and trimer subunits of the Fenna-Matthews-Olson (FMO) complex. We derive an analytical expression of the relation between steady state coherence and excitionic population distribution. We analytically showed that steady state coherence in equilibrium bath states is governed by interchromophoric coupling (J) whereas coherence in excited bath states is dictated by fluctuation strength (Vd) for the spatially correlated bath model. For the spatially uncorrelated bath model, we observe that at the low temperature limit coherence in the excited bath states dominates over coherence in equilibrium bath states and vice versa. In the study of the localization problem, we analytically show that, in the limit of a negligibly small fluctuation rate (bd), the diffusion coefficient is exactly proportional to the fluctuation rate, leading to complete breakdown of the Haken-Strobl-Silbey Markovian prediction.

Multicolor Quantum Control for Suppressing Ground State Coherences in Two-Dimensional Electronic Spectroscopy.

The measured multidimensional spectral response of different light harvesting complexes exhibits oscillatory features which suggest an underlying coherent energy transfer. However, making this inference rigorous is challenging due to the difficulty of isolating excited state coherences in highly congested spectra. In this work, we provide a coherent control scheme that suppresses ground state coherences, thus making rephasing spectra dominated by excited state coherences. We provide a benchmark for the scheme using a model dimeric system and numerically exact methods to analyze the spectral response. We argue that combining temporal and spectral control methods can facilitate a second generation of experiments that are tailored to extract desired information and thus significantly advance our understanding of complex open many-body structure and dynamics.

Relaxation of Coherent Excited States of a Superconductor to a Superconducting Reservoir

Relaxation of Coherent Excited States of a Superconductor to a Superconducting Reservoir

Role of Vibrational Dynamics on Excited-State Electronic Coherence in a Binuclear Platinum Complex.

Long-lived quantum coherence between excited electronic states can enable highly efficient energy and charge transport processes in chemical systems. Recent pump-probe experiments on binuclear platinum complexes identified persistent, periodic beating of transient absorption anisotropy signals, indicating long excited-state coherence lifetimes. Our previous simulations of the electronic dynamics of these complexes indicate that coherence lifetimes are sensitive to the balance between competitive electronic couplings. The complexes with shorter Pt-Pt distances underwent no appreciable dephasing in the limit of static nuclei, motivating the inclusion of nuclear motion into our simulations. The tert-butyl-substituted complex is studied in this work using the Ehrenfest method for mixed quantum-classical dynamics to investigate the role of vibrational dynamics on a complex shown to support long coherence lifetimes. Results indicate that the inclusion of excited-state vibrations drives a rapid collapse of the two-state coherence prior to the experimentally determined intersystem crossing. This further suggests singlet excited-state coherences may not be prerequisites for long-lived triplet coherences.

J-aggregation in porphyrin nanoparticles induced by diphenylalanine

In this report, L-diphenylalanine-decorated tetraphenylporphyrin (TPPtFFC) was synthesized and self-assembled into regular nano-architechtures. The morphology of the assemblies varied with the concentration of TPPtFFC. The absorption spectra of the nanoparticles show the Soret band merges with the Q bands and redistributes with great red-shift, indicative of the formation of J-aggregates of the porphyrin molecules. The fluorescence emission of the nanoparticles is merged and red-shifted to near-infrared region. Studies of absorption and fluorescence spectra reveal an indispensible role of diphenylalanine group in the formation of J-aggregates. The Raman spectra disclose that diprotonation of the porphyrin core contributes to delocalized coherent excited states in the nanoparticles. The positive cotton effect in circular dichroism spectra corresponding to the Soret band of TPPtFFC in solution confirms the formation of J-aggregates with right-handed chirality of the dipole moment. This report will shed light on the rational design of porphyrin-peptide conjugates to mimic naturally light-harvesting complexes.

Coherent Excited States in Superconductors due to a Microwave Field.

We describe theoretically the depairing effect of a microwave field on diffusive s-wave superconductors. The ground state of the superconductor is altered qualitatively in analogy to the depairing due to a dc current. In contrast to dc depairing, the density of states acquires, for microwaves with frequency ω_{0}, steps at multiples of the photon energy Δ±nℏω_{0} and shows an exponential-like tail in the subgap regime. We show that this ac depairing explains the measured frequency shift of a superconducting resonator with microwave power at low temperatures.

Vibronic resonances facilitate excited-state coherence in light-harvesting proteins at room temperature.

Until recently it was believed that photosynthesis, a fundamental process for life on earth, could be fully understood with semiclassical models. However, puzzling quantum phenomena have been observed in several photosynthetic pigment-protein complexes, prompting questions regarding the nature and role of these effects. Recent attention has focused on discrete vibrational modes that are resonant or quasi-resonant with excitonic energy splittings and strongly coupled to these excitonic states. Here we unambiguously identify excited state coherent superpositions in photosynthetic light-harvesting complexes using a new experimental approach. Decoherence on the time scale of the excited state lifetime allows low energy (56 cm(-1)) oscillations on the signal intensity to be observed. In conjunction with an appropriate model, these oscillations provide clear and direct experimental evidence that the persistent coherences observed originate from quantum superpositions among vibronic excited states.