Photon Echo Experiments Research Articles

Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics

We investigate the physics of an adiabatic transition from a BCS superconductor to a Fermi liquid for an exponentially slow decreasing pairing interaction. We show that, depending on the order of the thermodynamic limit and large times, a situation can arise in which the Fermi liquid keeps a memory of the parent BCS state. Furthermore, a time inversion of the interaction, supplemented by a manipulation analogous to a spin-/photon-echo experiment, allows us to recover the parent BCS state. Moreover, we study the evolution of the order parameter phase $\ensuremath{\phi}$ in transforming the BCS superconductor to a conventional metal. Since the global phase is the conjugate variable of the density, we explicitly show how to use the dynamics of $\ensuremath{\phi}$ together with gauge invariance to build up the noninteracting chemical potential away from particle-hole symmetry. We further analyze the role of $\ensuremath{\phi}$ in restoring the gauge-invariant current response when the noninteracting Fermi liquid is approached starting from a BCS superconductor in the presence of an external vector field.

Vibrational dynamics of iron pentacarbonyl in cryogenic matrices.

Iron pentacarbonyl is a textbook example of fluxionality. We trap the molecule in cryogenic matrices to study the vibrational dynamics of CO stretching modes involved in the fluxional rearrangement. The infrared spectrum in Ar and N2 is composed of about ten narrow bands in the spectral range of interest, indicating the population of various lattice sites and a lowering of the molecular symmetry in the trapping sites. The vibrational dynamics is explored by means of infrared stimulated photon echoes at the femtosecond scale. Vibrational dephasing and population relaxation times are obtained. The non-linear signals exhibit strong oscillations useful to disentangle the site composition of the absorption spectrum. The population relaxation involves at least two characteristic times. An evolution of the photon echo signals with the waiting time is observed. The behavior of all the signals can be reproduced within a simple model that describes the population relaxation occurring in two steps: relaxation of v = 1 (population time T1 < 100ps) and return to v = 0 (recovery time > 1ns). These two steps explain the evolution of the oscillations with the waiting time in the photon echo signals. These results discard fluxional rearrangement on the time scale of hundreds of ps in our samples. Dephasing times are of the same order of magnitude as T1: dephasing processes due to the matrix environment are rather inefficient. The photon echo experiments also reveal that intermolecular resonant vibrational energy transfers between guest molecules occur at the hundreds of ps time scale in concentrated samples (guest/host > 104).

In-plane anisotropy of the hole g factor in CdTe/(Cd,Mg)Te quantum wells studied by spin-dependent photon echoes

We use the two-pulse spin-dependent photon echo technique to study the in-plane hole spin anisotropy in a 20~nm-thick CdTe/Cd$_{0.76}$Mg$_{0.24}$Te single quantum well by exciting the donor-bound exciton resonance. We take advantage of the photon echo sensitivity to the relative phase of the electron and hole spin precession and study various interactions contributing to the hole in-plane spin properties. The main contribution is found to arise from the crystal cubic symmetry described by the Luttinger parameter $q=0.095$, which is substantially larger than the one theoretically expected for CdTe or found in other quantum well structures. Another contribution is induced by the strain within the quantum well. These two contributions manifest as different harmonics of the spin precession frequencies in the photon echo experiment, when strength and orientation of the Voigt magnetic field are varied. The magnitude of the effective in-plane hole $g$ factor is found to vary in the range $|\tilde{g_h}|$=0.125--0.160 in the well plane.

Spectrally resolved photon-echo spectroscopy of CdSe quantum dots at far from resonance excitation condition $$^{\S }$$ §

Spectrally resolved photon echo spectroscopy in the off-resonance condition is reported for the first time to study the coherence and population dynamics of CdSe quantum dots. In this case, the information related to the system dynamics can be inferred indirectly. This is especially useful when such dynamical information might be hidden under the absorption maxima of the sample. We observe that a substantial intensity of the photon echo signal was obtained in two different CdSe quantum dot samples (CdSe 610 and CdSe 640), which have absorption maxima at 620 nm and 590 nm, respectively. Due to the difference in sizes of these two quantum dots, a small change is observed in the molecular dynamics of these two quantum-dot samples. Specifically, the spectral diffusion of CdSe 640 occurs within the first 50 fs, whereas that for CdSe 610 occurs at about 100 fs timescale. The integrated plots of the photon echo signal, as a function of population time, result in two decay constants. The faster among the two decay components is pulse width limited and is in between 30 and 40 fs at different fixed coherence times for both samples. The slower decay component for the CdSe 610 sample is found to be in the range of 75–85 fs, while that for CdSe 640, it is between 82 and 92 fs at different fixed coherence times. SYNOPSIS Excitonic dynamics of CdSe quantum-dots is presented using time-dependent spectrally-resolved photon-echo spectroscopy at 810 nm, which is ~160 nm red-shifted from their absorption maxima. Information related to system dynamics is inferred indirectly from such ‘far-from-resonance’ photon-echo experiments, which would be especially useful when the information is hidden within the sample’s absorption maxima.

Evidence of Molecular Heterogeneities in Amide-Based Deep Eutectic Solvents.

The liquid structure of five different amide-based deep eutectic solvents (DESs) as a function of the chemical structure of the hydrogen bond acceptor (HBA) was investigated by linear Fourier transform infrared (FTIR) and two-dimensional infrared (2DIR) spectroscopies. Linear FTIR spectroscopy shows that the amide band of the DESs is not significantly affected by the chemical structure and symmetry of the HBA cation. However, its excitonic nature does not allow us to draw further conclusions. Analysis of the 13C amide line shapes derived from the 2DIR spectra reveals that the different DESs do not show appreciable differences in the level of disorganization. The vibrational dynamics, derived from the photon echo experiments on the 13C amide, shows that there is a fast component with a time scale of ∼1 ps irrespective of the HBA. The ultrafast dynamics is assigned to hydrogen bond making and breaking between amides. In addition, a slow dynamical component is observed in the time evolution of the photon echo signal. This contribution appears to be correlated with the asymmetry and polarity of the moieties of the HBA. The overall dynamics is rationalized in terms of a microscopic heterogeneous structure of the DESs, where the heterogeneities create domains that slow the hydrogen bond making and breaking. Molecular dynamics simulations provide additional support for our modeling of the data. In addition, the presence of nanoscopic heterogeneities is consistent with the observation of an endortherm at 23 °C in the differential scanning calorimetry thermogram, which evidenced a phase transition at 23 °C, even though the tested DESs have a melting temperature below -40 °C.

Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties.

Methane solids present more than one accessible crystalline phase at low temperature at zero pressure. We trap W(CO)6 in CH4 and CD4 matrices between 8 and 35 K to probe the interaction between an impurity and its surrounding molecular solid under various physical conditions. Linear and nonlinear vibrational spectroscopies of W(CO)6 highlight different kinds of interaction and reveal new and remarkable signatures of the phase transition of methane. The structures in the absorption band of the antisymmetric CO stretching mode exhibit a clear modification at the transition between phase II and phase I in CH4 and motional narrowing is observed upon temperature increase. The vibrational dynamics of this mode is probed in stimulated photon echo experiments performed with a femtosecond IR laser. A short component around 10 ps is detected in the population relaxation lifetime in the high temperature phase of solid CH4 (phase I) and disappears at lower temperatures (phase II) where the vibrational lifetime is in the hundreds of ps. The analysis of the nonlinear time-resolved results suggests that the short component comes from a fast energy transfer between the vibrational excitation of the guest and the lattice in specific families of sites. Such fast transfers are observed in the case of W(CO)6 trapped in CD4 because of an energy overlap of the excitation of W(CO)6 and a lattice vibron. In solid CH4, even when these V-V transfers are not efficient, pure dephasing processes due to the molecular nature of the host occur: they are temperature dependent without a clear modification at the phase transition.

High-Resolution Optical Line Width Measurements as a Material Characterization Tool

We present a case study on Eu3+-doped Y2O3 transparent ceramics in which high-resolution laser spectroscopy is used as a material characterization tool. By comparing the results from coherent and incoherent optical spectroscopy with other characterization methods, we show that optical techniques can deliver supplementary information about the local environment of the activator ions in materials. Thus, high-resolution spectroscopy may be of interest for the investigation of a wider range of rare earth doped optical materials beyond materials studied for quantum information technology. The refinement of optical spectroscopy for the study of narrow optical transitions in rare earth ion single crystals has demonstrated that these techniques are extremely sensitive tools for probing the local environment of the rare earth ion. These techniques, such as photon echo experiments, have been important in developing materials for quantum information technology and spectral filtering applications. Here, we apply thes...

Ultrafast 2D-IR and simulation investigations of preferential solvation and cosolvent exchange dynamics.

Using a derivative of the vitamin biotin labeled with a transition-metal carbonyl vibrational probe in a series of aqueous N,N-dimethylformamide (DMF) solutions, we observe a striking slowdown in spectral diffusion dynamics with decreased DMF concentration. Equilibrium solvation dynamics, measured with the rapidly acquired spectral diffusion (RASD) technique, a variant of heterodyne-detected photon-echo peak shift experiments, range from 1 ps in neat DMF to ∼3 ps in 0.07 mole fraction DMF/water solution. Molecular dynamics simulations of the biotin-metal carbonyl solute in explicit aqueous DMF solutions show marked preferential solvation by DMF, which becomes more pronounced at lower DMF concentrations. The simulations and the experimental data are consistent with an interpretation where the slowdown in spectral diffusion is due to solvent exchange involving distinct cosolvent species. A simple two-component model reproduces the observed spectral dynamics as well as the DMF concentration dependence, enabling the extraction of the solvent exchange time scale of 8 ps. This time scale corresponds to the diffusive motion of a few Å, consistent with a solvent-exchange mechanism. Unlike most previous studies of solvation dynamics in binary mixtures of polar solvents, our work highlights the ability of vibrational probes to sense solvent exchange as a new, slow component in the spectral diffusion dynamics.

Multidimensional resonance Raman spectroscopy by six-wave mixing in the deep UV.

Two-dimensional (2D) resonance Raman spectroscopies hold great potential for uncovering photoinduced relaxation processes in molecules but are not yet widely applied because of technical challenges. Here, we describe a newly developed 2D resonance Raman experiment operational at the third-harmonic of a Titanium-Sapphire laser. High-sensitivity and rapid data acquisition are achieved by combining spectral interferometry with a background-free (six-pulse) laser beam geometry. The third-harmonic laser pulses are generated in a filament produced by the fundamental and second-harmonic pulses in neon gas at pressures up to 35 atm. The capabilities of the setup are demonstrated by probing ground-state wavepacket motions in triiodide. The information provided by the experiment is explored with two different representations of the signal. In one representation, Fourier transforms are carried out with respect to the two experimentally controlled delay times to obtain a 2D Raman spectrum. Further insights are derived in a second representation by dispersing the signal pulse in a spectrometer. It is shown that, as in traditional pump-probe experiments, the six-wave mixing signal spectrum encodes the wavepacket's position by way of the (time-evolving) emission frequency. Anharmonicity additionally induces dynamics in the vibrational resonance frequency. In all cases, the experimental signals are compared to model calculations based on a cumulant expansion approach. This study suggests that multi-dimensional resonance Raman spectroscopies conducted on systems with Franck-Condon active modes are fairly immune to many of the technical issues that challenge off-resonant 2D Raman spectroscopies (e.g., third-order cascades) and photon-echo experiments in the deep UV (e.g., coherence spikes). The development of higher-order nonlinear spectroscopies operational in the deep UV is motivated by studies of biological systems and elementary organic photochemistries.

Simulating signatures of two-dimensional electronic spectra of the Fenna-Matthews-Olson complex: By using a numerical path integral

A framework for simulating electronic spectra from photon-echo experiments is constructed by using a numerical path integral technique. This method is non-Markovian and nonperturbative and, more importantly, is not limited by a fixed form of the spectral density functions of the environment. Next, a two-dimensional (2D) third-order electronic spectrum of a dimer system is simulated. The spectrum is in agreement with the experimental and theoretical results previously reported [for example, M. Khalil, N. Demirdöven, and A. Tokmakoff, Phys. Rev. Lett. 90, 047401 (2003)]. Finally, a 2D third-order electronic spectrum of the Fenna-Matthews-Olson (FMO) complex is simulated by using the Debye, Ohmic, and Adolphs and Renger spectral density functions. It is shown that this method can clearly produce the spectral signatures of the FMO complex by using only the Adolphs and Renger spectral density function. Plots of the evolution of the diagonal and cross-peaks show that they are oscillating with the population time.

A luminescence visualizer for exact convergence of laser beams in photon-echo spectroscopy, four-wave mixing, and related techniques

A convenient and efficient technique for controlling exact focusing of several noncollinear laser beams into the same point of a luminescent sample is proposed for optical photon-echo spectroscopy and four-wave mixing experiments. The technique proposed is based on a confocal luminescence microscope equipped with a sensitive multichannel detector for visualizing samples with a large magnification. The high efficiency of the scheme developed is confirmed by experimental study of photon echo in a polymer film doped with luminescent dye molecules.

Three-Pulse Photon Echo of Finite Numbers of Molecules: Single-Molecule Traces

In conventional bulk nonlinear spectroscopy, the contribution from molecules with different environmental conditions sometimes conceals the properties of interest and prevents the assessment of the heterogeneity of complex systems. This is especially true when exploring mechanisms of coherence loss in multicomponent systems [Ishizaki and Fleming, J. Phys. Chem. B 2011, 115, 6227]. To avoid this drawback of ensemble measurements and evaluate single-molecule behavior, a quantum theory is proposed to study the three-pulse photon echo signal of a two-level system in a bath and reveal the fluctuations inherent to single molecules. The current method takes advantage of the coherent state representation to understand the photon echo experiment in a wave function formalism rather than the reduced density matrix. Information regarding the environmental degrees of freedom (DoF) is explicitly encoded in the initial state of the system plus bath. The thermal fluctuations of the initial states induce variation of the photon echo signal, which is clearly different from the ensemble average echo signal. We use our formalism to demonstrate the recovery of the conventional ensemble response signal from the single-molecule signal.

Vibrational Frequency Fluctuation of Ions in Aqueous Solutions Studied by Three-Pulse Infrared Photon Echo Method

In liquid water, hydrogen bonds form three-dimensional network structures, which have been modeled in various molecular dynamics simulations. Locally, the hydrogen bonds continuously form and break, and the network structure continuously fluctuates. In aqueous solutions, the water molecules perturb the solute molecules, resulting in fluctuations of the electronic and vibrational states. These thermal fluctuations are fundamental to understanding the activation processes in chemical reactions and the function of biopolymers. In this Account, we review studies of the vibrational frequency fluctuations of solute molecules in aqueous solutions using three-pulse infrared photon echo experiments. For comparison, we also briefly describe dynamic fluorescence Stokes shift experiments for investigating solvation dynamics in water. The Stokes shift technique gives a response function, which describes the energy relaxation in the nonequilibrium state and corresponds to the transition energy fluctuation of the electronic state at thermal equilibrium in linear response theorem. The dielectric response of water in the megahertz to terahertz frequency region is a key physical quantity for understanding both of these frequency fluctuations because of the influence of electrostatic interactions between the solute and solvent. We focus on the temperature dependence of the three experiments to discuss the molecular mechanisms of both the frequency fluctuations in aqueous solutions. We used a biexponential function with sub-picosecond and picosecond time constants to characterize the time-correlation functions of both the vibrational and electronic frequency fluctuations. We focus on the slower component, with time constants of 1-2 ps for both the frequency fluctuations at room temperature. However, the temperature dependence and isotope effect for the time constants differ for these two types of fluctuations. The dielectric interactions generally describe the solvation dynamics of polar solvents, and hydrodynamic theory can describe the slow component for the electronic states. Compared with the slow component of the solvation dynamics, however, the picosecond component for the vibrational frequency fluctuations is less sensitive to temperature. Therefore, the slow component of the vibrational frequency fluctuation is determined by different underlying dynamics, which are important for the solvation dynamics of the electronic state. The time constant for the picosecond component for the vibrational frequency fluctuation does not significantly depend on the solute. We propose that the vibrational frequency fluctuates because of the constant structural changes in the hydrogen-bonding network of water molecules around the solute.

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.

Quantum state and process tomography of energy transfer systems via ultrafast spectroscopy

The description of excited state dynamics in energy transfer systems constitutes a theoretical and experimental challenge in modern chemical physics. A spectroscopic protocol that systematically characterizes both coherent and dissipative processes of the probed chromophores is desired. Here, we show that a set of two-color photon-echo experiments performs quantum state tomography (QST) of the one-exciton manifold of a dimer by reconstructing its density matrix in real time. This possibility in turn allows for a complete description of excited state dynamics via quantum process tomography (QPT). Simulations of a noisy QPT experiment for an inhomogeneously broadened ensemble of model excitonic dimers show that the protocol distills rich information about dissipative excitonic dynamics, which appears nontrivially hidden in the signal monitored in single realizations of four-wave mixing experiments.

Theoretical Study of Coherent Excitation Energy Transfer in Cryptophyte Phycocyanin 645 at Physiological Temperature

Recent two-dimensional photon-echo experiments suggest that excitation energy transfer in light harvesting systems occurs coherently rather than by incoherent hopping. The signature quantum beating of coherent energy transfer has been observed even at ambient temperatures. In this letter, we use an iterative linearized density matrix (ILDM) propagation approach to study this dynamics in a realistic multistate system−bath model. Our calculations reproduce the observed 400 fs decoherence time, and studies that vary the system Hamiltonian and structured spectral density describing the chromophore network−protein environment interactions give results that enable us to explore the role of initial coherence in energy transfer efficiency of the model network. Our findings suggest that the initial coherence has only a slight effect on energy transfer in this model system. We explore energy transfer optimization of different chromophores in the network by controlling environmental properties. This study points to the importance of stochastic resonance behavior in determining optimal network throughput.

Exciton Delocalization and Energy Transport Mechanisms in R-Phycoerythrin

Energy transport mechanisms in R-Phycoerythrin (RPE), a light harvesting protein located at the top of the phycobilisome antenna in red algae, are investigated using nonlinear optical spectroscopies and theoretical models. The RPE hexamer possesses a total of 30 bilin pigments, which can be subdivided into three classes based on their molecular structures and electronic resonance frequencies. Of particular interest to this study is the influence of exciton delocalization on the real-space paths traversed by photoexcitations as they concentrate on the lowest energy pigment sites. Transient grating measurements show that significant nuclear relaxation occurs at delay times less than 100 fs, whereas energy transport spans a wide range of time scales depending on the proximity of the initial and final states involved in the process. The fastest energy transport dynamics within the RPE complex are close to 1 ps; however, evidence for sub-100 fs exciton self-trapping is also obtained. In addition, photon echo experiments reveal vibronic interactions with overdamped and underdamped nuclear modes. To establish signatures of exciton delocalization, energy transport is simulated using both modified Redfield and Förster theories, which respectively employ delocalized and localized basis states. We conclude that exciton delocalization occurs between six pairs of phycoerythrobilin pigments (i.e., dimers) within the protein hexamer. It is interesting that these dimers are bound in locations analogous to the well-studied phycocyanobilin dimers of cyanobacterial allophycocyanin and c-phycocyanin in which wave function delocalization is also known to take hold. Strong conclusions regarding the electronic structures of the remaining pigments cannot be drawn based on the present experiments and simulations due to overlapping resonances and broad spectroscopic line widths, which prevent the resolution of dynamics at particular pigment sites.

Temperature dependence of vibrational frequency fluctuation of N3− in D2O

We have studied the temperature dependence of the vibrational frequency fluctuation of the antisymmetric stretching mode of N(3) (-) in D(2)O by three-pulse infrared (IR) photon echo experiments. IR pump-probe measurements were also carried out to investigate the population relaxation and the orientational relaxation of the same band. It was found that the time-correlation function (TCF) of the frequency fluctuation of this mode is well described by a biexponential function with a quasistatic term. The faster decay component has a time constant of about 0.1 ps, and the slower component varies from 1.4 to 1.1 ps in the temperature range from 283 to 353 K. This result indicates that liquid dynamics related to the frequency fluctuation are not highly sensitive to temperature. We discuss the relationship between the temperature dependence of the vibrational frequency fluctuation and that of the molecular motion of the system to investigate the molecular origin of the frequency fluctuation of the solute. We compare the temperature dependence of the frequency fluctuation with that of other dynamics such as dielectric relaxation of water. In contrast to the Debye dielectric relaxation time of D(2)O, the two time constants of the TCF of the frequency fluctuation do not exhibit strong temperature dependence. We propose a simple theoretical model for the frequency fluctuation in solutions based on perturbation theory and the dipole-dipole interaction between the vibrational mode of the solute and the solvent molecules. This model suggests that the neighboring solvent molecules in the vicinity of the solute play an important role in the frequency fluctuation. We suggest that the picosecond component of the frequency fluctuation results from structural fluctuation of the hydrogen-bonding network in water.

Photon echo in oscillator-type multilevel systems

The effect of photon echo is studied in several multilevel systems with quasi-equidistant spectra. The analysis focuses on the echo schemes that are of interest for femtosecond photon echo experiments involving both fundamental and combination vibrational modes of molecules.

Energy transfer, entanglement and decoherence in a molecular dimer interacting with a phonon bath

We study the dynamics of energy transfer and dephasing in a molecular dimer with degenerate energies interacting with an anti-correlated, collective vibrational bath. By diagonalizing the total Hamiltonian, we obtain an analytic expression for the dephasing rate as a function of temperature, resonance coupling, system–bath coupling and the spectrum of the bath. Eigenstates of the total Hamiltonian are identified as a natural basis set for studies of decoherence dynamics, and the study is motivated by observations of persistent coherence in two-dimensional (2D) photon echo experiments on photosynthetic light-harvesting proteins (Collini et al 2010 Nature463 644–7). We find that, under the influence of a collective phonon bath, coherence survives longer in systems with weak electronic couplings, in agreement with observations of long-lasting coherence in weakly coupled multichromophoric systems.