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Vibrational polaritons are formed by strong coupling of molecular vibrations and photon modes in an optical cavity. Experiments have demonstrated that vibrational strong coupling can change molecular properties and even affect chemical reactivity. However, the interactions in a molecular ensemble are complex, and the exact mechanisms that lead to modifications are not fully understood yet. We simulate two-dimensional infrared spectra of molecular vibrational polaritons based on the double quantum coherence technique to gain further insight into the complex many-body structure of these hybrid light-matter states. Double quantum coherence uniquely resolves the excitation of hybrid light-matter polaritons and allows to directly probe the anharmonicities of the resulting states. By combining the cavity Born-Oppenheimer Hartree-Fock ansatz with a full quantum dynamics simulation of the corresponding eigenstates, we go beyond simplified model systems. This allows us to study the influence of self-polarization and the response of the electronic structure to the cavity interaction on the spectral features even beyond the single-molecule case.

The quantum dynamics of vibrational polaritonic states arising from the interaction of a bistable molecule with the quantized mode of a Fabry-Perot microcavity is investigated using an asymmetric double-well potential as a simplified one-dimensional model of a reactive molecule. After discussing the role of the light-matter coupling strength in the emergence of avoided crossings between polaritonic states, we investigate the possibility of using these crossings in order to trigger a dynamical switching of these states from one potential well to the other. Two schemes are proposed to achieve this coherent state switching, either by preparing the molecule in an appropriate vibrational excited state before inserting it into the cavity, or by applying a short laser pulse inside the cavity to obtain a coherent superposition of polaritonic states. The respective influences of the dipole amplitude and potential asymmetry on the coherent switching process are also discussed., Comment: Submitted to Physical Chemistry Chemical Physics. 10 pages, 8 figures, 4 tables

The quantum dynamics of a low-dimensional system in contact with a large but finite harmonic bath is theoretically investigated by coarse-graining the bath into a reduced set of effective energy states. In this model, the couplings between the system and the bath are obtained from the statistical average over the discrete, degenerate effective states. Our model is aimed at intermediate bath sizes in which non-Markovian processes and energy transfer between the bath and the main system are important. The method is applied to a model system of a Morse oscillator coupled to 40 harmonic modes. The results are found to be in excellent agreement with the direct quantum dynamics simulations of Bouakline et al. [J. Phys. Chem. A 116, 11118-11127 (2012)], but at a much lower computational cost. Extension to larger baths is discussed in comparison to the time-convolutionless method. We also extend this study to the case of a microcanonical bath with finite initial internal energies. The computational efficiency and convergence properties of the effective bath states model with respect to relevant parameters are also discussed., Comment: Accepted in J. Chem. Phys. 16 pages, 10 figures

Anharmonicities provide a wealth of information about the vibrational dynamics, mode coupling and energy transfer within a polyatomic system. In this contribution we show how driven molecular dynamics trajectories can be used to extract anharmonicity properties under very short times of a few hundreds of vibrational periods, using two exciting fields at- and slightly off-resonance. Detailed analyses on generic quartic potential energy surfaces and applications to various model systems are presented, giving good agreement with perturbation theory. Application to a realistic molecule, cubane (C$_8$H$_8$), modeled with a tight-binding quantum force field, further indicates how the method can be applied in practical cases., Comment: Published in Theoretical Chemistry Accounts. 17 pages, 5 figures, 2 tables

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystaline actetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model alpha-helix and beta-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy which directly probes dipole-dipole interactions. By including explicitly thermal velocity, we show that temperature has an important impact on the self-broadening mechanism of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening the double quantum spectrum scales with the atomic density while when Doppler broadening dominates it scales as the square of the density.

The effects of a finite temperature on the equilibrium structures of hydrocarbon molecules are computationally explored as a function of size and relative chemical composition in hydrogen and carbon. Using parallel tempering Monte Carlo simulations employing a reactive force field, we find that in addition to the phases already known for pure carbon, namely cages, flakes, rings and branched structures, strong effects due to temperature and the addition of little amounts of hydrogen are reported. Both entropy and the addition of moderate amounts of hydrogen favor planar structures such as nanoribbons over fullerenes. Accurate phase diagrams are proposed, highlighting the possible presence of multiple phase changes at finite size and composition. Astrophysical implications are also discussed.

Together with the second generation REBO reactive potential, replica-exchange molecular dynamics simulations coupled with systematic quenching were used to generate a broad set of isomers for neutral C$_n$ clusters with $n=24$, 42, and 60. All the minima were sorted in energy and analyzed using order parameters to monitor the evolution of their structural and chemical properties. The structural diversity measured by the fluctuations in these various indicators is found to increase significantly with energy, the number of carbon rings, especially 6-membered, exhibiting a monotonic decrease in favor of low-coordinated chains and branched structures. A systematic statistical analysis between the various parameters indicates that energetic stability is mainly driven by the amount of sp$^2$ hybridization, more than any geometrical parameter. The astrophysical relevance of these results is discussed in the light of the recent detection of C$_{60}$ and C$_{60}^+$ fullerenes in the interstellar medium.

While powerful techniques exist to accurately account for anharmonicity in vibrational molecular spectroscopy, they are computationally very expensive and cannot be routinely employed for large species and/or at non- zero vibrational temperatures. Motivated by the study of Polycyclic Aromatic Hydrocarbon (PAH) emission in space, we developed a new code, which takes into account all modes and can describe all IR transitions including bands becoming active due to resonances as well as overtones, combination and difference bands. In this article, we describe the methodology that was implemented and discuss how the main difficulties were overcome, so as to keep the problem tractable. Benchmarking with high-level calculations was performed on a small molecule. We carried out specific convergence tests on two prototypical PAHs, pyrene (C$_{16}$H$_{10}$) and coronene (C$_{24}$H$_{12}$), aiming at optimising tunable parameters to achieve both acceptable accuracy and computational costs for this class of molecules. We then report the results obtained at 0 K for pyrene and coronene, comparing the calculated spectra with available experimental data. The theoretical band positions were found to be significantly improved compared to harmonic Density Functional Theory (DFT) calculations. The band intensities are in reasonable agreement with experiments, the main limitation being the accuracy of the underlying calculations of the quartic force field. This is a first step towards calculating moderately high-temperature spectra of PAHs and other similarly rigid molecules using Monte Carlo sampling., Comment: accepted for publication on Journal of Chemical Physics

We report the observation of double-quantum coherence signals in a gas of potassium atoms at twice the frequency of the one-quantum coherences. Since a single atom does not have a state at the corresponding energy, this observation must be attributed to a collective resonance involving multiple atoms. These resonances are induced by weak inter-atomic dipole-dipole interactions, which means that the atoms cannot be treated in isolation, even at a low density of $10^{12}$ cm$^{-3}$.

By using a Generalized Hubbard model for bosons, the energy transfer in a nonlinear quantum lattice is studied, with special emphasis on the interplay between local and nonlocal nonlinearity. For a strong local nonlinearity, it is shown that the creation of v quanta on one site excites a soliton band formed by bound states involving v quanta trapped on the same site. The energy is first localized on the excited site over a significant timescale and then slowly delocalizes along the lattice. As when increasing the nonlocal nonlinearity, a faster dynamics occurs and the energy propagates more rapidly along the lattice. Nevertheless, the larger is the number of quanta, the slower is the dynamics. However, it is shown that when the nonlocal nonlinearity reaches a critical value, the lattice suddenly supports a very fast energy propagation whose dynamics is almost independent on the number of quanta. The energy is transfered by specific bound states formed by the superimposition of states involving v-p quanta trapped on one site and p quanta trapped on the nearest neighbour sites, with p=0,..,v-1. These bound states behave as independent quanta and they exhibit a dynamics which is insensitive to the nonlinearity and controlled by the single quantum hopping constant., Comment: 28 pages, 8 figures

The two-vibron dynamics associated to amide-I vibrations in a 3D $\alpha$-helix is described according to a generalized Davydov model. The helix is modeled by three spines of hydrogen-bonded peptide units linked via covalent bonds. It is shown that the two-vibron energy spectrum supports both a two-vibron free states continuum and two kinds of bound states, called TVBS-I and TVBS-II, connected to the trapping of two vibrons onto the same amide-I mode and onto two nearest neighbor amide-I modes belonging to the same spine, respectively. At low temperature, non vanishing interspine hopping constants yield a three dimensional nature of both TVBS-I and TVBS-II which the wave functions extend over the three spines of the helix. At biological temperature, the pairs are confined in a given spine and exhibit the same features as the bound states described within a one-dimensional model. The interplay between the temperature and the 3D nature of the helix is also responsible for the occurrence of a third bound state called TVBS-III which refers to the trapping of two vibrons onto two different spines. The experimental signature of the existence of bound states is discussed through the simulation of their infrared pump-probe spectroscopic response. Finally, the fundamental question of the breather-like behavior of two-vibron bound states is addressed., Comment: 12 pages, 8 figures

The vibron dynamics associated to amide-I vibrations in a 3D alpha-helix is described according to a generalized Davydov model. The helix is modeled by three spines of hydrogen-bonded peptide units linked via covalent bonds. To remove the intramolecular anharmonicity of each amide-I mode and to renormalized the vibron-phonon coupling, two unitary transformation have been applied to reach the dressed anharmonic vibron point of view. It is shown that the vibron dynamics results from the competition between inter-spine and intra-spine vibron hops and that the two kinds of hopping processes do not experience the same dressing mechanism. Therefore, at low temperature (or weak vibron-phonon coupling), the polaron behaves as an undressed vibron delocalized over all the spines whereas at biological temperature (or strong vibron-phonon coupling), the dressing effect strongly reduces the vibrational exchanges between different spines. As a result the polaron propagates along a single spine as in the 1D Davydov model. Although the helix supports both acoustical and optical phonons, this feature originates in the coupling between the vibron and the acoustical phonons, only. Finally, the lattice distortion which accompanies the polaron has been determined and it is shown that residues located on the excited spine are subjected to a stronger deformation than the other residues., Comment: 13 pages, 7 figures

The small polaron theory is applied to describe the vibron dynamics in an adsorbed nanowire with a special emphasis onto finite size effects. It is shown that the finite size of the nanowire discriminates between side molecules and core molecules which experience a different dressing mechanism. Moreover, the inhomogeneous behavior of the polaron hopping constant is established and it is shown that the core hopping constant depends on the lattice size. However, the property of a lattice with translational invariance is recovered when the size of the nanowire is greater than a critical value. Finally, it is pointed out that these features yield the occurrence of high energy localized states which both the nature and the number are summarized in a phase diagram in terms of the relevant parameters of the problem (small polaron binding energy, temperature, lattice size)., Comment: 17 pages, 10 figures

Relaxation channels for two-vibron bound states in an anharmonic alpha-helix protein are studied. It is pointed out that the relaxation originates in the interaction between the dressed anharmonic vibrons and the remaining phonons. This interaction is responsible for the occurrence of transitions between two-vibron eigenstates mediated by both phonon absorption and phonon emission. At biological temperature, it is shown that the relaxation rate does not significantly depends on the nature of the two-vibron state involved in the process. Therefore, the lifetime for both bound and free states is of the same order of magnitude and ranges between 0.1 and 1.0 ps for realistic parameters. By contrast, the relaxation channels strongly depend on the nature of the two-vibron states which is a consequence of the breather-like behavior of the two-vibron bound states., Comment: octobre 2003 - soumis Phys. Rev. E

We study the two-dimensional +/-J Ising model, three-state Potts model and four-state Potts model, by the numerical transfer matrix method to investigate the behaviour of the sample-to-sample fluctuations of the internal energy on the Nishimori line. The result shows a maximum at the multicritical point in all the models we investigated. The large sample-to-sample fluctuations of the internal energy as well as the existence of a singularity in these fluctuations imply that the bond configuration (or, equivalently, the distribution of frustrated plaquettes) may be experiencing a non-trivial change of its behaviour at the multicritical point. This observation is consistent with the picture that the phase transition at the multicritical point is of geometry-induced nature., Comment: 9 pages, 7 figures; Note added