A quantum/semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested and applied to simulate and interpret ultrafast optical signals. Linear wave-packet interferometry and time-resolved coherent anti-Stokes Raman scattering signals for a model of molecular iodine in a 2D krypton lattice are calculated and used to study the vibrational decoherence and energy dissipation of iodine molecules in condensed media. The total wave function of the whole model is approximately obtained instead of a reduced system density matrix, and therefore the theory enables us to analyze the behavior and the role of the host matrix in quantum dynamics. \n \nThis dissertation includes previously published co-authored material.
A quantum/semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested and applied to simulate and interpret ultrafast optical signals. Linear wave-packet interferometry and time-resolved coherent anti-Stokes Raman scattering signals for a model of molecular iodine in a 2D krypton lattice are calculated and used to study the vibrational decoherence and energy dissipation of iodine molecules in condensed media. The total wave function of the whole model is approximately obtained instead of a reduced system density matrix, and therefore the theory enables us to analyze the behavior and the role of the host matrix in quantum dynamics. \n \nThis dissertation includes previously published co-authored material.
Time-resolved, electronically resonant, coherent anti-Stokes Raman scattering is used to prepare and interrogate vibronic coherences of molecular iodine in matrix Ar. Coherences that involve evolution on the excited B(3Π0u) state, first- and third-order coherences, decay in less than one vibrational period (τ<300 fs). In contrast, as many as 200 vibrational periods of motion can be observed for Raman-prepared wave packets consisting of zero-phonon vibrational superpositions on the ground electronic state (second-order coherence). Packets consisting of v=4, 5 and v=3, 4, 5 on the X(1Σg) state decay with a half-life of 10±1 ps at 31 K, allowing a more accurate measure of vibrational level spacings and decoherence time than has been possible in frequency domain. The harmonic frequency of the molecule is reduced by 1.5 cm−1 (0.7%) in the matrix. The lack of recurrence in the excited electronic state ensures that the resonant anti-Stokes scattering arises only from the negative momentum component of the Raman packet. This momentum filter, which should be ubiquitous in condensed media, leads to a signal with deeper modulation than in the gas phase.
We study the vibrational decoherence dynamics of an iodine molecule in a finite krypton cluster comprising the first solvation shell. A normal mode analysis allows us to successively increase the complexity of the description. For the ground state dynamics, comparison with experimental matrix results shows that already four degrees of freedom are sufficient to capture the main decoherence mechanism. For electronically excited iodine, we model the vibrational dynamics of initial Schrödinger cat-like states by the semiclassical hybrid dynamics [Grossmann, F. J. Chem. Phys. 2006, 125, 014111] and full quantum calculations, where available. Good agreement of the results is found for a reduced model with three degrees of freedom. We find non-Gaussian distortions of the bath density matrix, which is a necessary condition, if Schrödinger catlike states in the bath are to be identified. However, in contrast to the experiment [Segale, D.; et al. J. Chem. Phys. 2005, 122, 111104], we observe only incoherent superpositions of bath vibrational states.
The thesis involves three different aspects of quantum dynamics in cold and isolated molecular systems that are investigated theoretically with methods ranging from wavepacket dynamics to density matrix propagation. In the first part the efficiency of cavity sideband cooling of trapped molecules is theoretically investigated for the case in which the infrared transition between two ro-vibrational states is used as a cycling transition. The molecules are assumed to be trapped either by a radio frequency or optical trapping potential, depending on whether they are charged or neutral, and confined inside a high-finesse optical resonator that enhances radiative emission into the cavity mode. Using realistic experimental parameters and Carbonyl sulfide as a molecular representative, we show that in this setup, cooling to the trap ground state is feasible. The second part investigates femtosecond pump-probe spectroscopy of single MgH+ ions confined in an ion trap. The molecular ions are embedded in a coulomb crystal of atomic magnesium ions which are laser cooled to a few millikelvin. Single molecules are addressed by femtosecond ultraviolet laserpulses and the induced molecular processes are investigated. The simulations of the wave packet motion and dissociation behavior were used to predict the experimental parameter regime and are compared directly to the laboratory results. For this purpose a multiscale model is developed which involves the wave packet motion as well as the problem of vibrational heating occurring on a millisecond time scale under laboratory conditions. The third part investigates the gas phase SN2 collision reaction of chloride and methyl iodine. Motivated by the experimental results of Roland Wester and co-workers [Mikosch et al., Science 319, 183 (2008)], remaining questions were addressed. The collision reaction is simulated by solving the time dependent Schrödinger equation on ab initio potential energy surfaces. With the chosen reactive coordinates it is possible to reproduce the basic features of the immediate collision reaction. The internal molecular coordinates are transformed into reaction path based model which allows for an efficient numerical description of the nuclear dynamics. The energy transfer in the system is investigated and compared to the experimental results. From the new insight into the process, an intuitive concept of a dynamical barrier can be derived. Moreover the role of the spectator mode can be clarified.
Revealing possible long-living coherence in ultrafast processes allows detecting genuine quantum mechanical effects in molecules. To investigate such effects from a quantum chemistry perspective, we have developed a method for simulating the time evolution of molecular systems based on ab initio calculations, which includes relaxation and environment-induced dephasing of the molecular wave function whose rates are external parameters. The proposed approach combines a quantum chemistry description of the molecular target with a real-time propagation scheme within the time-dependent stochastic Schrödinger equation. Moreover, it allows a quantitative characterization of the state and dynamics coherence through the l1-norm of coherence and the linear entropy, respectively. To test the approach, we have simulated femtosecond pulse-shaping ultrafast spectroscopy of terrylenediimide, a well-studied fluorophore in single-molecule spectroscopy. Our approach is able to reproduce the experimental findings [R. Hildner et al., Nat. Phys. 7, 172 (2011)], confirming the usefulness of the approach and the correctness of the implementation.
During the last half century, quantum coherence has been of great interest due to its own right and also due to its broad range of applications in many areas of physics. The reason for that is the technological progress made last century, specially, the invention of coherent light sources and their commercialization. Indeed, coherent laser sources allow us to coherently excite atoms and molecules, as a consequence, to study variety of coherent and collective phenomena in atomic physics, for instance, coherent optical spectroscopy, superradiance, superflourescence, lasing without inversion and so forth. Interestingly, recent studies in biological systems also seem to exhibit coherent processes, in particular, photosynthetic transport and avian compass.\n\nIn this dissertation, we present some of the theory and applications of the quantum coherence. This study considers (i) application of quantum coherence to enhance output signals of coherent anti-Stokes Raman spectroscopy of optically active media (chiral molecules), (ii) a way to find general formulas of single- and double-excited subradiant Dicke states using symmetry group theory, (iii) an impact of Fano-Agarwal coupling and other virtual processes arising from non-rotating wave approximation on the decay of super and subradiant timed Dicke states, and finally (iv) quantum coherence and collective phenomena of relativistically and uniformly accelerating atoms.\n\nApplications of the results presented in the dissertation may be a new method for resolving chirality of molecules using coherent anti-Stokes Raman spectroscopy - Raman optical activity, and a sidewise excitation method for single- and double-excited subradiant states. The obtained results also advance our theoretical understanding of quantum coherence specially theory of super and subradiance.
Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out for iodine (I2) in solid krypton matrices. The dependence of vibrational dephasing time on temperature and vibrational quantum number v is studied. The v dependence is approximately quadratic, while the temperature dependence of both vibrational dephasing and spectral shift, although weak, fits the exponential form characteristic of dephasing by pseudolocal phonons. The analysis of the data indicates that the frequency of the pseudolocal phonons is approximately 30 cm(-1). The longest dephasing times are observed for v = 2 being approximately 300 ps and limited by inhomogeneous broadening. An increase in the dephasing rate of v = 2 as the temperature is lowered to T = 2.6 K is taken as a clear indication of lattice-strain-induced inhomogeneity of the ensemble coherence.