We analyze the dynamics of a molecular field incoherently pumped by the photoassociation of fermionic atoms and coupled by quantum tunneling in a double-well potential. The relative phase distribution of the molecular modes in each well and their phase coherence are shown to build up owing to quantum-mechanical fluctuations starting from the vacuum state. We identify three qualitatively different steady-state phase distributions, depending on the ratio of the molecule-molecule interaction strength to interwell tunneling, and examine the crossover from a phase-coherent regime to a phase-incoherent regime as this ratio increases.
We analyze the dynamics of a molecular field incoherently pumped by the photoassociation of fermionic atoms and coupled by quantum tunneling in a double-well potential. The relative phase distribution of the molecular modes in each well and their phase coherence are shown to build up owing to quantum-mechanical fluctuations starting from the vacuum state. We identify three qualitatively different steady-state phase distributions, depending on the ratio of the molecule-molecule interaction strength to interwell tunneling, and examine the crossover from a phase-coherent regime to a phase-incoherent regime as this ratio increases.
We numerically investigate quantum dynamics in a one-dimensional double-well system emphasizing influence of a parametrically polychromatic perturbation on the dynamics. It is found that time dependence of transition probability for an initially localized wave packet between the wells shows two types of motion, coherent and incoherent motion, depending on the perturbation parameters. As the strength and/or the number of frequency components of the perturbation increase, coherent motion changes into incoherent one. The former is related to coherent tunneling of the wave packet due to coherence; the latter is related to a delocalized state caused by decoherence. In coherent motion, by virtue of coherence of the dynamics, the expectation value and the standard deviation of a dynamical variable such as the energy of the system show oscillatory time dependence around the initial values. On the contrary in incoherent motion, because of the decoherence, the time dependence fluctuates irregularly around a certain value after a rapid increase due to the resonance. We find that negativity of the Wigner function also show similar time dependence in each type of motion. We compare the classification of the quantum dynamics based on regularity of the time dependence with the one of corresponding classical dynamics based on the Lyapunov exponent. The classifications of the quantum and classical dynamics overlap well in the parameter space. Furthermore, we confirm decoherence of quantum dynamics in a kicked double-well system.
Wave-mechanical phenomena such as resonance and interference, in both light and matter, are central to the principles of quantum coherent control over molecular processes. Focusing on the dynamical aspects, this dissertation is a compilation of studies on the interaction physics involving wave packets in molecules, the driving light field, and the underlying coherence and control. In each work, we will demonstrate interesting correlations between the properties of a carefully designed excitation light field and desirable outcomes of the molecules quantum dynamics. We will analyze the dynamical effect of a Feshbach resonance in the adiabatic Raman photoassociation for ultracold diatomic molecule formation from ultracold atoms. A narrow resonance is shown to be able to increase the effective number of collisions, in an ultracold atomic gas, that are available for photoassociation. This results in an optimal resonance width much smaller than the atomic collision energy bandwidth, due to the balance between the effective collision rate and single-collision transfer probability. Next, we demonstrate the linear molecular response to high-intensity, broadband, shaped optical fields. We show that this originates from interferences based on intra-pulse Raman excitations, and thus response linearity is not unique to the first-order perturbative limit and can not be used to infer the strength of the field. In the last study, we simulate the stochastic vibrational wave packet and dissociation-flux dynamics in a molecule excited by light with temporal and spectral incoherent properties. Between this case and that using a coherent pulse with the same spectral profile, we compare the vibrational wave functions and the loss of electronic and vibrational coherence, and demonstrate the qualitative difference between coherently and incoherently driven dynamics in molecules.
We investigate coherent and incoherent tunneling phenomena in conditions of crossing diabatic potentials. We consider a model of two crossing parabolic diabatic potentials with an independent of coordinates constant adiabatic coupling. As a result of the coupling and level crossing avoiding, we get the asymmetric double-well lower adiabatic potential with a variable shape. We show that the doublet structure of levels (generic for double-well potentials) is remained valid as long as the transition matrix element is smaller than characteristic inter-level spacings (the latter ones in own turn decrease upon increasing of a difference between the diabatic potential minima). In the adiabatic limit the tunneling transitions do not depend on the upper potential. In the over-barrier energy region there is an oscillating behavior due to the resonances between the states in the lower and in the upper adiabatic potentials. A new phenomenom emanated from this oscillating dependence namely, multiple coherent - incoherent regime transitions for the upper adiabatic potential state evolution, is our main concern in this paper. The problem is not only of intellectual interest but also of relevance to various molecular systems undergoing conversion of electronic states or isomerization reactions. Our model exhausts all cases practically relevant for spectroscopy of non-rigid molecules, and can capture many of the features exhibited by experiment.
Abstract We investigate the dynamical phase transition of two-component Bose–Einstein condensate with nonlinear tunneling, which is trapped inside a double-well and dispersively coupled to a single mode of a high-finesse optical cavity with one moving end mirror driven by a single mode standing field. In the mean-field approximation, the Hamiltonian of the system with nonlinear tunneling is characterized by the population difference of the particles and relative phase in double wells. The characteristics of the system’s stability points are determined by the corresponding Hessian matrices. However, the number of the system’s stability points depends on the roots of the first derivative of the energy. In the absence of the nonlinearity, the Hamiltonian of the system is a binary quadratic equation. When there is nonlinear tunneling, the Hamiltonian of the system is a binary quartic equation. Therefore, from a mathematical point of view, it can be found that the roots of the equation will increase, which means that the number of stability points in the system will increase. We also build the phase portrait from classical analysis. Considering the strong pair tunneling case, we confirm that nonlinear tunneling interaction leads to an increment of stability points and enriches the phase diagram of the system. We further analyze the phase portrait with the moving end mirror. It is shown that the semiclassical dynamics of the system undergoes a bifurcation of stability points with an increase in the coupling strength or detuning. In other words, the system experiences a phase transition.
One of the most pertinent problems in the debate on non-trivial quantum effects in biology concerns natural photosynthesis. Since sunlight is composed of thermal photons, it was argued to be unable to induce quantum coherence in matter, and that quantum mechanics is therefore irrelevant for the dynamical processes following photoabsorption. Our present analysis of a toy 'molecular aggregate'—composed of two dipole–dipole interacting two-level atoms treated as an open quantum system—however shows that incoherent excitations indeed can trigger persistent, coherent dynamics in both the site and the exciton bases: we demonstrate that collective decay processes induced by the dipole–dipole interactions create coherent intermolecular transport—regardless of the coherence properties of the incoming radiation. Our analysis shows that the steady state coherence is mediated by the population imbalance between the molecules and, therefore, increases with the energy difference between the two-level atoms. Our results establish the importance of collective decay processes in the study of ultrafast photophysics, and especially their potential role to generate stationary coherence in incoherently driven quantum transport.
We study the effect of atom-molecule internal tunneling on the ground state of atom-molecule Bose-Einstein condensates in a double-well potential. In the absence of internal tunneling between atomic and molecular states, the ground state is symmetric, which has equal-particle populations in two wells. From the linear stability analysis, we show that the symmetric stationary state becomes dynamically unstable at a certain value of the atom-molecule internal tunneling strength. Above the critical value of the internal tunneling strength, the ground state bifurcates to the particle-localized ground states. The origin of this transition can be attributed to the effective attractive interatomic interaction induced by the atom-molecule internal tunneling. This effective interaction is similar to that familiar in the context of BCS-BEC crossover in a Fermi gas with Feshbach resonance. Furthermore, we point out the possibility of reentrant transition in the case of the large detuning between the atomic and molecular states.