Laser-controlled ultrafast state-selective vibrational dynamics of diatomic molecules, which are coupled to an unobserved quasiresonant environment is investigated using the reduced density-matrix formalism beyond and within a Markov-type approximation. Dissipative quantum dynamics in a classical electric field of shaped infrared ultrashort laser pulses is simulated for a one-dimensional nondissociative Morse oscillator, representing the local OH bond in the ${\mathrm{H}}_{2}$ O and HOD molecules in the electronic ground state. Localization of population at a prescribed vibrational target level of OH up to v=10 with probability of about 90% is demonstrated on a picosecond time scale, while the strength of the quasiresonant molecule-environment coupling results in subpicosecond lifetimes of the vibrational states. The laser-controlled stabilization of selective excitation in the restricted set of vibrational states against a background of strongly diminished relaxation to lower vibrational states is also shown. The laser-control scheme may include a superposition of several laser pulses. A Markov-type approximation results in slightly increased lifetimes of the vibrational states, along with decreased predicted probability of state-selective excitation of a molecule by about 20--30%. Several results obtained within the fourth-order perturbation theory in interaction of a molecule with an environment are in a good agreement with the non-Markov analysis.
Laser-controlled ultrafast state-selective vibrational dynamics of diatomic molecules, which are coupled to an unobserved quasiresonant environment is investigated using the reduced density-matrix formalism beyond and within a Markov-type approximation. Dissipative quantum dynamics in a classical electric field of shaped infrared ultrashort laser pulses is simulated for a one-dimensional nondissociative Morse oscillator, representing the local OH bond in the H2 O and HOD molecules in the electronic ground state. Localization of population at a prescribed vibrational target level of OH up to v=10 with probability of about 90% is demonstrated on a picosecond time scale, while the strength of the quasiresonant molecule-environment coupling results in subpicosecond lifetimes of the vibrational states. The laser-controlled stabilization of selective excitation in the restricted set of vibrational states against a background of strongly diminished relaxation to lower vibrational states is also shown. The laser-control scheme may include a superposition of several laser pulses. A Markov-type approximation results in slightly increased lifetimes of the vibrational states, along with decreased predicted probability of state-selective excitation of a molecule by about 20--30%. Several results obtained within the fourth-order perturbation theory in interaction of a molecule with an environment are in a good agreement with the non-Markov analysis.
We study the dynamics of two-photon nonresonant electronic excitation of diatomic molecules driven by chirped pulses. While the majority of the experimental results address the role of the chirp for fixed pulse bandwidth, we analyze the possibility of selective excitation for fixed time, as a function of the pulse bandwidth, depending on the sign of the chirp. With strong picosecond pulses and positive chirp it is shown that the dynamics always prepare the molecule in the ground vibrational level of the excited electronic state. The robustness of the dynamics inherits the properties of an effective Landau–Zener crossing. For negative chirp the final state is very sensitive to the specific pulse bandwidth. The dynamics of the system follow a complex convoluted behavior, and the final state alternates between low vibrational levels of the excited electronic state and excited vibrational levels of the ground potential, which become increasingly more excited with increasing bandwidth. The final electronic populations follow a double-period oscillatory behavior. We present a model based on sequential independent crossings which correlates the long-oscillation period with changes in the final vibrational state selected. We show that the short-oscillation period is related with nonadiabatic effects that give rise to fast dynamic Rabi flipping between the electronic states, providing only information of the field–molecule effective coupling. Although the short-oscillation period partially masks the expected results of the final populations, we show that it is still possible to retrieve information from the long-oscillation period regarding the frequencies of the electronic potentials. In order to do so, or in order to control the outcome of the dynamics, it is necessary to perform experiments scanning very different pulse bandwidths, and we propose a possible experimental implementation. All the numerical results of the paper are calculated for a model of the Na2 dimer.
We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much more advantageous scaling of the computational cost with respect to the increase of the dimensionality of the system. The factorizable method is found to provide an accurate description of the dissipative quantum dynamics of the model system, specifically of the time evolution of the state populations and of the probability density distribution of the molecular wave packet. The influence of intra-molecular vibrational energy redistribution appears to be properly taken into account by the new model on the whole range of coupling strengths. It demontrates that most of the mode mixing during relaxation is due to the potential part of the Hamiltonian and not to the coupling among relaxation operators.
We have studied quantum-mechanical behavior of a driven Morse oscillator coupled to a bath of harmonic oscillators. The purpose is to compare the quantum behavior of such a system with the classical solutions of a driven damped Morse oscillator. We start with the quantum Liouville equation, in which the Hamiltonian of the Morse oscillator is expressed in terms of generators of an su(2) Lie algebra. This algebra and the Markovian approximation allow us to derive the generalized master equation (for the reduced density matrix of the Morse oscillator), which contains level-dependent energy and phase relaxation terms. We have numerically integrated the differential equations of the matrix elements to obtain the time evolution of the reduced density matrix and the energy of the Morse oscillator. We show that the energy of the Morse oscillator in general varies with time and eventually reaches an asymptotic oscillatory state. The mean energy value of the asymptotic oscillatory state is studied as a function of the relaxation rates and laser frequency and amplitude. Vibrational distributions have also been found as functions of laser frequency and amplitude. The shape of the distribution changes gradually as laser amplitude increases; it first peaks at the ground state at a small field amplitude, then it peaks at some excited state at a large field amplitude, and for an amplitude in between it can have two maxima. This bimodal vibrational distribution reflects the bistability observed in the classical and semiclassical models. Thus bistability exists in quantum results, not as a hysteresis loop, but as a bimodal distribution. Finally, we show that as laser intensity increases, the time series of the oscillator energy evolves from regular to quasiperiodic behavior, and eventually a chaotic-looking series appears.
The dynamics of populations of the vibrational states in a NO molecule (one-photon absorption) and of the electronic states in a 4,4'-bis(dimethylamino) stilbene molecule (two-photon absorption) is studied versus the frequency, intensity and shape of the laser pulse. We show that specially designed infrared laser pulses can build selective populations of certain vibrational states. A detuning of light frequency from the vibrational resonance qualitatively changes the dynamics of populations. It is found out that the populations of the nonresonant levels follow the pulse shape adiabatically if the detuning significantly exceeds the inverse characteristic time of the change of the pulse. Depopulation of the nonresonant vibrational states leads to a high population of the resonant state at the end of the pulse. Complete breakdown of the standard rotating wave approximation for a two-photon absorption process is observed even for a rather small intensity of the laser pulse. An analytical solution for the interaction of a pulse with a three-level system beyond the rotating wave approximation is obtained, and it is in close agreement with the strict numerical solution of the amplitude equations. Special attention is paid to the population dynamics of randomly oriented molecules. The orientational disorder as well as the vibrations limit the coherent population transfer. Calculations show the strong role of the anisotropy of photoexcitation in the coherent control of populations which can affect the anisotropy of photobleaching.
Any real system, no matter how well isolated, unavoidably interacts with the environment. This interaction makes the evolution of a quantum system nonunitary and destroys the coherence of quantum superpositions. This process, known as decoherence, is widely regarded as the most important and fundamental obstacle to the practical realization of quantum information processing. On the other hand, the objectives of quantum control are predicated on the ability to manipulate the system coherently over a period of time. Quantum control has been applied successfully to several experimental systems and coupling such a controlled system to an environment makes the study of coherence loss possible. The standard model of decoherence is formulated in terms of a system, defined by the observables that can be measured, and a reservoir, de¯ned by those degrees of freedom that are not accessed by observation. The vibrational and rotational degree of freedom of diatomic molecules form an experimental model of such a system and bath 1. The nature of the ro-vibrational coupling does not allow a Decoherence Free Subspace, instead we try to identify a Decoherence Resistant Subspace using closed loop control. We set up a learning control loop experiment to monitor the coherence in a vibrational wavepacket, consisting of about 6 vibrational states of the A(1Σ+g ) electronic state, excited by a shaped, ultrashort optical pulse, and then to determine the pulse shape that yielded the longest coherence lifetime. The coherence of the vibrational wavepacket was monitored by measuring the fluorescence quantum beats from the outer turning point of the wave packet's trajectory. The closed loop controller altered the shape of the driving optical pulse to maximize the the depth of modulation of the quantum beats at a prescribed time after excitation, within the constraints of the laser system. The outcome of this closed loop control experiment shows an improvement of the beat decay constant of about 60%, as shown in Fig. (1), a result which occurs for several di®erent pulse shapes. Our experiments show that a number of interesting decoherence-resistant excitations exist. The nature of the dephasing was examined theoretically. Using measured optical pulse shapes, we simulated numerically the molecular wavepacket in the limit of perturbation theory. The experiment and simulations show that there are di®erent mechanisms contributing to the decoherence resistant excitation. The shaped pulse reduces the °uctuations in the wave packet spatial extent, which in turn changes the system reservoir coupling. Other components of the optimal pulse are a sequence of pulses that creates constructive interference of the vibrational wavepacket at the desired time, and chirp which compensates for the anharmonicity of the adiabatic potential. The experimental results show general agreement with numerical simulations. We conclude that wavepackets resistant to dephasing do exist,and that learning algorithms provide an effcient means for finding them.
In this paper, I discuss the selective and efficient vibrational population transfer between electronic states of diatomic molecules by a weak, ultrashort pulse train. The spectrum of each individual pulse in the train is wide enough to simultaneously excite several vibrational levels of the molecule. However, selectivity is achieved by mismatching the frequency comb, associated with the pulse train, to the excited vibrational levels. Efficiency results from the coherent accumulation of population from one pulse in the train to the next.