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The Journal of Chemical Physics

Pump-dump control and the related transient absorption spectroscopies

Zhenwen Shen, YiJing Yan, Ji‐Xin Cheng, Feng Shuang, Yi Zhao, Guo‐Zhong He

Published Apr 15, 1999• 21 citations
Publisher

Abstract

We combine theories of optimal pump-dump control and the related transient probe absorption spectroscopy in order to elucidate the relation between these two optical processes and the possibility of experimental realization. In the weak response regime, we identify the globally optimal pair of pump-dump control fields, and further propose a second-order difference detection scheme to monitor the wave packets dynamics that is jointly controlled by both the pump and dump fields. The globally optimal solution serves also as the initial input for the iterative search for the optimal control fields in the strong response regime. We use a model I2 molecule to demonstrate numerically the pump-dump control and the detection of a highly vibrationally excited wave packet focusing dynamics on the ground X surface in both the weak and strong response regimes. The I2B surface serves as the intermediate to assist the pump-dump control and the optical detection processes. Demonstrated in the strong response regime are the optimal pair of pump-dump molecular-π pulses that invert nearly total population onto the predefined target region within a half period of vibration motion.

DOI
10.1063/1.478623

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Physical Review A•Sep 23, 2010•1 citation
We combine theories of optimal pump-dump control and the related transient probe absorption spectroscopy in order to elucidate the relation between these two optical processes and the possibility of experimental realization. In the weak response regime, we identify the globally optimal pair of pump-dump control fields, and further propose a second-order difference detection scheme to monitor the wave packets dynamics that is jointly controlled by both the pump and dump fields. The globally optimal solution serves also as the initial input for the iterative search for the optimal control fields in the strong response regime. We use a model I2 molecule to demonstrate numerically the pump-dump control and the detection of a highly vibrationally excited wave packet focusing dynamics on the ground X surface in both the weak and strong response regimes. The I2B surface serves as the intermediate to assist the pump-dump control and the optical detection processes. Demonstrated in the strong response regime are the optimal pair of pump-dump molecular-π pulses that invert nearly total population onto the predefined target region within a half period of vibration motion.
A generalized eigenequation is derived for the optimal pairs of phase-unlocked pump-dump fields in the control of pure state molecular systems in the weak response regime. The associated eigenvalues are further correlated to the yields of pump-dump control, thus the globally optimal pair of phase-unlocked pump-dump fields is identified unambiguously. Presented is also a hierarchy of reduction from the general Liouville-space density matrix control formulation in the strong response regime to various linearized control equations in the weak response regime. Application to the control of a molecular ro-vibronic level in the ground electronic surface reveals a novel symmetry relation between the optimal pump field and its counterpart of the optimal dump field.
Quantum optimal control theory is applied to find optimal pulses for controlling the motion of an ion and a molecule for two different applications. Those optimal pulses enable the control of the dynamics of the system by driving the atom or the molecule from an initial state to desired states.The evolution equations obtained by means of the quantum optimal control theory are resolved iteratively using a monotonic convergent algorithm. A number of simulation parameters are varied in order to get the optimal pulses including the duration of the pulses, the time step of the time grid, a penalty factor that limits the maximal intensity of the fields, and a guess pulse which is used to start the optimal control.The optimal pulses obtained for each application are analyzed by Fourier transform, and also by looking at the time evolution of the populations that they generate in the system.The first application is the preparation of specific vibrational states of acetylene that are usually not reachable from the ground state, and that would remain unpopulated by usual spectroscopy. Relevant state energies and transition dipole moments are extracted from the experimental literature and especially from the global acetylene Hamiltonian conferring an uncommon precision to the control simulation. The control starts from the ground state. The target states belongs to the polyad Ns=1, Nr=5 of acetylene which includes two vibrational dark states and one vibrational bright state. First, the simulation is performed with the Schrödinger equation and in a second step, with the Liouville--von Neumann equation, as mixed states are prepared. Indeed, the control starts from a Boltzmann distribution of population in the rotational levels of the vibrational ground state chosen in order to simulate an experimental condition. But the distribution is truncated to limit the computational effort. One of the dark states appears to be a potential target for a realistic experimental investigation because the average population of the Rabi oscillation remains high and decoherence is expected to be weak. The optimal pulses obtained have a high fidelity, have a spectrum with well-resolved peak frequencies, and their experimental feasibility seems achievable within the current abilities of experimental laboratories.The second application is to propose an experimental realization of a microscopic physical device able to simulate quantum dynamics. The idea is to use the motional states of a Cd^+ ion trapped in an anharmonic potential to realize a quantum dynamics simulator of a single-particle Schrödinger equation. In this way, the motional states store the information and the optimal pulse manipulates this information to realize operations. In the present case, the simulated dynamics was the propagation of a wave packet in a harmonic potential. Starting from an initial quantum state, the pulse acts on the system to modify the motional states of the ion in such a way that the final superposition of motional states corresponds to the results of the dynamics. This simulation is performed with the Liouville--von Neumann equation and also with the Lindblad equation as dissipation is included to test the robustness of the pulse against perturbations of the potential. The optimal pulses that are obtained have a high fidelity which shows that the ion trap system has correctly realized the quantum dynamics simulation. The optimal pulses are valid for any initial condition if the potential of the simulation or the mass of the propagated wave packet is unchanged.
In a model system, i.e. the K2 dimer molecule, a vibrationally excited wave packet around a prechosen target state in the electronic ground state is generated by an ultrafast resonant stimulated Raman process. By choosing the pump and dump wavelengths along the difference potential between the excited electronic |B〉-state and the electronic ground state |X〉 and optimizing the delay time between the pump and dump processes, one can increase considerably the efficiency of the population transfer of this quantum control experiment. Copyright © 2000 John Wiley & Sons, Ltd.
The free motion of a nonstationary vibrational wave packet in an electronic potential is a source of interesting quantum properties. In this work we propose an iterative scheme that allows continuous stretching and squeezing of a wave packet in the ground or in an excited electronic state, by switching the wave function between both potentials with pi pulses at certain times. Using a simple model of displaced harmonic oscillators and delta pulses, we derive the analytical solution and the conditions for its possible implementation and optimization in different molecules and electronic states. We show that the main constraining parameter is the pulse bandwidth. Although in principle the degree of squeezing (or stretching) is not bounded, the physical resources increase quadratically with the number of iterations, while the achieved squeezing only increases linearly.
Iterative vibrational wave packet squeezing by a sequence of femtosecond pulses is proposed. Analytic formulas are derived for the harmonic oscillator case, and the practical implementation of the scheme is tested on different electronic transitions in Rb2{\mathrm{Rb}}_{2}Rb2​.
An excitation scheme is proposed for transferring population between ground-vibrational levels of a molecule. The transfer is accomplished by pumping and dumping population with a pair of coherent ultrashort-pulse trains via a stationary state. By mismatching the teeth of the frequency combs associated with the pulse trains to the vibrational levels, high selectivity in the excitation, along with high transfer efficiency, is predicted. The pump-dump scheme does not suffer from spontaneous emission losses, it is insensitive to the pump-dump-train delay, and it requires only basic pulse shaping.