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IEEE International Workshop on Workload Characterization (WWC)

Laser control of quantum dynamics

Pavel A. Golovinski, P. V. Ryasnoi, V.M. Nazarov

Published Apr 23, 2004• 9 citations
Publisher

Abstract

The concept of ultrafast optimal control based on Schrodinger equation is developed for quantum systems. General properties of optimal dynamics are illustrated by computer simulation for two-level system and Morse potential. A number of maximums for transition probability are realized for different contributions of laser pulse parameters.

DOI
10.1109/phycon.2003.1237013

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The concept of ultrafast optimal control based on Schrodinger equation is developed for quantum systems. General properties of optimal dynamics are illustrated by computer simulation for two-level system and Morse potential. A number of maximums for transition probability are realized for different contributions of laser pulse parameters.
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.
A scheme of designing laser pulses for controlling discrete quantum states has been proposed, relying on the recently developed highly accurate Maxwell-Schr\"odinger hybrid simulation. A single electron confined in a quasi-one-dimensional nanoscale potential well has been used as an illustrative example and a control pulse transferring completely the probability density from the ground state to the first excited state has been designed by the present Maxwell-Schr\"odinger hybrid scheme and by the conventional one that solves the time-dependent Schr\"odinger equation only without accounting for feedback from the electron system to the external electromagnetic field. The resultant pulses obtained by these two methods can be different largely owing to the modification of the laser field by the locally strong radiation from the excited electron. The present study demonstrates that light control pulses designed by the conventional method may need to be rectified for practical implementation in experiments.
Coherent carrier control in quantum nanostructures is studied within the framework of optimal control. We develop a general solution scheme for the optimization of an external control (e.g., lasers pulses), which allows to channel the system's wave function between two given states in its most efficient way; physically motivated constraints, such as limited laser resources or population suppression of certain states, can be accounted for through a general cost functional. Using a generic three-level scheme for the quantum system, we demonstrate the applicability of our approach and identify the pertinent calculation and convergence parameters.