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The Journal of Chemical Physics

External field control of condensed phase reactions

Peter Groß, Steven D. Schwartz

Published Sep 22, 1998• 12 citations
Publisher

Abstract

Control of tunneling in a symmetric double well coupled to a bath via an external field is demonstrated. Optimal control theory is employed to design a laser field which couples to the reaction coordinate and drives a localized wave packet on the reactant side to the product side at a specified target time τ. Both a very quantumlike system (high barrier) and a low barrier double well are examined; excellent results are obtained for a range of reduced bath viscosities. Analysis of the control fields and corresponding localization dynamics shows that the frequency components of the control field are more or less in resonance with eigenstates of the double well and that the laser field enhances the natural dynamics of the individual wells. Future extension to more complicated models where the field couples to the bath is discussed.

DOI
10.1063/1.477095

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Control of tunneling in a symmetric double well coupled to a bath via an external field is demonstrated. Optimal control theory is employed to design a laser field which couples to the reaction coordinate and drives a localized wave packet on the reactant side to the product side at a specified target time τ. Both a very quantumlike system (high barrier) and a low barrier double well are examined; excellent results are obtained for a range of reduced bath viscosities. Analysis of the control fields and corresponding localization dynamics shows that the frequency components of the control field are more or less in resonance with eigenstates of the double well and that the laser field enhances the natural dynamics of the individual wells. Future extension to more complicated models where the field couples to the bath is discussed.
We show that a field of frequency omega combined with its second harmonic 2omega driving a double-well potential allows us to localize the wave packet by adiabatic passage, starting from the delocalized ground state. The relative phase of the fields allows us to choose the well of localization. We can suppress (and restore) the tunneling subsequently by switching on (and off) abruptly the fields at well-defined times. The mechanism relies on the fact that the dynamics is driven to an eigenstate of the Floquet Hamiltonian which is a localized state.
We investigate the coherent control of a single particle held in a quartic double well with a symmetric or asymmetric driving and exhibit time evolutions of relative probability of the particle in one of the double-well wells. It is shown analytically and numerically that the coherent destruction of tunneling could occur only for the symmetric intense driving, and application of the asymmetric sawtooth driving leads to an increase in the tunneling rate. The results agree with the recent experimental data reported by Kierig et al. [Phys. Rev. Lett. 100, 190405 (2008)]. We also exhibit the effect of multiple photon resonances on the tunneling through a dc field. Finally, we demonstrate a connection between the classically chaotic barrier crossing and quantum tunneling numerically.
A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the nonperturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum ZZZ gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significantly is a multicomponent low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.
The aim to control the internal and external degrees of freedom of quantum systems is of great interest for many fields of physics and chemistry. One opportunity to realize such a coherent control is provided by strong, time depended, external fields. In this work the experimental realization of a model-system is presented. The coherent control of the tunneling dynamics of single atoms by means of a time-periodic, external field is demonstrated. Depending on the parameters of the driving force the tunneling rate can be varied up to a total suppression of the tunneling process in the extreme. This type of dynamical localization is known as "coherent destruction of tunneling". The experimental setup allows a direct access to the tunneling dynamics of single atoms in a double well structure and enables great freedom concerning the parameters. Not only the double well potential, the driving frequency and the driving amplitude can be varied, but also the temporal and spatial symmetry of the driving. A coherent beam of slow, metastable argon atoms serves as source of particles, which can be detected spatially resolved enabling the direct observation of the tunneling dynamics in momentum space.