Initial state laser control of curve-crossing reactions using the Rayleigh–Ritz variational procedure

Abstract

A new two-step procedure for laser control of photodissociation is presented. In the first step of the procedure, we show that control of photodissociation product yields can be exerted through preparation of the initial wave function prior to application of the photodissociation field in contrast to previous laser control studies where attention has focused on the design of the field which induces dissociation. Specifically, for a chosen channel from which maximum product yield is desired and a given photodissociation field, the optimal linear combination of vibrational eigenstates which comprise the initial wave function is found using a straightforward variational calculation. Any photodissociation pulse shape and amplitude can be assumed since the Schrödinger equation is solved directly. Application of this method to control of product yields in the photodissociation of hydrogen iodide is demonstrated. The second step of the control procedure involves the preparation of the coherent superposition of discrete levels obtained from the previous step; design of the preparatory field can be done analytically for two or three level systems as demonstrated here or with other well-studied iterative field design methods.

Photodynamic control using field optimized initial state: A mechanistic investigation of selective control with application to IBr and HI photodissociation

“…Since the initial vibrational state which is subjected to photolysis is critical in determining the photodissociation products, it is reasonable to expect an appropriately optimized linear superposition of these vibrational eigenstates to serve as a better initial condition for selective maximization of the desired product. Towards this end, a scheme to establish the optimal linear mix of the field free vibrational eigenstates for the given photolysis pulse and chosen photodissociation objective has been pursued in our group 20,21 whereby, the emphasis is shifted from control through design of an appropriate field, to control through the design of an optimal linear combination of the field free vibrational eigenstates for the chosen photolysis pulse. Applications of field optimized initial state ͑FOIST͒ based selective control to HI 20 and IBr 21 have successfully identified the optimal linear combinations for multicolor continuous wave ͑cw͒ and Gaussian fields of different intensities, frequencies, and phase differences and considerable enhancement in selectivity and product yield using these field optimized initial states has been demonstrated.…”

“…Applications of field optimized initial state ͑FOIST͒ based selective control to HI 20 and IBr 21 have successfully identified the optimal linear combinations for multicolor continuous wave ͑cw͒ and Gaussian fields of different intensities, frequencies, and phase differences and considerable enhancement in selectivity and product yield using these field optimized initial states has been demonstrated. 20,21 The optimal combinations depend on the choice of the photodissociation objective, i.e., the linear combination which will maximize flux out of the IϩBr( 2 P 3/2 ) in the IBr differs markedly from that which will maximize flux out of the excited IϩBr*( 2 P 1/2 ) channel. 21 Similar considerations hold in the photodissociation of HI as well.…”

“…b͒ Electronic mail: mmishra@chem.iitb.ernet.in of this article. The results to be discussed are an attempt to search for simplifying features so that the onus for selective control of chemical reactions does not lie entirely on the laser fields which thereby may come out to be complicated 26 but the task of selective control is split into different parts 20,21 which could be comparatively easier to realize in ordinary laboratory conditions.…”

“…21 Similar considerations hold in the photodissociation of HI as well. 20 The FOIST scheme achieves selective flux maximization by altering the spatial profile of the initial state to be subjected to the photolysis pulse and since changes in flux are due to the flow of probability density, it is our purpose here to analyze the probability density profiles of the optimal superpositions to try and isolate the mechanistic features which may be responsible for selective control. These optimal linear combinations being field specific, a comprehensive analysis will require the optimizations to be carried out and the structural features of the optimal initial state to be analyzed for a sufficiently large number of field parameters.…”

“…Towards this end, a scheme to establish the optimal linear mix of the field free vibrational eigenstates for the given photolysis pulse and chosen photodissociation objective has been pursued in our group 20,21 whereby, the emphasis is shifted from control through design of an appropriate field, to control through the design of an optimal linear combination of the field free vibrational eigenstates for the chosen photolysis pulse. Applications of field optimized initial state ͑FOIST͒ based selective control to HI 20 and IBr 21 have successfully identified the optimal linear combinations for multicolor continuous wave ͑cw͒ and Gaussian fields of different intensities, frequencies, and phase differences and considerable enhancement in selectivity and product yield using these field optimized initial states has been demonstrated. 20,21 The optimal combinations depend on the choice of the photodissociation objective, i.e., the linear combination which will maximize flux out of the IϩBr( 2 P 3/2 ) in the IBr differs markedly from that which will maximize flux out of the excited IϩBr*( 2 P 1/2 ) channel.…”