Optimal control of molecular rotation in the sudden limit

Abstract

1047highest probability via direct collisional activation at high translational energies (So > 0.01 for EN > 65 kJ/mol) rather than via trapping or precursor mediated-processes at low incident translational energies (ET < 40 kJ/mol).Optimal control theory is introduced for the control of quantum molecular rotational excitations induced by electric fields. Particular emphasis is given to the case where the electric field pulse is sufficiently short (-1 ps) so that the sudden approximation can be made. Co:isequently, the time evolution of the rotational wave functions can be obtained analytically for general molecular rotations. A hyperbolic curve is shown to explicitly describe the relationship between the rotational energy and the action integral, x ( T ) = JrdSc(t) dt where d is the molecular permanent dipole moment, S the direction cosine matrix, and c ( r ) the applied electric field over time [0, r ] . For the case that the control cost functional has the form Q = F(x(T)) + /3.frc2(t) dt, it is found that the optimal fields are constant in time. The controllability of both rotational energy and transition probability is investigated. A detailed discussion on properties of the optimal fields, as well as the initial and final rotational states, is presented. Numerical calculations are performed for the molecule CsF.

Robust optimal control of quantum molecular systems in the presence of disturbances and uncertainties

“…(11)and the formal solutions of Eqs. (11) and (13) in these particular cases. The formal solutions may not be needed in a fully numerical computation, however, they provide a basis for further analytical approximations as developed in Sec.…”

“…We have from Eq. (11) A. Constraint on the total integrated fluence of the disturbance Here, the constraint is expressed as…”

“…(11) and (14) (taking into account that p is a constant now and G is a functional of w), we have 5J' (16) with c0 being a specific constant. Note that if w is only a function of x (or t), the integration in (14) will be only over x (or t).…”

“…Recent developments in molecular optimal control theory have shown promise for controlling molecular motion by specifically designed laser pulses [1][2][3][4][5][6][7][8][9][10][11][12]. It has been found that a molecule can be transformed into a prescribed state by a designed laser fieldthe so-called controller.…”

Ab initio design of picosecond infrared laser pulses for controlling vibrational-rotational excitation of CO molecules

“…Peirce et al 8,9 subsequently introduced the ideas of optimal control theory coupled with the concept of a "closed loop" or feedback mechanism. 10,11 These ideas have led to a large number of successful experimental applications [12][13][14][15][16][17][18][19][20][21][22][23][24] and also a substantial number of theoretical papers [25][26][27][28][29][30][31][32][33][34][35] in which optimal control theory is used to design laser pulses to achieve predetermined chemical objectives.…”