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This Rapid Communication presents a fast-kick-off search algorithm for quickly finding optimal control fields in the state-to-state transition probability control problems, especially those with poorly chosen initial control fields. The algorithm is based on a recently formulated monotonically convergent scheme [T.-S. Ho and H. Rabitz, Phys. Rev. E 82, 026703 (2010)]. Specifically, the local temporal refinement of the control field at each iteration is weighted by a fractional inverse power of the instantaneous overlap of the backward-propagating wave function, associated with the target state and the control field from the previous iteration, and the forward-propagating wave function, associated with the initial state and the concurrently refining control field. Extensive numerical simulations for controls of vibrational transitions and ultrafast electron tunneling show that the new algorithm not only greatly improves the search efficiency but also is able to attain good monotonic convergence quality when further frequency constraints are required. The algorithm is particularly effective when the corresponding control dynamics involves a large number of energy levels or ultrashort control pulses. Quantum control problems are generally concerned with finding optimal control fields that maximize some physical objectives. A common quantum control objective is to drive a quantum system from a given initial state to a final state that maximizes the corresponding transition probability [1,2]. In recent years, much progress in the quantum control study has been made by drawing on powerful computers and state-of-the-art laser-pulse-shaping technologies [3], as well as optimal control theory [4][5][6][7][8]. Computationally, two key issues are usually encountered for solving optimal quantum control problems: (1) to find optimal control fields numerically and (2) to impose necessary frequency constraints on the calculated control fields. The former may require numerous iterations for solving the corresponding time-dependent Schrödinger equations, especially when starting with poorly chosen initial control fields (which often occurs when involving large numbers of energy levels or ultrashort control pulses), rendering it computationally formidable, whereas the latter usually requires frequency filtering at the end of each iteration, becoming detrimental to search effort.The first issue has typically been addressed by invoking various conventional optimization schemes, including conjugategradient and quasi-Newtonian methods [9], and, especially, a class of monotonically convergent algorithms specifically formulated for optimal quantum control problems. The existing monotonically convergent approaches include the well-known Krotov method [10,11], Zhu-Rabitz method [12,13], MadayTurinici method [14], and a recently formulated two-point boundary-value quantum control paradigm (TBQCP) method based on the local control theory [15][16][17]. These monotonically convergent methods, especially the TBQCP-based schemes [16], allow fo...

Recently, single-cycle THz pulses have been demonstrated in the laboratory to successfully induce field-free orientation in gas-phase polar molecules at room temperature [Phys. Rev. Lett. 107, 163603 (2011)]. In this paper, we examine the maximum attainable field-free molecular orientation with optimally shaped linearly polarized near-single-cycle THz laser pulses of a thermal ensemble. Large-scale benchmark optimal control simulations are performed, including rotational energy levels with the rotational quantum numbers up to J = 100 for OCS linear molecules. The simulations are made possible by an extension of the recently formulated fast search algorithm, the two-point boundary-value quantum control paradigm, to the mixed-states optimal control problems in the present work. It is shown that a very high degree of field-free orientation can be achieved by strong, optimally shaped near-single-cycle THz pulses. The extensive numerical simulations showed that the maximum attainable J -dependent field-free orientation (equal to 0.714 for J = 60 and 0.837 for J = 100 at 100 K) in the near-single-cycle THz pulse region is close to 92% of the corresponding optimal bound that can be attained by arbitrarily long pulses. It is also found that a smaller amplitude for the optimal control field corresponds to a smaller J (e.g., ≈ 0.005 a.u. for J = 60 and ≈ 0.01 a.u. for J = 100) in the model simulations. The latter finding may underline the actual experimental performance of the field-free molecular orientation, since presently the available amplitude of single-cycle THz pulses can only reach slightly beyond 20 MV/cm (≈0.0038 a.u.).

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