Colloquium: Coherently controlled adiabatic passage

Abstract

The merging of coherent control ͑CC͒ and adiabatic passage ͑AP͒ and the type of problems that can be solved using the resulting coherently controlled adiabatic passage ͑CCAP͒ method are discussed. The discussion starts with the essence of CC as the guiding of a quantum system to arrive at a given final state via a number of different quantum pathways. The guiding is done by "tailor-made" external laser fields. Selectivity in a host of physical and chemical processes is shown to be achieved by controlling the interference between such quantum pathways. The AP process is then discussed, in which a system is navigated adiabatically along a single quantum pathway, resulting in a complete population transfer between two energy eigenstates. The merging of the two techniques ͑CCAP͒ is shown to achieve both selectivity and completeness. Application of CCAP to the solution of the nondegenerate quantum control problem is first discussed and shown that it is possible to completely transfer population from an initial wave packet of arbitrary shape, composed of a set of nondegenerate energy eigenstates, to a final arbitrary wave packet, also composed of nondegenerate states. The treatment is then extended to systems with degenerate states and shown how to induce isomerization between the broken-symmetry local minima of a Jahn-Teller Al 3 O molecule. These approaches can be further generalized to situations with many initial, intermediate, and final states and applied to quantum coding and decoding problems. CCAP is then applied to cyclic population transfer ͑CPT͒, induced by coupling three states of a chiral molecule in a cyclic fashion, ͉1͘ ↔ ͉2͘ ↔ ͉3͘ ↔ ͉1͘. Interference between two adiabatic pathways in CPT allows for a complete population transfer, coupled with multichannel selectivity, by virtue of its phase sensitivity. CPT can be used to show the purification of mixtures of right-handed and left-handed chiral molecules. Finally, quantum-field coherent control is introduced, where CCAP is extended to the use of nonclassical light. This emerging field may be used to generate new types of entangled radiation-matter states.

Propagation of two short laser pulse trains in a Λ-type three-level medium under conditions of electromagnetically induced transparency

“…(5)- (11). We consider realistic values for the atomic and lasers parameters and represent the propagation length in units of µ p ζ which is the so-called optical depth [18].…”

“…Now, we solve the coupled differential Eqs. (5)-(7), (10) and (11) for the atoms and laser fields with arbitrary temporal shapes and field strengths. This is a complicated mathematical problem and there is no analytical solution for the general case.…”

“…Recently it has been shown that the accumulation ef-fects of coherence by a laser pulse train play an important role for coherent control of atomic or molecular systems [9,10]. The use of a chirped laser pulse train is another way for coherent control of population transfer [11]. Recent advances of laser technology allows us to actively control the amplitude and phase of the laser field from pulse to pulse, and the application of such techniques to a frequency-comb laser irradiated to a Λ-type molecule results in a robust population transfer [12].…”

Robust coherent superposition of states using quasiadiabatic inverse engineering

“…[1,2,3,4,5,6] An important class of coherent manipulation involves the production of robust superpositions of states [7,8,9]. For two-level systems, there are several techniques for coherent manipulation of the states of a quantum system, for example, π-pulses [1], composite pulses [10,11,12,13], optimal control theory (OCT) techniques [14,15], and adiabatic techniques [3,6,16].…”

Trichromatic π-Pulse for Ultrafast Total Inversion of a Four-Level Ladder System

“…Several techniques have been reported for control of population transfer between a pair of quantum states involving multiphoton transitions, such as spectral shaping of the fields illuminating the medium [4,5], adiabatic methods [6][7][8][9] and π-pulse polychromatic control [10][11][12][13].…”