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Physical Review A

Coherently controlled adiabatic passage to multiple continuum channels

Ioannis Thanopulos, Moshe Shapiro

Published Sep 1, 2006• 11 citations
Publisher

Abstract

We present a solution to the multichannel quantum control problem, where selective and complete population transfer from an initial bound state to $M$ energetically degenerate continuum channels is achieved under loss-free conditions. The control is affected by adiabatic passage proceeding via $N$ bound intermediate states, where even in the presence of real loss from these states, the control efficiency remains significant, about $40--50\phantom{\rule{0.2em}{0ex}}%$. We illustrate the viability of the method by computationally controlling the ${\mathrm{CH}}_{3}(v)+{\mathrm{I}}^{*}(^{2}P_{1∕2})\ensuremath{\leftarrow}{\mathrm{CH}}_{3}\mathrm{I}\ensuremath{\rightarrow}{\mathrm{CH}}_{3}(v)+\mathrm{I}(^{2}P_{3∕2})$ multichannel photodissociation process.

DOI
10.1103/physreva.74.031401

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We present a solution to the multichannel quantum control problem, where selective and complete population transfer from an initial bound state to MMM energetically degenerate continuum channels is achieved under loss-free conditions. The control is affected by adiabatic passage proceeding via NNN bound intermediate states, where even in the presence of real loss from these states, the control efficiency remains significant, about 40−−5040--50\phantom{\rule{0.2em}{0ex}}%40−−50. We illustrate the viability of the method by computationally controlling the CH3(v)+I∗(2P1∕2)\ensuremath←CH3I\ensuremath→CH3(v)+I(2P3∕2){\mathrm{CH}}_{3}(v)+{\mathrm{I}}^{*}(^{2}P_{1∕2})\ensuremath{\leftarrow}{\mathrm{CH}}_{3}\mathrm{I}\ensuremath{\rightarrow}{\mathrm{CH}}_{3}(v)+\mathrm{I}(^{2}P_{3∕2})CH3​(v)+I∗(2P1∕2​)\ensuremath←CH3​I\ensuremath→CH3​(v)+I(2P3∕2​) multichannel photodissociation process.
The merging of coherent control (CC) and adiabatic passage (AP) and the type of problems that can be solved using the resulting coherently controlled adiabatic passage (CCAP) 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 (CCAP) 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 Al3O{\mathrm{Al}}_{3}\mathrm{O}Al3​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 (CPT), induced by coupling three states of a chiral molecule in a cyclic fashion, $\ensuremath{\mid}1⟩\ensuremath{\leftrightarrow}\ensuremath{\mid}2⟩\ensuremath{\leftrightarrow}\ensuremath{\mid}3⟩\ensuremath{\leftrightarrow}\ensuremath{\mid}1⟩$. 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.
We present an analytic solution to the "degenerate quantum control problem," which enables the transfer of any desired fraction of population between arbitrary initial and final pure wave packets, made up of nearly degenerate energy eigenstates. It consists of two two-photon adiabatic passage steps, in which the population of the initial wave packet is first transferred, via a number of nondegenerate intermediate states, to a single eigenstate and then returned to a different target superposition state. We demonstrate the approach by executing a stepwise isomerization of three Jahn-Teller states of the Al3O molecule, where a proper optical coupling can easily be established.
We consider the optimal control problem of transferring population between states of a quantum system where the coupling proceeds only via intermediate states that are subject to decay. We pose the question whether it is generally possible to carry out this transfer. For a single intermediate decaying state, we recover the stimulated Raman adiabatic passage process, which we identify as the global optimum in the limit of infinite control time. We also present analytical solutions for the case of transfer that has to proceed via two consecutive intermediate decaying states. We show that in this case, for finite power the optimal control does not approach perfect state transfer even in the infinite time limit. We generalize our findings to characterize the topologies of paths that can be achieved by coherent control under the assumption of finite power. If two or more consecutive states in an NNN-level chain are subject to decay, complete population transfer with finite-power controls is not possible.
We propose a selective, efficient, and robust way to realize control of coherent population transfer in a $\ensuremath{\Lambda}$-type four-level system with a closely spaced doublet in the final state with time-separated chirped pump pulse and Stokes pulse pair by merging stimulated Raman adiabatic passage, temporal coherent control, and chirped adiabatic passage techniques. Moreover, an arbitrary coherent superposition between the final doublet, or between the intermediate state and either of the doublets can be created. This method holds the ability to ``control with control'' and has potential applications in coherent control of chemical reactions and quantum information processing.
Selective population transfer in electronic states of dissociative molecular systems is illustrated by adopting a control scheme based on Stark-chirped rapid adiabatic passage (SCRAP). In contrast to the discrete N-level system, dynamical Stark shift is induced in a more complex manner in the molecular electronic states. Wavepacket dynamics on the light-induced potentials, which are determined by the detuning of the pump pulse, can be controlled by additional Stark pulse in the SCRAP scheme. Complete population transfer can be achieved by either lowering the energy barrier along the adiabatic passage or placing the initial wavepacket on a well-defined dressed state suitable for the control. The determination of the pulse sequence is sufficient for controlling population transfer to the target state.