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Coherent control and geometric phase

Xuan Li

Published Jan 1, 2008• 2 citations
OpenAlex

Abstract

We present the ability to coherently control triatomic chemical reactions with pulsed-laser techniques. We show that one can control the final state probability distribution of triatomic chemical reactions with nearly 100% selectivity. We develop the population transfer by adiabatic passage theory to coherently control the chemical reaction with the ability of choosing the translational energies of the final reaction products. We also show a new way to achieve the creation of both homonuclear and heteronuclear diatomic molecules at an ultracold temperature using laser catalysis.

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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 ${\mathrm{Al}}_{3}\mathrm{O}$ 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.

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Physical Review A•Sep 25, 2008•18 citations
We present the ability to coherently control triatomic chemical reactions with pulsed-laser techniques. We show that one can control the final state probability distribution of triatomic chemical reactions with nearly 100% selectivity. We develop the population transfer by adiabatic passage theory to coherently control the chemical reaction with the ability of choosing the translational energies of the final reaction products. We also show a new way to achieve the creation of both homonuclear and heteronuclear diatomic molecules at an ultracold temperature using laser catalysis.
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 a new theory of population transfer by adiabatic passage. This theory relates laser catalysis to adiabatic passage, enhancing chemical reactions with the freedom to choose the translational energies of the reactants and products separately. The process, A+BC<-->(Planck's over omega(p) )ABC*(v)<-->(Planck's over omega(s))AB+C, involves two laser fields that are slowly varying so the process is adiabatic, and sufficiently intense so the population of the intermediate bound complex (ABC) is minimized. We apply this theory to the collinear exchange reaction (6)Li+(7)Li(2)(T(r))<-->(Planck's over omega(p))((6)Li(7)Li(7)Li)*<-->(variant Planck's over 2piomega(s) ) (6)Li(7)Li(T(p))+(7)Li. We show that at translational energies T(p)=T(r)=1 mK with a narrow energy bandwidth of delta(E)=0.01 mK, we can obtain nearly total (> or =98%) population transfer from the reactant to the product states. This can be done with a pump laser and a Stokes laser in an "intuitive" sequence (t(p)<t(s)) at a low intensity (I(p)< or =600 MW/cm(2)) and a "coincident" sequence (t(p)=t(s)) at a higher intensity.
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.
A chirped laser pulse transfers population from one level to another level accessible by one photon dipole transition. We have used a pair of phase-locked chirped pulses of same frequency instead of a single chirped pulse to achieve phase control over the population transfer and thus creating coherent population distribution in hydrogen molecule. Simultaneous actions of the phase controlled interference and rapid adiabatic passages due to chirped pulses lead to the control in population transfer from the ground X(v = 0, j = 0) level to the C(v = 2, j = 1) level. We have extended this two-level system to a three-level 1 + 1 ladder system for population transfer from the X level to the J(v = 2, j = 2) level via the C intermediate level using two pairs of phase-locked laser chirped pulses and have achieved laudable control over the coherent population distribution.
Recently, Pu et al. developed an efficient strategy to find the adiabatic condition of a nonlinear system---i.e., the atom-homonuclear dimer conversion [Phys. Rev. Lett. 98, 050406 (2007)]. Here, by applying their method, we extend it to study the adiabatic condition of coherent atom--heteronuclear-diatomic- or -triatomic-molecule conversion. The different adiabatic evolutions in creating the homo- or heteronuclear dimers are compared. The impact of the two different reaction paths on the adiabatic conditions in creating the heteronuclear triatomic molecules is also discussed.