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Journal of Chemical Physics / Volume 126 / Issue 9 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 126, 094105 (2007); doi:10.1063/1.2434177 (10 pages)

Photonic reagent control of dynamically homologous quantum systems

Vincent Beltrani1, Jason Dominy2, Tak-San Ho1, and Herschel Rabitz1

1Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544
2Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544

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(Received 19 July 2006; accepted 22 December 2006; published online 7 March 2007)

The general objective of quantum control is the manipulation of atomic scale physical and chemical phenomena through the application of external control fields. These tailored fields, or photonic reagents, exhibit systematic properties analogous to those of ordinary laboratory reagents. This analogous behavior is explored further here by considering the controlled response of a family of homologous quantum systems to a single common photonic reagent. A level set of dynamically homologous quantum systems is defined as the family that produces the same value(s) for a target physical observable(s) when controlled by a common photonic reagent. This paper investigates the scope of homologous quantum system control using the level set exploration technique (L-SET). L-SET enables the identification of continuous families of dynamically homologous quantum systems. Each quantum system is specified by a point in a hypercube whose edges are labeled by Hamiltonian matrix elements. Numerical examples are presented with simple finite level systems to illustrate the L-SET concepts. Both connected and disconnected families of dynamically homologous systems are shown to exist.

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. QUANTUM CONTROL LANDSCAPES AND LEVEL SETS
  3. LEVEL SET EXPLORATION TECHNIQUE
    1. L-SET equations for exploration of subspaces of math
    2. Choice of the free functions
  4. NUMERICAL ILLUSTRATIONS
    1. Deterministic free functions
    2. Stochastic free functions
    3. Homologous systems with varying energy differences and dipole elements: Multiple observables
  5. CONCLUSION

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KEYWORDS and PACS

Keywords

quantum optics, atom-photon collisions

PACS

  • 42.50.-p

    Quantum optics

  • 32.80.Qk

    Coherent control of atomic interactions with photons

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.2434177

PUBLICATION DATA

ISSN:

0021-9606 (print)  
1089-7690 (online)

Publisher:

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000)RSINAK000071000005001929000001.

    R. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).

    J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, Appl. Phys. Lett. 77, 924 (2000)APPLAB000077000007000924000001.

    A. Rothman, T.-S. Ho, and H. Rabitz, Phys. Rev. A 72, 023416 (2005).

    A. Rothman, T.-S. Ho, and H. Rabitz, J. Chem. Phys. 123, 134104 (2005)JCPSA6000123000013134104000001.

    A. Rothman, T.-S. Ho, and H. Rabitz, Phys. Rev. A 73, 053401 (2006).

    A. Mitra and H. Rabitz, Phys. Rev. A 67, 033407 (2003).

    J. Roslund, M. Roth, and H. Rabitz, Phys. Rev. A 74, 043414 (2006).


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