Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Atoms as structured particles
- 3 Radiation
- 4 The laser–atom interaction
- 5 Picturing quantum structure and changes
- 6 Incoherence: Rate equations
- 7 Coherence: The Schrödinger equation
- 8 Two-state coherent excitation
- 9 Weak pulse: Perturbation theory
- 10 The vector model
- 11 Sequential pulses
- 12 Degeneracy
- 13 Three states
- 14 Raman processes
- 15 Multilevel excitation
- 16 Averages and the statistical matrix (density matrix)
- 17 Systems with parts
- 18 Preparing superpositions
- 19 Measuring superpositions
- 20 Overall phase; interferometry and cyclic dynamics
- 21 Atoms affecting fields
- 22 Atoms in cavities
- 23 Control and optimization
- Appendix A Angular momentum
- Appendix B The multipole interaction
- Appendix C Classical radiation
- Appendix D Quantized radiation
- Appendix E Adiabatic states
- Appendix F Dark states; the Morris–Shore transformation
- Appendix G Near-periodic excitation; Floquet theory
- Appendix H Transitions; spectroscopic parameters
- References
- Index
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Atoms as structured particles
- 3 Radiation
- 4 The laser–atom interaction
- 5 Picturing quantum structure and changes
- 6 Incoherence: Rate equations
- 7 Coherence: The Schrödinger equation
- 8 Two-state coherent excitation
- 9 Weak pulse: Perturbation theory
- 10 The vector model
- 11 Sequential pulses
- 12 Degeneracy
- 13 Three states
- 14 Raman processes
- 15 Multilevel excitation
- 16 Averages and the statistical matrix (density matrix)
- 17 Systems with parts
- 18 Preparing superpositions
- 19 Measuring superpositions
- 20 Overall phase; interferometry and cyclic dynamics
- 21 Atoms affecting fields
- 22 Atoms in cavities
- 23 Control and optimization
- Appendix A Angular momentum
- Appendix B The multipole interaction
- Appendix C Classical radiation
- Appendix D Quantized radiation
- Appendix E Adiabatic states
- Appendix F Dark states; the Morris–Shore transformation
- Appendix G Near-periodic excitation; Floquet theory
- Appendix H Transitions; spectroscopic parameters
- References
- Index
Summary
Quantum changes of three-state systems have some similarities with those of two-state systems. When subject to steady illumination the populations may undergo oscillations similar to the Rabi cycling of two-state systems, and various forms of adiabatic following are possible. Analytic solutions to the relevant TDSE exist [Sho90, Chap. 23]. The additional degree of freedom, typically allowing controllable parameters of a second laser pulse, allows a wider variety of controlled excitation. The resulting differences and similarities to two-state systems have been discussed at length [Whi76; Sho77; Rad82b; Yoo85; Car87].
Three-state linkages
Two-field linkages. The simplest extension of two-state excitation allows two laser fields, here identified by letters P (for pump) and S (for Stokes), as befits the stimulated Raman process discussed in Chap. 14. The carrier frequencies of the two fields, ωP and ωS, are each assumed to be close to resonance with one, and only one, Bohr frequency, so that each field can be uniquely identified with a particular transition (failure of this restriction, and the resulting linkage ambiguity, is discussed in [Una00]). I will assume that the P field is (near) resonance only with the 1–2 transition, while the S field is (near) resonant only with the 2–3 transition; these interactions thereby form a two-step linkage chain. This system has three possible linkage patterns, shown in Fig. 13.1.
The linkage patterns (sometimes called configurations) differ by the ordering of the energies of the linked states.With the assumption that population initially occupies state 1, as in Fig. 13.1, the definitions are:
Ladder: The ladder system has the energy ordering E1 < E2 < E3.
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- Information
- Manipulating Quantum Structures Using Laser Pulses , pp. 186 - 221Publisher: Cambridge University PressPrint publication year: 2011