Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems
Abstract
:1. Introduction
2. Single Periodically Modulated Quantum System
2.1. General Settings
2.2. Effective Hamiltonian,
2.3. Examples
2.3.1. Semi-Classical Rabi Model
2.3.2. Quantum Parametric Oscillator
2.4. Effective Hamiltonian,
2.5. Modulated Quantum System with Intensity Dependent Coupling
3. Two Periodically Modulated Coupled Quantum Systems
- (i)
- Both X and Y systems are described by the algebra. In this case is a linear form on ;
- (ii)
- One of the systems is described by and another by algebra. In this case the leading term in is a second degree polynomial on and , and the first correction is of a third degree one;
- (iii)
- The leading term in is a third degree polynomial if both systems have symmetry.
3.1. Modulated Quantum Parametric Amplifier
3.1.1. Dicke Model with Modulated Frequency
3.1.2. Non-Symmetric Excitation of an Atomic System in a Vacuum Field
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. Single Periodically Modulated Quantum System
Appendix A.1. Frequency Corrections
Appendix B. Two Coupled Systems with Modulated Frequency
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Appendix B.1. Non-Symmetric Excitation of an Atomic System in a Vacuum
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Sainz, I.; García, A.; Klimov, A.B. Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems. Quantum Rep. 2021, 3, 173-195. https://doi.org/10.3390/quantum3010011
Sainz I, García A, Klimov AB. Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems. Quantum Reports. 2021; 3(1):173-195. https://doi.org/10.3390/quantum3010011
Chicago/Turabian StyleSainz, Isabel, Andrés García, and Andrei B. Klimov. 2021. "Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems" Quantum Reports 3, no. 1: 173-195. https://doi.org/10.3390/quantum3010011