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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Quasienergy anholonomy and its application to adiabatic quantum state manipulation
Atushi Tanaka1, Manabu Miyamoto
1Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo 192-0397, Japan. tanaka@phys.metro-u.ac.jp
Physical Review Letters
|May 16, 2007
Summary
Quantum maps with rank-1 perturbations show periodic Floquet operators but non-periodic quasienergies and eigenvectors. This anholonomy in quantum systems offers potential for quantum state manipulations.
Area of Science:
- Quantum mechanics
- Quantum chaos
- Quantum information
Background:
- Investigating parametric dependence in quantum maps is crucial for understanding their behavior under external influences.
- Rank-1 perturbations introduce specific changes to quantum systems, necessitating detailed analysis.
Purpose of the Study:
- To explore the parametric dependence of a quantum map subjected to a rank-1 perturbation.
- To analyze the periodicity of the Floquet operator, spectrum, quasienergies, and eigenvectors with respect to perturbation strength.
Main Methods:
- The study involves analyzing the Floquet operator and its spectrum under varying perturbation strengths (lambda).
- Mathematical investigation of quasienergies and eigenvectors to identify periodic or non-periodic behaviors.
Main Results:
- The Floquet operator and its spectrum exhibit periodicity with respect to perturbation strength.
- However, quasienergies and eigenvectors do not follow the same periodicity, demonstrating anholonomy.
- A periodic increment in perturbation strength leads to a shift to the next quasienergy level, not the initial one.
Conclusions:
- The discovered anholonomy in quasienergies and eigenvectors governs similar behavior in eigenvectors.
- This phenomenon has potential applications in precise quantum state manipulations.
- Understanding these parametric dependencies is key for controlling quantum systems.
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