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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Sharp tunneling peaks in a parametric oscillator: quantum resonances missing in the rotating wave approximation
V Peano1, M Marthaler, M I Dykman
1Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA.
Physical Review Letters
|September 26, 2012
Summary
A new tunneling mechanism in nonlinear oscillators is revealed, driven by fast oscillations missed by the rotating wave approximation (RWA). This mechanism shows significantly amplified tunneling amplitudes at specific modulation frequencies.
Area of Science:
- Nonlinear dynamics and quantum mechanics
- Oscillatory systems and chaos theory
Background:
- Parametrically modulated oscillators exhibit complex dynamics.
- The rotating wave approximation (RWA) simplifies analyses by neglecting fast oscillating terms.
- Understanding tunneling between vibrational states is crucial for nonlinear systems.
Purpose of the Study:
- To introduce and elucidate a novel mechanism for tunneling between period-two vibrational states.
- To investigate the role of fast oscillating terms in inducing resonant transitions.
- To quantify the tunneling amplitude in relation to modulation frequency.
Main Methods:
- Analysis of a weakly nonlinear, parametrically modulated oscillator.
- Inclusion of fast oscillating terms typically disregarded by the rotating wave approximation (RWA).
- Examination of tunneling amplitude as a function of modulation frequency.
Main Results:
- A new tunneling mechanism between period-two vibrational states was identified.
- Resonant transitions, induced by fast oscillating terms, were found to drive the tunneling.
- Tunneling amplitude exhibits resonant peaks, significantly exceeding RWA predictions near maxima.
Conclusions:
- Fast oscillating terms play a critical role in nonlinear oscillator dynamics, enabling enhanced tunneling.
- The proposed mechanism offers a more complete description of tunneling in modulated systems.
- This finding has implications for understanding energy transfer and state transitions in nonlinear physics.
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