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Entanglement tongue and quantum synchronization of disordered oscillators
Tony E Lee1, Ching-Kit Chan1, Shenshen Wang2
1ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
Summary
Quantum van der Pol oscillators synchronize and entangle in the quantum limit. Synchronization occurs above a critical coupling strength, which depends on frequency differences and disorder, and is observable in trapped ion experiments.
Area of Science:
- Quantum physics
- Nonlinear dynamics
- Quantum optics
Background:
- Dissipatively coupled van der Pol oscillators are a key model in nonlinear dynamics.
- Understanding quantum synchronization is crucial for quantum technologies.
- The quantum limit describes systems near their ground state energy.
Purpose of the Study:
- To investigate quantum synchronization and entanglement in dissipatively coupled van der Pol oscillators.
- To explore the quantum analog of Arnold tongues (entanglement tongues).
- To analyze the effect of frequency disorder on synchronization in an ensemble of oscillators.
Main Methods:
- Theoretical analysis of quantum van der Pol oscillators in the quantum limit.
- Calculation of critical coupling strength for synchronization and entanglement.
- Analytical derivation of the dependence of critical coupling on frequency disorder.
Main Results:
- Two quantum oscillators with different frequencies exhibit an entanglement tongue, a steady-state entanglement phenomenon.
- A critical coupling strength is required for entanglement, increasing with frequency detuning.
- An ensemble of oscillators with random frequencies shows a synchronization phase transition in the quantum limit.
Conclusions:
- Quantum synchronization and entanglement are robust phenomena in dissipatively coupled van der Pol oscillators.
- The critical coupling strength is analytically determined as a function of frequency disorder.
- Experimental observation is feasible using trapped ions or neutral atoms.
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