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Journal Article

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles

MPS-Authors
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Navarrete-Benlloch,  Carlos
Marquardt Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Weiss,  Talitha
Marquardt Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Walter,  Stefan
Marquardt Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Fulltext (public)

PhysRevLett.119.133601.pdf
(Any fulltext), 2MB

Supplementary Material (public)

2017_General_linearized.png
(Supplementary material), 63KB

Citation

Navarrete-Benlloch, C., Weiss, T., Walter, S., & de Valcarcel, G. J. (2017). General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles. Physical Review Letters, 119(13): 133601. doi:10.1103/PhysRevLett.119.133601.


Cite as: http://hdl.handle.net/21.11116/0000-0000-859F-7
Abstract
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.