Instabilities of the degenerate optical parametric oscillator

Pettiaux, Nicolas; Li, Ruo-Ding; Mandel, P.

doi:10.1016/0030-4018(89)90407-0

Cited by 26 publications

(10 citation statements)

References 12 publications

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“…It is possible to show that the portion of the nontrivial solution with I s > I HB s becomes unstable, and the limit cycles become chaotic for large enough injections [82][83][84]. The main effect of optomechanics, that is, of increasing g, is both changing the location of this dynamical instability already present for g = 0, as well as creating new ones that cannot be understood as a deformation of the latter.…”

Section: Let Us Collect the Variables Of The System In A Vectormentioning

confidence: 99%

“…Let us first note that in the absence of optomechanical coupling (g = 0) there is a single Hopf bifurcation located at (see Appendix A and [82][83][84])…”

Section: Let Us Collect the Variables Of The System In A Vectormentioning

confidence: 99%

“…However, working with a dissipative system, we are mainly interested in its behavior for long times (asymptotic limit), and there is a lot that we can say about this without really solving the full nonlinear equations; in particular, we follow closely the procedure already applied to detuned DOPOs [82][83][84].…”

Section: Classical Analysismentioning

confidence: 99%

“…Concerning the classical limit, we show that, with respect the usual DOPO scenario [82][83][84], the most relevant effect that the optomechanical interaction has is the generation of new dynamical instabilities, as well as the…”

Section: Introductionmentioning

confidence: 99%

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Classical and quantum-linearized descriptions of degenerate optomechanical parametric oscillators

et al. 2016

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Recent advances in the development of modern quantum technologies have opened the possibility of studying the interplay between spontaneous parametric down-conversion and optomechanics, two of the most fundamental nonlinear optical processes. Apart from practical reasons, such scenario is very interesting from a fundamental point of view, because it allows exploring the optomechanical interaction in the presence of a strongly quantum-correlated field, the spontaneously down-converted mode. In this work we analyze such problem from two approximate but valuable perspectives: the classical limit and the limit of small quantum fluctuations. We show that, in the presence of optomechanical coupling, the well-known classical phase diagram of the optical problem gets modified by the appearance of new dynamical instabilities. As for the quantum-mechanical description, we prove the ability of the squeezed down-converted field to cool down the mechanical motion not only to thermal but also to squeezed thermal mechanical states, and in a way that can be much less sensitive to parameters (e.g., detuning of the driving laser) than standard sideband cooling.

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Section: Let Us Collect the Variables Of The System In A Vectormentioning

confidence: 99%

“…Let us first note that in the absence of optomechanical coupling (g = 0) there is a single Hopf bifurcation located at (see Appendix A and [82][83][84])…”

Section: Let Us Collect the Variables Of The System In A Vectormentioning

confidence: 99%

Section: Classical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Classical and quantum-linearized descriptions of degenerate optomechanical parametric oscillators

et al. 2016

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“…Se ∆ 0 ∆ 1 − 1 > 0, existe uma região de potência do bombeio em que há dois valores distintos possíveis para a potência do sinal, a região de biestabilidade [32,33].…”

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