752 research outputs found
Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation
Open quantum systems can display periodic dynamics at the classical level
either due to external periodic modulations or to self-pulsing phenomena
typically following a Hopf bifurcation. In both cases, the quantum fluctuations
around classical solutions do not reach a quantum-statistical stationary state,
which prevents adopting the simple and reliable methods used for stationary
quantum systems. Here we put forward a general and efficient method to compute
two-time correlations and corresponding spectral densities of time-periodic
open quantum systems within the usual linearized (Gaussian) approximation for
their dynamics. Using Floquet theory we show how the quantum Langevin equations
for the fluctuations can be efficiently integrated by partitioning the time
domain into one-period duration intervals, and relating the properties of each
period to the first one. Spectral densities, like squeezing spectra, are
computed similarly, now in a two-dimensional temporal domain that is treated as
a chessboard with one-period x one-period cells. This technique avoids
cumulative numerical errors as well as efficiently saves computational time. As
an illustration of the method, we analyze the quantum fluctuations of a damped
parametrically-driven oscillator (degenerate parametric oscillator) below
threshold and far away from rotating-wave approximation conditions, which is a
relevant scenario for modern low-frequency quantum oscillators. Our method
reveals that the squeezing properties of such devices are quite robust against
the amplitude of the modulation or the low quality of the oscillator, although
optimal squeezing can appear for parameters that are far from the ones
predicted within the rotating-wave approximation.Comment: Comments and constructive criticism are welcom
General linearized theory of quantum fluctuations around arbitrary limit cycles
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, which is
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 testbed 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.Comment: Constructive suggestions and criticism are welcom
Dissipative structures in optomechanical cavities
Motivated by the increasing interest in the properties of multimode
optomechanical devices, here we study a system in which a driven mode of a
large-area optical cavity is despersively coupled to a deformable mechanical
element. Two different models naturally appear in such scenario, for which we
predict the formation of periodic patterns, localized structures (cavity
solitons), and domain walls, among other complex nonlinear phenomena. Further,
we propose a realistic design based on intracavity membranes where our models
can be studied experimentally. Apart from its relevance to the field of
nonlinear optics, the results put forward here are a necessary step towards
understanding the quantum properties of optomechanical systems in the multimode
regime of both the optical and mechanical degrees of freedom.Comment: Updated version with a more general model and a specific
implementation proposal. Comments and (constructive) criticism are welcom
Domain wall dynamics in an optical Kerr cavity
An anisotropic (dichroic) optical cavity containing a self-focusing Kerr
medium is shown to display a bifurcation between static --Ising-- and moving
--Bloch-- domain walls, the so-called nonequilibrium Ising-Bloch transition
(NIB). Bloch walls can show regular or irregular temporal behaviour, in
particular, bursting and spiking. These phenomena are interpreted in terms of
the spatio-temporal dynamics of the extended patterns connected by the wall,
which display complex dynamical behaviour as well. Domain wall interaction,
including the formation of bound states is also addressed.Comment: 15 pages Tex file with 11 postscript figures. Resubmitted to Phys.
Rev.
Non-critically squeezed light via spontaneous rotational symmetry breaking
We theoretically address squeezed light generation through the spontaneous
breaking of the rotational invariance occuring in a type I degenerate optical
parametric oscillator (DOPO) pumped above threshold. We show that a DOPO with
spherical mirrors, in which the signal and idler fields correspond to first
order Laguerre-Gauss modes, produces a perfectly squeezed vacuum with the shape
of a Hermite-Gauss mode, within the linearized theory. This occurs at any
pumping level above threshold, hence the phenomenon is non-critical.
Imperfections of the rotational symmetry, due e.g. to cavity anisotropy, are
shown to have a small impact, hence the result is not singular.Comment: 4 pages, 1 figure, replaced with resubmitted versio
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