Kinetic Theory for Transverse Optomechanical Instabilities (original) (raw)

Optomechanical self-organization in cold atomic gases

2013 Sixth "Rio De La Plata" Workshop on Laser Dynamics and Nonlinear Photonics, 2013

We discuss the formation of optomechanical structures from the interaction between linear dielectric scatterers and a light field via dipole forces without the need for optical nonlinearities. The experiment uses a high density sample of Rb atoms in a single mirror feedback geometry. We observe hexagonal structures in the light field and a complementary honeycomb pattern in the atomic density. Different theoretical approaches are discussed assuming either viscous damping of the atomic velocity or not. The interplay between electronic and optomechanical nonlinearities is analyzed. A prediction for dissipative light -matter density solitons is given. The investigations demonstrate novel prospects for the manipulation of matter in a pattern forming system in which quantum effects should be accessible.

Spontaneous optomechanical pattern formation in cold atoms

Physical Review A, 2012

Transverse pattern formation in an optical cavity containing a cloud of cold two-level atoms is discussed. We show that density modulation becomes the dominant mechanism as the atomic temperature is reduced. Indeed, for low but achievable temperatures the internal degrees of freedom of the atoms can be neglected, and the system is well described by treating them as mobile dielectric particles. A linear stability analysis predicts the instability threshold and the spatial scale of the emergent pattern. Numerical simulations in one and two transverse dimensions confirm the instability and predict honeycomb and hexagonal density structures, respectively, for the blue and red detuned cases.

Non-equilibrium Dynamics of an Optomechanical Dicke Model

Communications in Theoretical Physics, 2015

Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of two level BEC atoms with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portraits of the system. The rich phase portraits generated by analytical arguments display two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in reaching their attractors. Further, we add an external mechanical pump to the mirror which is capable of changing the mirror frequency through radiation pressure and study the impact of the pump on the phase portraits and the dynamics of the system. We find the external mirror frequency changing the phase portraits and even shifting the critical transition point, thereby predicting a system with controllable phase transition.

Exploring corrections to the Optomechanical Hamiltonian

Scientific Reports, 2018

We compare two approaches for deriving corrections to the "linear model" of cavity optomechanics, in order to describe effects that are beyond first order in the radiation pressure coupling. In the regime where the mechanical frequency is much lower than the cavity one, we compare: (I) a widely used phenomenological Hamiltonian conserving the photon number; (II) a two-mode truncation of C. K. Law's microscopic model, which we take as the "true" system Hamiltonian. While these approaches agree at first order, the latter model does not conserve the photon number, resulting in challenging computations. We find that approach (I) allows for several analytical predictions, and significantly outperforms the linear model in our numerical examples. Yet, we also find that the phenomenological Hamiltonian cannot fully capture all high-order corrections arising from the C. K. Law model. Cavity quantum optomechanics is a rapidly developing research field exploring the interaction of quantised light with macroscopic mirrors, membranes and levitated nano-objects through radiation pressure 1-4. The field has recently witnessed impressive experimental progress, including demonstrations of near-ground-state cooling of mechanical oscillators 5 and normal-mode splitting due to phonon-photon interaction 2,6. Among its many applications, optomechanics is a promising platform to demonstrate nonclassical behaviour in massive objects 7,8 , and may provide novel avenues for the coherent manipulation of quantum light 9-12. Recently it was also suggested that optomechanics may allow for ultra-high precision measurements, for example probing Planck-scale corrections to the canonical commutation relations 13,14. The simplest optomechanical setup features a single optical cavity mode, whose frequency ω(x) depends parametrically on the coordinate x (the 'position') of a mechanical oscillator 15. Perhaps the most notable example is embodied by a Fabry-Perot resonator with one movable mirror-see Fig. 1. Most experiments to date have explored the weak coupling regime, in which radiation pressure effects are only visible upon strong driving of the cavity, and the system can be described as a pair of coupled harmonic oscillators 1. Several experimental platforms, however, are now approaching the single-photon strong coupling regime 2-4,16-18 (strong coupling, or SC, for brevity), in which the anharmonic nature of the radiation pressure interaction must be taken into account. Strong coupling occurs when the the coupling rate of a single photon is greater than the typical loss rates of the setup. Such regime features clear departures from classical behaviour 11,16,19 , and facilitates the production of nonclassical states in both light and mechanics 20-22. A further appealing feature of strong coupling optomechanics is that the Hamiltonian can be diagonalized analytically upon linearising the cavity frequency around the origin, as per ω ω ω + ′  x x () (0) (0) (equivalently, this may be seen as a first order expansion in the coupling constant). We shall call linear model the resulting Hamiltonian, arguably the most widely used modelling tool in SC optomechanics. Despite the undeniable success of the linear model as a theoretical device, the need is arising to go beyond this approximation. For example, it was noted by Brunelli et al. 23 that the linearized optomechanical Hamiltonian is unbounded from below, with (unphysical) negative energies cropping up at very high photon numbers. While this pathology may be seen as somewhat mathematical (see Appendix A), it highlights that the model must be eventually refined, particularly in view of future experiments aiming to achieve ever larger coupling strengths. Even in systems that are far from the SC, the quest for ultra-precise measurements (e.g. those pertaining Planck scale physics) 14 , or for the detection of dynamical Casimir effects 24 , demand a more accurate Hamiltonian description of quantum optomechanics. Armed with these motivations, in this paper we explore and compare two different starting points that may be used to go beyond the linear model: (I) a widely used phenomenological Hamiltonian, which conserves the cavity photon number (phenomenological approach); (II) a two-mode truncation of C. K. Law's microscopic Hamiltonian

Optical beam instabilities in nonlinear nanosuspensions

Optics Letters, 2007

We investigate the modulation instability of plane waves and the transverse instabilities of soliton stripe beams propagating in nonlinear nanosuspensions. We show that in these systems the process of modulational instability depends on the input beam conditions. On the other hand, the transverse instability of soliton stripes can exhibit new features as a result of 1D collapse caused by the exponential nonlinearity.

Dissipation induced Instabilities and the Mechanical Laser

2001

We study the 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allow us to show that a slightly pumping optical cavity is unstable when one takes into account the dissipative effects. The Maxwell-Bloch equations are the asymptotic normal form that describe this instability when energy is injected through forcing at zero frequency. We display a simple mechanical system, close to the 1:1 resonance, which is a mechanical analog of the Laser.

Optomechanics of a Quantum-Degenerate Fermi Gas

Physical Review Letters, 2010

We explore theoretically the optomechanical interaction between a light field and a mechanical mode of ultracold fermionic atoms inside a Fabry-Pérot cavity. The low-lying phonon mode of the fermionic ensemble is a collective density oscillation associated with particle-hole excitations, and is mathematically analogous to the momentum side-mode excitations of a bosonic condensate. The mechanical motion of the fermionic particle-hole system behaves hence as a "moving mirror." We derive an effective system Hamiltonian that has the form of generic optomechanical systems. We also discuss the experimental consequences the optomechanical coupling in optical bistability and in the noise spectrum of the system.

Nonlinear Optomechanical Patterns and Dissipative Solitons

Advanced Photonics, 2014

Experimental, theoretical and numerical evidence of optomechanical self-structuring of a laser beam in a cloud of cold atoms in a single-mirror feedback configuration is presented. Optomechanical dissipative solitons can be encoded in the atomic density.