Symmetry-Breaking Instability of Multimode Vector Solitons

Cambournac, Cyril; Sylvestre, Thibaut; Maillotte, H.; Vanderlinden, Bruno; Kockaert, Pascal; Emplit, Philippe; Haelterman, Marc

doi:10.1103/physrevlett.89.083901

Cited by 85 publications

(67 citation statements)

References 39 publications

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“…This result opens the way to highly nonlinear photonic phenomena such as polarization chaos 13 , or spontaneous symmetry breaking and pitchfork bifurcations 17,28,29 , expected to give rise to highly squeezed macroscopic states 14 . By reducing the size of the system, the many-particle interactions evidenced here could be taken into the regime of single-photon nonlinearities 30,31 .…”

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“…For photonic systems, mostly theoretical results have been obtained so far. Despite the observation of symmetry breaking in photonic Kerr media 17,18 , nonlinear Josephson oscillations 9,10,19 have remained inaccessible owing to the short lifetimes and very weak effective photon-photon interactions in standard nonlinear optical systems.In this work we present the experimental observation of nonlinear Josephson physics in a highly nonlinear photonic system, namely cavity polaritons confined in coupled micropillars 8 . Polaritons are quasiparticles arising from the strong coupling between quantum well excitons and photons confined in a semiconductor microcavity.…”

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Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons

et al. 2013

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The coupling of two macroscopic quantum states through a tunnel barrier gives rise to Josephson phenomena 1 such as Rabi oscillations 2 , the a.c. and d.c. effects 3 , or macroscopic self-trapping, depending on whether tunnelling or interactions dominate 4 . Nonlinear Josephson physics was first observed in superfluid helium 5 and atomic condensates 6,7 , but it has remained inaccessible in photonic systems because it requires large photon-photon interactions. Here we report on the observation of nonlinear Josephson oscillations of two coupled polariton condensates confined in a photonic molecule formed by two overlapping micropillars etched in a semiconductor microcavity 8 . At low densities we observe coherent oscillations of particles tunnelling between the two sites. At high densities, interactions quench the transfer of particles, inducing the macroscopic self-trapping of polaritons in one of the micropillars 9,10 . The finite lifetime results in a dynamical transition from self-trapping to oscillations with π phase. Our results open the way to the experimental study of highly nonlinear regimes in photonic systems, such as chaos 11-13 or symmetry-breaking bifurcations 14,15 .A bosonic Josephson junction is a device in which two macroscopic ensembles of bosons, each of them occupying a single quantum state, are coupled by a tunnel barrier. The system can be described by the following coupled nonlinear Schrödinger equations 1 :where ψ L,R are the bosonic wavefunctions with particle densities |ψ L,R | 2 localized to the left (L) and to the right (R) of the barrier, E 0 L,R is the single particle energy of the quantum states, U is the particle-particle interaction strength and J is the tunnel coupling constant. In the absence of interactions, equations (1a) and (1b) can be diagonalized in a basis of bonding (). An initial state prepared in a linear combination of these two (for instance, all particles in the left site) will result in density oscillations between the two sites. This is the main principle of the bosonic Josephson effect, which manifests in an ensemble of oscillatory regimes. In the absence of interactions, sinusoidal oscillations take place 4,7 with a frequencȳ Josephson physics shows the most spectacular phenomena in the nonlinear regime, when the interaction energy (U |ψ| 2 ) is greater than the coupling J . The transfer of particles from one site to the other gives rise to a dynamical renormalization of the energy in each site, resulting in anharmonic oscillations. If interactions are strong enough (U |ψ| 2 J ), the self-induced energy renormalization quenches the tunnelling, and most of the particles remain localized in one of the sites. This out of equilibrium metastable regime is called macroscopic quantum self-trapping.A number of bosonic systems have demonstrated Josephson physics. Harmonic oscillations in the linear regime have been observed in superconductor junctions 2 or in nanoscale apertures connecting superfluid helium vessels 5 . Bose-Einstein condensates of ultracold atoms in cou...

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Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons

et al. 2013

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“…Importantly, a large volume of theoretical studies has accompanied these developments, first in the context of atomic BECs, through investigations related to finite-mode reductions and symmetry-breaking bifurcations [40][41][42][43][44][45][46][47][48][49], quantum effects [50], and nonlinear variants of the double-well potential [51], and more recently in the context of polariton condensates, especially as concerns Josephson oscillations therein [52][53][54][55]. It should be mentioned in passing that similar (spontaneous symmetry breaking) effects have been monitored in the realm of nonlinear optics: in this context, formation of asymmetric states in dual-core fibers [56][57][58][59][60][61][62], self-guided laser beams in Kerr media [63], and optically-induced dual-core waveguiding structures in photorefractive crystals [64] have been reported.…”

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Symmetry-Breaking Effects for Polariton Condensates in Double-Well Potentials

Rodrigues

Cuevas

Carretero-González

et al. 2012

Progress in Optical Science and Photonics

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We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in doublewell potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the realm of atomic condensates. Nevertheless, there are also some nontrivial differences including, e.g., the unstable nature of both the parent and the daughter branch emerging in the relevant pitchfork bifurcation for slightly larger values of atom numbers. Another interesting feature that does not appear in the atomic condensate case is that the bifurcation for attractive interactions is slightly sub-critical instead of supercritical. are corroborated by direct numerical simulations examining the dynamics of the system in the unstable regime.

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“…DWPs have also inspired theoretical studies of various topics, such as finite-mode reductions, finding exact analytical results for specially designed shapes of the potential, quantum effects [7,8,9,10,11,12,13,14,15], and a nonlinear DWP (alias double-well pseudopotential), which is induced by the respective spatial modulation of the nonlinearity coefficient [16]. It is relevant to mention that DWPs have also been studied in the context of nonlinear optics, including twin-core self-guided laser beams in Kerr media [17] and optically-induced waveguiding structures in photorefractive crystals [18].…”

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Two-dimensional paradigm for symmetry breaking: The nonlinear Schrödinger equation with a four-well potential

et al. 2009

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We study the existence and stability of localized states in the two-dimensional (2D) nonlinear Schrödinger (NLS)/Gross-Pitaevskii equation with a symmetric four-well potential. Using a fourmode approximation, we are able to trace the parametric evolution of the trapped stationary modes, starting from the corresponding linear limits, and thus derive the complete bifurcation diagram for the families of these stationary modes. The predictions based on the four-mode decomposition are found to be in good agreement with the numerical results obtained from the NLS equation. Actually, the stability properties coincide with those suggested by the corresponding discrete model in the large-amplitude limit. The dynamics of the unstable modes is explored by means of direct simulations. Finally, while we present the full analysis for the case of the focusing nonlinearity, the bifurcation diagram for the defocusing case is briefly considered too.

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Symmetry-Breaking Instability of Multimode Vector Solitons

Cited by 85 publications

References 39 publications

Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons

Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons

Symmetry-Breaking Effects for Polariton Condensates in Double-Well Potentials

Two-dimensional paradigm for symmetry breaking: The nonlinear Schrödinger equation with a four-well potential

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