We study the role of the quantum geometric tensor (QGT) in the evolution of two-band quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor ...and on the trajectory of an accelerated wave packet in any realistic finite-duration experiment. While the adiabatic phase is determined by the Berry curvature (the imaginary part of the tensor), the nonadiabaticity is determined by the quantum metric (the real part of the tensor). We derive, for geodesic trajectories (corresponding to acceleration from zero initial velocity), the semiclassical equations of motion with nonadiabatic corrections. The particular case of a planar microcavity in the strong coupling regime allows us to extract the QGT components by direct light polarization measurements and to check their effects on the quantum evolution.
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We study gap solitons which appear in the topological gap of 1D bosonic dimer chains within the mean-field approximation. We find that such solitons have a nontrivial texture of the sublattice ...pseudospin. We reveal their chiral nature by demonstrating the anisotropy of their behavior in the presence of a localized energy potential.
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Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor
-comprising the Berry curvature
(crucial ...for topological matter)
and the quantum metric
, which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands
, orbital magnetic susceptibility
, the exciton Lamb shift
and the non-adiabatic anomalous Hall effect
. However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium-a high-finesse planar microcavity
-together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton-photon modes (exciton polaritons) that are subject to photonic spin-orbit coupling
from which Dirac cones emerge
, and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics
. These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands
. The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems.
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FZAB, GEOZS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Topological defects, such as quantum vortices, determine the properties of quantum fluids. Their study has been at the center of activity in solid state and BEC communities. In parallel, the ...nontrivial behavior of linear wave packets with complex phase patterns was investigated by singular optics. Here, we study the formation, evolution, and interaction of optical vortices in wave packets at the Dirac point in photonic graphene. We show that while their exact behavior goes beyond the Dirac equation and requires a full account of the lattice properties, it can be still approximately described by an effective theory considering the phase singularities as "particles". These particles are capable of mutual interaction, with their trajectory obeying the laws of dynamics.
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We consider a zigzag chain of coupled micropillar cavities, taking into account the polarization of polariton states. We show that the TE-TM splitting of photonic cavity modes yields topologically ...protected polariton edge states. During the strongly nonadiabatic process of polariton condensation, the Kibble-Zurek mechanism leads to a random choice of polarization, equivalent to the dimerization of polymer chains. We show that dark-bright solitons appear as domain walls between polarization domains, analogous to the Su-Schrieffer-Heeger solitons in polymers. The soliton density scales as a power law with respect to the quenching parameter.
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Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of ...honeycomb lattices where the polariton low-energy dispersion is analogous to that of electrons in graphene. Using energy-resolved photoluminescence, we directly observe Dirac cones, around which the dynamics of polaritons is described by the Dirac equation for massless particles. At higher energies, we observe p orbital bands, one of them with the nondispersive character of a flatband. The realization of this structure which holds massless, massive, and infinitely massive particles opens the route towards studies of the interplay of dispersion, interactions, and frustration in a novel and controlled environment.
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Polariton Z topological insulator Nalitov, A V; Solnyshkov, D D; Malpuech, G
Physical review letters,
2015-Mar-20, Volume:
114, Issue:
11
Journal Article
Peer reviewed
We demonstrate that honeycomb arrays of microcavity pillars behave as an optical-frequency two-dimensional photonic topological insulator. We show that the interplay between the photonic spin-orbit ...coupling natively present in this system and the Zeeman splitting of exciton polaritons in external magnetic fields leads to the opening of a nontrivial gap characterized by a C=±2 set of band Chern numbers and to the formation of topologically protected one-way edge states.
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Topologically protected pseudospin transport, analogous to the quantum spin Hall effect, cannot be strictly implemented for photons and in general bosons because of the lack of symmetry-protected ...pseudospins. Here we show that the required protection can be provided by the real-space topological excitation of an interacting quantum fluid: a quantum vortex. We consider a Bose-Einstein condensate at the Γ point of the Brillouin zone of a quantum valley Hall system based on two staggered honeycomb lattices. We demonstrate the existence of a coupling between the vortex winding and the valley of the bulk Bloch band. This leads to chiral vortex propagation on each side of the zigzag interface between two regions of inverted staggering. The topological protection provided by the vortex winding prevents valley pseudospin mixing and resonant backscattering, allowing a truly topologically protected valley pseudospin transport.
We study the spin-orbit coupling induced by the splitting between TE and TM optical modes in a photonic honeycomb lattice. Using a tight-binding approach, we calculate analytically the band ...structure. Close to the Dirac point, we derive an effective Hamiltonian. We find that the local reduced symmetry (D_{3h}) transforms the TE-TM effective magnetic field into an emergent field with a Dresselhaus symmetry. As a result, particles become massive, but no gap opens. The emergent field symmetry is revealed by the optical spin Hall effect.
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Abstract
Topological physics relies on Hamiltonian’s eigenstate singularities carrying topological charges, such as Dirac points, and – in non-Hermitian systems – exceptional points (EPs), lines or ...surfaces. So far, the reported non-Hermitian topological transitions were related to the creation of a pair of EPs connected by a Fermi arc out of a single Dirac point by increasing non-Hermiticity. Such EPs can annihilate by reducing non-Hermiticity. Here, we demonstrate experimentally that an increase of non-Hermiticity can lead to the annihilation of EPs issued from different Dirac points (valleys). The studied platform is a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Non-Hermiticity is provided by polarization-dependent losses. By increasing the non-Hermiticity degree, we control the position of the EPs. After the intervalley annihilation, the system becomes free of any band singularity. Our results open the field of non-Hermitian valley-physics and illustrate connections between Hermitian topology and non-Hermitian phase transitions.
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