Spin-Orbit Coupling for Photons and Polaritons in Microstructures

Sala, V. G.; Solnyshkov, D. D.; Carusotto, Iacopo; Jacqmin, T.; Lemaı̂tre, A.; Terças, Hugo; Nalitov, A. V.; Abbarchi, Marco; Galopin, Élisabeth; Sagnes, I.; Bloch, J.; Malpuech, Guillaume; Amo, A.

doi:10.1103/physrevx.5.011034

Cited by 207 publications

(236 citation statements)

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“…While KZM, as a universal mechanism, has already been widely studied in various systems sharing some common properties with our proposal, such as zigzag ionic chains [37][38][39][40], where the phase transition and the topology correspond to physical arrangement of atoms, none of these possess the same key ingredients. A topologically non-trivial polaritonic chain therefore appears as an ideal system to study the complex interplay of topological ordering and KZM [41].In this work, we describe polariton BEC in a zigzag chain of polariton micropillars with photonic spin-orbit coupling (SOC) [34,42,43]. As a result, the polariton band is characterized by a non-zero Zak phase and the chain supports topologically protected edge states.…”

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confidence: 99%

“…In this work, we describe polariton BEC in a zigzag chain of polariton micropillars with photonic spin-orbit coupling (SOC) [34,42,43]. As a result, the polariton band is characterized by a non-zero Zak phase and the chain supports topologically protected edge states.…”

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confidence: 99%

“…On the other hand, the optical eigenmodes of the cavity are TE and TM polarized and have different effective masses [46]. This makes the tunneling coefficients polarizationdependent [34,42,43] and different for the polarizations oriented longitudinal and transverse with respect to the link. We therefore have t < t for D-polarization, for which the first link (labeled by t ) is longitudinal ( Fig.…”

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Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

2016

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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 non-adiabatic process of polariton condensation, the Kibble-Zurek mechanism leads to a random choice of polarization, equivalent to 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.As initially shown by Kibble [1] for the expansion and cooling of the early Universe, and then for liquid helium by Zurek [2], a system undergoing a second-order phase transition on a finite timescale develops domains with independent order parameters. The Kibble-Zurek mechanism (KZM) allows predicting the typical size of the domains and, therefore, the densities of the topological defects on their boundaries. Their scaling as a function of the quench rate is given by a power law, with the critical exponent of the transition being determined by its universality class [3].A very relevant system to study the KZM are the quantum fluids such as atomic Bose-Einstein condensates (BECs) formed by cooling. Indeed, quantum fluids support topological defects [4,5], their most famous example being a quantum vortex, which, contrary to a classical vortex, like a tornado, cannot disappear "by itself", via a continuous transformation. This property is due to the difference in vortex and ground state topologies, which is guaranteed by the irrotational nature of the fluid described by a complex wavefunction [6]. The nonadiabatic cooling of such a fluid allows the development of topological defects obeying the KZM scaling, as confirmed by experiments [7] and also predicted for multicomponent BECs [8,9]. However, solitons in 1D and half-vortices in 2D spinor BECs [4,5,10] are only quasitopological defects. Indeed, a dark soliton transforms into a grey and eventually disappears by simple acceleration, and a half-vortex can be unwound by a divergent magnetic field. Another system of interest to study the KZM are cavity exciton-polariton quantum fluids [11,12]. Because of the finite polariton lifetime, polariton condensation can be an out-of-equilibrium process driven by the condensation kinetics rather than by thermodynamics [12,13]. As previously pointed out [14,15], the establishment of a steady state by non-resonant pumping in an initially empty system cannot be an adiabatic process and is therefore equivalent to a quenching of the parameters of the system, leading to the appearance of topological defects.Another class of systems which possess topologically protected states are periodic lattices with topologically non-trivial band structures characterized by non-zero Chern numbers, or Zak phase, depending on their dimensionality. The most well-known examples of such systems are the topological insu...

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Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

2016

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“…The first experimental proof of NBEC [4] has been rapidly followed by the demonstration of superfluidity [9] and of a variety of related effects such as phase coherence [10] and the formation of topological defects [11,12]. The two spin projections of polaritons allow the generation of controllable spin currents [13,14] and the formation of a spinor condensate hosting exotic excitations [15,16] in the presence of spin-orbit interaction or artificial gauge fields [17,18].…”

Section: Introductionmentioning

confidence: 99%

Nonclassical statistics from a polaritonic Josephson junction

Flayac

Savona

2017

Phys. Rev. A

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We theoretically study the emission statistics of a weakly nonlinear photonic dimer during coherent oscillations. We show that the phase and population dynamics allow to periodically meet an optimal squeezing condition resulting in a strongly nonclassical emission statistics. By considering an exciton-polariton Josephson junction driven resonantly by a pulsed classical source, we show that a sizable antibunching should emerge in such a semiconductor system where intrinsic nonclassical signatures have remained elusive to date.

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“…As striking examples, coupled cavities have been used to realise highly efficient sources of entangled photon pairs based on semiconductor quantum dots [10], macroscopic Josephson oscillations of exciton polaritons [11] and photonic graphene [12,13]. They are a versatile building block for the realisation of enhanced sensors [14], single photon sources [15], effective hamiltonian engineering [16] and may allow advances in photonic quantum simulations [17], the study of Tonks-Girardeau gases [18] and many-body physics in general [19].…”

Section: Introductionmentioning

confidence: 99%

Spectral engineering of coupled open‐access microcavities

Flatten

Trichet

Smith

2015

Laser & Photonics Reviews

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Open-access microcavities are emerging as a new approach to confine and engineer light at mode volumes down to the λ 3 regime. They offer direct access to a highly confined electromagnetic field while maintaining tunability of the system and flexibility for coupling to a range of matter systems. This article presents a study of coupled cavities, for which the substrates are produced using Focused Ion Beam milling. Based on experimental and theoretical investigation the engineering of the coupling between two microcavities with radius of curvature of 6 µm is demonstrated. Details are provided by studying the evolution of spectral, spatial and polarisation properties through the transition from isolated to coupled cavities. Normal mode splittings up to 20 meV are observed for total mode volumes around 10 × λ 3 . This work is of importance for future development of lab-on-a-chip sensors and photonic open-access devices ranging from polariton systems to quantum simulators.

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Spin-Orbit Coupling for Photons and Polaritons in Microstructures

Cited by 207 publications

References 48 publications

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

Nonclassical statistics from a polaritonic Josephson junction

Spectral engineering of coupled open‐access microcavities

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