Topological Phases of Sound and Light

Peano, Vittorio; Brendel, Christian; Schmidt, M. P.; Marquardt, Florian

doi:10.1103/physrevx.5.031011

Cited by 366 publications

(380 citation statements)

References 66 publications

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“…Quenches across a non-equilibrium phase transition provide further insight into the interplay between noise and external drives on criticality and thermalization [7,8]. In this context photonic systems play a prominent role, thanks to their versatility [9][10][11][12][13][14][15].…”

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confidence: 99%

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

2016

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We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a singlemode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behaviour which is first dominated by coherent long-range forces, and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the selforganized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems. The quest for a systematic understanding of nonequilibrium phenomena is an open problem in theoretical physics for its importance in the description of dynamics from the microscopic up to astrophysical scales [1-3]. Aspects of these dynamics are studied in the relaxation of systems undergoing temporal changes (quenches) of the control field across a critical point [4][5][6]. Quenches across a non-equilibrium phase transition provide further insight into the interplay between noise and external drives on criticality and thermalization [7,8]. In this context photonic systems play a prominent role, thanks to their versatility [9][10][11][12][13][14][15].Polarizable particles in a high-finesse cavity, like in the setup illustrated in Fig. 1(a), offer a unique system to study relaxation in long-range interacting systems. Here, multiple photon scattering mediates particleparticle interactions whose range scales with the system size in a single-mode cavity [15][16][17][18]. In this limit, atomic ensembles in cavities are expected to share several features with other long-range interacting systems such as gravitational clusters and non-neutral plasmas in two or more dimensions [3,16,19]. The equilibrium thermodynamics of these systems can exhibit ensemble inequivalence [3,20], while quasi-stationary states (QSS) typically characterise the out-of-equilibrium dynamics [3,[21][22][23]. QSS are metastable states in which the system is expected to remain trapped in the thermodynamic limit, they are Vlasov-stable solutions and thus depend on the initial state. So far, however, evidence of QSS has been elusive. It has been conjectured that noise and dissipation can set a time scale that limits the QSS lifetime [24][25][26][27], and possibly gives rise to dynamical phase transitions [25]. In Ref. [28] it was shown that, in pr...

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confidence: 99%

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

2016

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“…These edge states do not rely on inter-particle interactions but are topologically protected: they are robust against disorder and perturbations. Different implementations of topologically nontrivial band structures have been studied theoretically and experimentally in various systems, including photonics [21,22], optomechanics [23,24], excitons [25], and plasmonic zigzag chains [26][27][28][29]. Optical systems offer an important advantage compared to the electronic ones and to atomic BECs, because of the facility of their fabrication and the complete accessibility of the wavefunction in time, real and reciprocal space.…”

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confidence: 99%

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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“…Additionally, the optomechanical coupling in the surface waveguides could be compared with that in the standard silicon waveguides. Last but not least, these results may potentially stimulate additional design rules for new topological insulators in optomechanics [49,50]. …”

Section: Discussionmentioning

confidence: 99%

Simultaneous Guidance of Surface Acoustic and Surface Optical Waves in Phoxonic Crystal Slabs

Wang

Zhang

2017

Crystals

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Phoxonic crystals, which exhibit simultaneous phononic and photonic bandgaps, are promising artificial materials for optomechanical and acousto-optical devices. In this paper, simultaneous guidance of surface acoustic and surface optical waves in truncated phoxonic crystal slabs with veins is investigated using the finite element method. The phoxonic crystal slabs with veins can show dual large bandgaps of phononic and photonic even/odd modes. Based on the phononic and photonic bandgaps, simultaneous surface acoustic and optical modes can be realized by changing the surface geometrical configurations. Both acoustic and optical energies can be highly confined in the surface region. The effect of the surface structures on the dispersion relations of surface modes is discussed; by adjusting the surface geometrical parameters, dual single guided modes and/or slow acoustic and optical waves with small group velocity dispersions can be achieved. The group velocities are about 40 and 10 times smaller than the transverse velocity of the elastic waves in silicon and the speed of light in vacuum, respectively.

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Topological Phases of Sound and Light

Cited by 366 publications

References 66 publications

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

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

Simultaneous Guidance of Surface Acoustic and Surface Optical Waves in Phoxonic Crystal Slabs

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