Topological properties of a dense atomic lattice gas

Bettles, Robert J.; Minář, Jiří; Adams, Charles S.; Lesanovsky, Igor; Olmos, Beatriz

doi:10.1103/physreva.96.041603

Cited by 112 publications

(118 citation statements)

References 79 publications

(164 reference statements)

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“…Quantum optical properties of lattices of atoms and atomlike emitters are being actively explored both theoretically and experimentally [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In such lattices, atoms are assumed to be confined such that tunneling between sites is negligible and they interact via photon-mediated dipole-dipole interactions giving rise to hybridized atom-photon bands.…”

Section: Introductionmentioning

confidence: 99%

“…The photonic band structure of three-dimensional (3D) atomic lattices has been investigated in a number of studies [2][3][4][5][6]. Recently, there has been significant interest in the photonic properties of two-dimensional (2D) atomic lattices, which have been shown to exhibit a variety of remarkable phenomena, including subradiance [15][16][17][18], near perfect reflection of radiation [12,14], and long-lived topological excitations [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…[5,6] and focus on 2D lattices, where the axial symmetry is broken along the third dimension. Previous * jperczel@mit.edu photonic calculations involving infinite 2D atomic lattices either were restricted to two-level atoms in a square lattice [15], required summations in real space where convergence is slow [11,14], or relied on the method that we will now describe in detail [10]. As an application of our method, we study the topological properties of both Bravais and non-Bravais lattices in free space.…”

Section: Introductionmentioning

confidence: 99%

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Photonic band structure of two-dimensional atomic lattices

et al. 2017

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Two-dimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation, and long-lived topological edge states. Studies of emission and scattering of photons in such lattices require complete treatment of the radiation pattern from individual atoms, including long-range interactions. We describe a systematic approach to perform the calculations of collective energy shifts and decay rates in the presence of such long-range interactions for arbitrary two-dimensional atomic lattices. As applications of our method, we investigate the topological properties of atomic lattices both in free space and near plasmonic surfaces.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Photonic band structure of two-dimensional atomic lattices

et al. 2017

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“…These include exotic states, such as those with filling fractions ν ¼ 5=2 and ν ¼ 12=5, which may feature non-Abelian excitations [69]. In addition, the inherent protection against losses may also be used for the realization of robust quantum nonlinear optical devices for potential applications in quantum information processing and quantum state transfer [70].…”

Section: Prl 119 023603 (2017) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Topological Quantum Optics in Two-Dimensional Atomic Arrays

et al. 2017

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We demonstrate that two-dimensional atomic emitter arrays with subwavelength spacing constitute topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space emission are strongly suppressed. Breaking timereversal symmetry with a magnetic field results in gapped photonic bands with nontrivial Chern numbers and topologically protected, long-lived edge states. Due to the inherent nonlinearity of constituent emitters, such systems provide a platform for exploring quantum optical analogs of interacting topological systems. DOI: 10.1103/PhysRevLett.119.023603 Charged particles in two-dimensional systems exhibit exotic macroscopic behavior in the presence of magnetic fields and interactions. These include the integer [1], fractional [2], and spin [3] quantum Hall effects. Such systems support topologically protected edge states [4,5] that are robust against defects and disorder. There is a significant interest in realizing topologically protected photonic systems. Photonic analogs of quantum Hall behavior have been studied in gyromagnetic photonic crystals [6][7][8][9][10][11], helical waveguides [12], two-dimensional lattices of optical resonators [13][14][15] and in polaritons coupled to optical cavities [16]. An outstanding challenge is to realize optical systems which are robust not only to some specific backscattering processes but to all loss processes, including scattering into unconfined modes and spontaneous emission. Another challenge is to extend these effects into a nonlinear quantum domain with strong interactions between individual excitations. These considerations motivate the search for new approaches to topological photonics.In this Letter, we introduce and analyze a novel platform for engineering topological states in the optical domain. It is based on atomic or atomlike quantum optical systems [17], where time-reversal symmetry can be broken by applying magnetic fields and the constituent emitters are inherently nonlinear. Specifically, we focus on optical excitations in a two-dimensional honeycomb array of closely spaced emitters. We show that such systems maintain topologically protected confined optical modes that are immune to large imperfections as well as to the most common loss processes such as scattering into free-space modes. Such modes can be used to control individual atom emission, and to create quantum nonlinearity at a single photon level.The key idea is illustrated in Fig. 1(a). We envision an array with interatomic spacing a and quantization axisẑ

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“…From the experimental side, recent proposals with Shiba states [31][32][33][34], Floquet Hamiltonians [35,36], atoms coupled to radiation fields [37][38][39], and trapped ions [40] opened the possibility to synthesize and observe the mentioned LR physics.…”

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confidence: 99%

Edge insulating topological phases in a two-dimensional superconductor with long-range pairing

2018

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We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest-neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases occur, not continuously connected with any short-range phase and not belonging to the standard families of topological insulators/superconductors. These phases are signaled by the violation of the area law for the Von Neumann entropy, by semi-integer Chern numbers, and by edge modes with nonzero mass. The latter feature results in the absence of single-fermion edge conductivity, present instead in the short-range limit. The definition of a bulk-topology and the presence of a bulk-boundary correspondence is suggested also for the long-range phases. Recent experimental proposals and advances open the possibility to probe the described long-range effects in near-future realistic set-ups. PACS numbers:Introduction -In recent years, the topological phases of matter have become a central focus for physical investigation. A groundbreaking result is the classification of the symmetry-protected topologically inequivalent classes for non interacting fermionic systems (topological insulators/superconductors) [1][2][3][4][5][6]. This theoretical breakthrough has been probed on particular solid-state compounds [7][8][9][10].Notwithstanding the presence of a nonvanishing bulk energy gap, the most relevant feature displayed by nontrivial topological insulators/superconductors is a conductivity localized on the edges, due to massless edge mode with a dynamics well distinguished from the bulk excitations. Moreover, continuous transitions with a vanishing mass gap generally divide phases with different topology (even if also first order transitions seem possible if perturbative interactions between fermions are added [11]). Regarding the entanglement content, topological insulators/superconductors display exponentially saturating entanglement and correlations, giving rise to the area-law for the Von Neumann entropy between the two elements of a real-space bipartition.These features characterize quantum systems governed by Hamiltonians with short-range (SR) terms. However, in recent years, long-range (LR) classical and quantum systems [12], obtained renewed attention. Independent theoretical works have concluded that LR systems can exhibit many interesting and unusual properties, essentially due to the violation of locality (see e.g. [13][14][15][16][17][18][19][20]). In particular, one-dimensional LR models can host new phases, manifesting striking properties, not present in the SR limit. [15][16][17][21][22][23][24][25][26][27][28][29][30].In spite of these relevant achievements, full comprehension and classification phases emerging from Hamiltonians with LR terms are still not available.In [29] a partial solution to these problems has been discussed, exploiting one-dimensional topological superconductive chains as playgrounds, but inferring nontrivial properties also for LR topological insulators...

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Topological properties of a dense atomic lattice gas

Cited by 112 publications

References 79 publications

Photonic band structure of two-dimensional atomic lattices

Photonic band structure of two-dimensional atomic lattices

Topological Quantum Optics in Two-Dimensional Atomic Arrays

Edge insulating topological phases in a two-dimensional superconductor with long-range pairing

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