Topological Quantum Optics in Two-Dimensional Atomic Arrays

Abstract

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

Topological properties of a dense atomic lattice gas

“…As was shown in [74] and also observed in [75], all states that lie outside the circle |k| = κ are subradiant, i.e., they decay with a rate much smaller than the single atom decay rate . Hence, remarkably, we find that while in case (i) the dissipation makes the excitation decay after only a few sites, the excitation in case (ii) is much less affected by the dissipation (see discussion in [57]).…”

“…We have shown that one can excite edge states that allow for the transport of an excitation over long distances along the edge of the lattice that are robust to the presence of defects. Moreover, these edge states are remarkably long-lived due to the collective character of the dissipation (this effect has also been investigated in [74,75]). Finally, we have found that, due to the long-ranged character of the interactions, the bulk-boundary relations, well established for topological insulators with short-range interactions, are not generally valid in our setting.…”

Photonic band structure of two-dimensional atomic lattices

“…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.…”

“…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].…”

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

“…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.…”