Quasiflat band enabling subradiant two-photon bound states

Abstract

We study theoretically the radiative lifetime of bound two-particle excitations in a waveguide with an array of two-level atoms, realising a 1D Dicke-like model. Recently, Zhang et al. [1] have numerically found an unexpected sharp maximum of the bound pair lifetime when the array period d is equal to 1/12th of the light wavelength λ0 [arXiv:1908.01818]. We uncover a rigorous transformation from the non-Hermitian Hamiltonian with the long-ranged radiative coupling to the nearest-neigbor coupling model with the radiative losses only at the edges. This naturally explains the puzzle of long lifetime: the effective mass of the bound photon pair also diverges for d = λ0/12, hampering an escape of photons through the edges. We also link the oscillations of the lifetime with the number of atoms to the nonmonotous quasi-flat-band dispersion of the bound pair.

Radiative topological biphoton states in modulated qubit arrays

“…The bound states in the bulk have a decay rate smaller than that of the bound-edge states by an order of magnitude. The intuitive explanation is that the radiative loss happens at the edge qubits, and the bound states in the bulk have less occupation at the edge than that of the bound-edge states [42]. These bound states can be classified as subradiant states, which have the radiative lifetime larger than that of the single qubit.…”

“…According to our calculations, the bound-edge states have the finite radiative decay rate on the order of ∼ϕ 2 0 . This is because these states appear at an interface between the qubit array and free space, where the radiative loss becomes significant [42]. However, if we connect two-qubit arrays with different modulation phases, there should be edge states with longer lifetime at the interface located in the bulk of the array.…”

Quantum Hall phases emerging from atom–photon interactions

“…The waveguide-mediated long-ranged couplings, intrinsic for the waveguide QED setup are quite uncharacteristic for traditional quantum systems and there is much more to explore. For example, we have focused here only on the regime of extremely subwavelength distances between the atoms, where two-polariton bound states 58,61 play no role. Polariton-polariton interactions could be even more interesting in Bragg-spaced lattices, where the non-Markovian effects are drastically enhanced [62][63][64] .…”

Polariton interaction in one-dimensional arrays of atoms coupled to waveguides

“…As a consequence applications of photon-interaction rely on indirect interaction via non-linear coupling to matter [1][2][3]. The absorption and re-emission of light in such non-linear media gives rise to a plethora of phenomena like super- [4][5][6] and subradiance [6][7][8][9], electromagnetically induced transparency [10], light-matter quantum interfaces [11], single photon transistors [12], bound states of light [13][14][15][16][17][18][19][20][21], as well as elastic and inelastic scattering [22][23][24]. Understanding such phenomena is of immense technological importance as a crucial ingredient for quantum computation and communication hardware based on photonic systems [1].…”