Bound states in the continuum in spin-orbit-coupled atomic systems

Abstract

We show that the interplay between spin-orbit coupling and Zeeman splitting in atomic systems can lead to the existence of bound states in the continuum (BICs) supported by trapping potentials. Such states have energies falling well within the continuum spectrum, but nevertheless they are localized and fully radiationless. We report the existence of BICs, in some cases in exact analytical form, in systems with tunable spin-orbit coupling and show that the phenomenon is physically robust. We also found that BIC states may be excited in spin-orbit-coupled Bose-Einstein condensates, where under suitable conditions they may be metastable with remarkably long lifetimes. [6,7] at the macroscopic scale. SOC is a fundamental mechanism that couples the momentum and spin degrees of freedom, thereby introducing a wealth of physical phenomena. For example, SOC [9] may change the spectrum of the system to an extent that stripe-phase states emerge [8], it modifies the band structure of periodic potentials thus strongly affecting Bloch oscillations [10], and introduces new properties in nonlinear states [11,12] supported by Bose-Einstein condensates (SO-BECs). However, to date attention has only been devoted to conventional localized modes. Here we uncover the existence of BICs, i.e., discrete localized states with energies falling into the continuous spectrum that contrary to intuition are radiationless, in atomic systems with SOC. In this paper we uncover the existence of BICs in a whole new class of physical systems, constituted by twolevel atoms, including BECs, with SOC. We find analytical expressions for BIC states in selected trapping potentials and, importantly, show that the phenomenon is robust, i.e., that BICs also exist in potentials deviating from the analytical ones. Also, calculations for nonlinear systems with two-body interactions suggest the existence of almost radiationless BICs in BECs with SOC, too.We start by addressing a two-level atom placed in an external (synthetic) magnetic field inducing a Zeeman splitting 2Ω. The atomic levels 1 and 2 are affected by the potentials V 1 (x) and V 2 (x), respectively. We address a one-dimensional geometry and account for SOC in the form γkσ y [6,7], with γ being the SOC strength. In the units where = m = 1, the Hamiltonian readswhere k = −i∂ x and σ x,y,z are the Pauli matrices. It is assumed that the potentials V 1,2 (x) have no singularities and that they decay at x → ±∞ exponentially or faster, i.e., lim x→±∞ V 1,2 (x) = 0. First we present qualitative arguments showing that a broad class of potentials V(x), satisfying quite general conditions, may support BICs in the presence of SOC. To this end, we recall that in the absence of the potential (i.e., when V(x) ≡ 0) the dispersion relation, de-

Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps

“…These exact solutions for BIC states in the two-component systems are somewhat similar to those found in Ref. [70], which addressed a system of spin-orbit-coupled linear Gross-Pitaevskii equations for a binary BEC. In that work, exact solutions were produced for a specially designed form of the trapping potential.…”

Formation of Bound States in the Continuum in Hybrid Plasmonic-Photonic Systems

“…BICs in photonic systems were realized for the first time in 2008 [14] and since then there has been growing interest in their implementations as well as practical applications [2,[15][16][17][18][19][20][21][22][23][24][25]. There have been numerous realizations of BICs in dielectric systems [ [2,18,[26][27][28][29].…”

Bound states in the continuum in a two-dimensional PT-symmetric system

“…Today different powerful theoretical approaches to construct potentials supporting BICs are known. They include ideas inspired in the techniques developed for super-symmetric quantum mechanics [5,6] or for engineering reflectionless potentials [7], as well las formalisms based on Darboux transformation [8], separability of Hamiltonians [9], or coupled spinor systems [10]. Experimental observations of BICs were reported in acoustics early [11] and more recently in diverse optical settings [12][13][14][15][16][17][18][19][20][21][22][23].…”