Selective band interaction and long-range hopping in a structured environment with giant atoms

TL;DR

The paper investigates phase-controlled giant atoms coupled to a 1D cross-stitch lattice with coexisting flat and dispersive bands. By tuning the relative phase between two coupling points, giant atoms selectively couple to either the dispersive or flat band, while small atoms interact non-selectively with both. In the band-gap regime, bound states form and enable high-fidelity, long-range dipole-dipole interactions between emitters; giant atoms can further suppress or enhance specific channels, providing precise control over energy exchange. The results suggest robust applications in quantum information processing, including deterministic routing of excitations and tunable quantum memories in structured photonic environments.

Abstract

Giant atoms, which couple to the environment at multiple discrete points, exhibit various nontrivial phenomena in quantum optics due to their nonlocal couplings. In this study, we propose a one-dimensional cross-stitch ladder lattice featuring both a dispersive band and a flat band. By modulating the relative phase between the coupling points, the giant atom selectively interacts with either band. First, we analyze the scenario where the dispersive and flat bands intersect at two points, and the atomic frequency lies within the band. Unlike the small atom, which simultaneously interacts with both bands, a single giant atom with a controllable phase interacts exclusively with the dispersive or flat band. Second, in the bandgap regime, where two atoms interact through bound-state overlaps manifesting as dipole-dipole interactions, we demonstrate that giant atoms enable deterministic long-range hopping and energy exchange with higher fidelity compared to small atoms. These findings provide promising applications in quantum information processing, offering enhanced controllability and selectivity for quantum systems and devices.

Figures (9)

• Figure 1: (a) A two-level emitter interacts with the 1D cross-stitch lattice structure. Each unit cell with two sublattices ($A$ and $B$) is shown in the orange dashed box. $J$ and $t$ are the inter-cell and intra-cell hopping amplitudes. (b) The equivalent lattice model after transformation. The hopping amplitude between the nearest-neighboring sites of the channel D is $2J$. (c) The band structure of the 1D cross-stitch model, featuring a flat band and a dispersive band. The parameters are $J=-1$, $t=1$.
• Figure 2: (a) Numerical and analytical results for the state population of a small emitter coupled to the flat band and the center of the dispersive band. The inset shows the evolution within the time interval $t_1=148$ to $t_2=155$. (b) Field amplitude at $t_1=148$ and $t_2=155$. The parameters used are $J=1$, $t=0$, $\omega_e=0$, and $g=0.3$.
• Figure 3: (a) A giant emitter interacts with the 1D stitch model at two coupling points, $x_a(0)$ and $x_b(0)$, with coupling strengths $g$ and $ge^{i\phi}$, respectively. (b) The equivalent model where the giant atom interacts exclusively with the dispersive band, decoupling from the flat band. The equivalent coupling strength is $G$. (c) The equivalent model where the giant atom interacts exclusively with the flat band, decoupling from the dispersive band.
• Figure 4: The evolution of $P_e(t)$ for a giant emitter inteacting with the flat band when $\phi=0$ (a), and the dispersive band when $\phi=\pi$ (b). Parameters of the whole system are $g=0.1$, $J=1$, and $t=0$.
• Figure 5: (a) The energy bands of the 1D ladder lattice and the emitter's frequency. The emitter's frequency is located in the band gap and near the lower edge of the dispersive band. (b) Numerical results for the excited-state population $P_e(t)=|c_e(t)|^2$ of the small and giant emitters as a function of time $t$. For sufficiently large $t$, $P_e(t)$ of the small emitter oscillates around a steady value, fitting well with the bound state of the giant emitter. (c) The field distributions of sublattices $x_a(n)$ and $x_b(n)$ when the giant emitter couples to sites $x_a(0)$ and $x_b(0)$, forming a bound state. The parameters for the small emitter are $\omega_e=-1.9$, $t=2.4$, $J=1$, and $g=0.1$. For the giant emitter, $\phi=0$ and $g=0.05$, with other parameters unchanged.