Engineering and Harnessing Giant Atoms in High-Dimensional Baths: A Proposal for Implementation with Cold Atoms

Emitters coupled simultaneously to distant positions of a photonic bath, the so-called giant atoms, represent a new paradigm in quantum optics. When coupled to one-dimensional baths, as recently implemented with transmission lines or SAW waveguides, they lead to striking effects such as chiral emission or decoherence-free atomic interactions. Here, we show how to create giant atoms in dynamical state-dependent optical lattices, which offers the possibility of coupling them to structured baths in arbitrary dimensions. This opens up new avenues to a variety of phenomena and opportunities for quantum simulation. In particular, we show how to engineer unconventional radiation patterns, like multidirectional chiral emission, as well as collective interactions that can be used to simulate nonequilibrium many-body dynamics with no analog in other setups. Additionally, the recipes we provide to harness giant atoms in high dimensions can be exported to other platforms where such nonlocal couplings can be engineered.

Figure 1

(a) State-dependent optical lattice scheme to simulate quantum optical phenomena: one deep lattice $V_b({\mathbf{R}}_b)$ (blue) traps the atomic state that mimics the QE behavior, whereas a shallower one, $V_a({\mathbf{R}}_a)$, lets matter-wave propagation at rate $J$. The two atomic states can be connected through a local laser(s) or microwave field (green) with strength ${\mathrm{\Omega }}_{{\mathbf{n}}_j}$. The relative position between the lattices, and of the local laser can be dynamically tuned ${\mathbf{R}}_b(t)$. (b) Pictorial representation on how the effective giant atom couplings emerge from the stroboscopic movement between the lattices.

Figure 2

Bath population at a time $tJ=N/4$ after the deexcitation of a single QE that moves between two lattice sites at positions (0,0), (1,1), such that $g_{{\mathbf{n}}_1[{\mathbf{n}}_2]}=g{\cos }^2(\omega t/2)[{\sin }^2(\omega t/2)]$, with $g=0.1J$ and $\omega$ as depicted in the legend. Bath linear size is $N=512$.

Figure 3

(a) Bath probability amplitude at a time $tJ=N/4$ for a single giant QE coupled with $G_{\mathrm{pur}}(\mathbf{k})$, $g=0.1J$ and bath linear size is $N=512$. (b) Comparison of the density of states of the structured bath (black), with the effective spectral density which includes the $\mathbf{k}$ dependence of $G_{\mathrm{pur}}(\mathbf{k})$, i.e., $D_{\mathrm{eff}}(E)=\sum _{\mathbf{k}}|G_{\mathrm{pur}}(\mathbf{k}){|}^2\delta \mathbf{(}E-\omega (\mathbf{k})\mathbf{)}$.

Figure 4

(a),(b) Bath probability amplitude at a time $tJ=N/4$ for a single giant QE coupled with $G_{\text{trunc}}(\mathbf{n};n_{\mathrm{tr}})$, respectively, $g=0.1J$ and bath linear size is $N=512$. Inset: Corresponding spatial coupling profile $|G(\mathbf{n})|$ using Eq. (7). The red outline indicates the truncation we use to plot the figure. (c)–(d) $1-F$, where $F$ is the fraction of the emission into the desired directions for the parameters of panels (a) and (b), as a function of the number of terms in the sum $G_{\text{trunc}}(\mathbf{n};n_{\mathrm{tr}})$.