Superstrong Dynamics and Directional Emission of a Giant Atom in a Structured Bath

TL;DR

This work demonstrates a giant atom formed by a transmon qubit non-locally coupled to a 44-site coupled cavity array implementing a dimerized photonic bath. Through engineered interference, the qubit predominantly couples to a subset of high-frequency symmetric modes, reaching a superstrong coupling regime ($G_n/\overline{\Delta\Omega_n}>1$) and inducing multimode hybridization and effective mode–mode interactions beyond the Jaynes–Cummings paradigm. By breaking inversion symmetry, the dressed CCA modes become spatially localized to one side of the qubit, enabling directional emission of single photons with measurable left/right discrimination and substantial, though not perfect, directionality. These results provide a precise platform for controlling multimode light–matter interactions in structured environments and suggest avenues toward non-perturbative multimode QED, directional quantum communication, and topologically informed quantum optics.

Abstract

Quantum emitters coupled to waveguides with nonlinear dispersion show rich quantum dynamics with the promise of implementing non-trivial non-Markovian quantum models. Recent advances in engineered photonic environments now allow the realization of discrete-site waveguides with tailored dispersion, yet most implementations of waveguide QED remain limited to a local qubit-waveguide coupling. Here, we study a transmon qubit non-locally coupled to a high-impedance coupled cavity array (CCA), thus implementing a \emph{giant atom} in a structured photonic environment. The non-local coupling produces interference with the CCA modes, selectively enhancing interaction with even and long-wavelength modes, while suppressing coupling to odd and short-wavelength modes. For a subset of symmetric, long-wavelength modes, we reach the superstrong coupling regime. In this regime, measurements of the atomic participation ratio reveal strongly hybridized eigenmodes on a par with a strongly reduced qubit participation at the frequency of maximum hybridization with the qubit, in agreement with theory. Time-domain measurements of the qubit dynamics show clear deviations from the single-mode Jaynes--Cummings model, marked by the emergence of mode--mode interactions. By breaking spatial inversion symmetry of the CCA, the qubit seeds dressed eigenmodes confined to either the right or left of the qubit, which we exploit to implement and characterize a directional photon-emission protocol. These results demonstrate precise control over multimode light--matter interaction in a structured photonic environment.

Figures (28)

• Figure 1: Giant atom interacting with a structured photonic bath.(a) Concept of a giant atom coupled non-locally to a dimerized coupled-cavity array (CCA). Resonators of bare frequency $\omega_r/2\pi$ are coupled with staggered rates $J_1/2\pi$ and $J_2/2\pi$. A qubit of frequency $\omega_q/2\pi$ couples to site $s$ with strength $g_s/2\pi$. (b) False-colored optical micrograph of a representative device (aluminum: light gray; silicon: dark gray; cavities: green; qubit: red; drive/readout/flux lines: pink/violet/blue). (c) False-colored scanning electron micrograph. NbN inductors of the CCA resonators are highlighted in light blue. The color code is the same as in the previous panel. (d) CCA mode spectrum $\Omega_n/2\pi$ vs mode index $n$ (gray dots). Bandgaps are shaded gray. Long green markers highlight the three modes analyzed in panel e. (e) Spatial profiles of CCA modes$\ket{\phi_{44}}$, $\ket{\phi_{43}}$, and $\ket{\phi_{1}}$ vs site index $s$ (three shades of green). Bars at the qubit-coupling sites are overlaid in red. The vertical dashed line marks the CCA center. (f) Superstrong-coupling metric $G_n/\overline{\Delta\Omega_n}$ vs CCA mode index $n$, where $\overline{\Delta\Omega_n}$ is the local average mode spacing around CCA mode $n$ (horizontal dashed line indicates the unity). Inset: spatial profile of the coupling, $g_s/2\pi$, between the qubit and cavity $s$ of the CCA. (g) Schematic illustrating how coupling a qubit away from the CCA center breaks inversion symmetry (middle), leading to hybridization between even- and odd-parity CCA modes (top) and resulting in left- and right-confined dressed modes at specific qubit frequencies (bottom). The vertical dashed line indicates the CCA center.
• Figure 1: Qubit–mode coupling $G_n/2\pi$ versus mode index $n$.
• Figure 2: Steady-state interaction of a giant atom with a structured photonic bath.(a) Single-tone transmission of the CCA as a function of bare qubit frequency $\omega_q/2\pi$. The dressed qubit frequency extracted from two-tone spectroscopy is shown above the upper band (purple circles) and inside the middle bandgap (pink circles). Model predictions according to \ref{['eq:normalSpaceHamiltonian']} for the dressed qubit are shown as purple and pink lines, and the bare qubit frequency as a red dashed line. Crosses indicate the dressed CCA modes analyzed in panel b. Inset: zoom-in from $\omega_p/2\pi = 7.7GHz$ to 8GHz; orange lines show eigenvalues, $\tilde{\omega}_m/2\pi$, of the fitted disorder-free model according to \ref{['eq:normalSpaceHamiltonian']}. (b) Atomic participation ratio of each dressed CCA modes, $|u_m|^2$. Continuous lines: expected atomic participation ratio, $|u_m|^2$, of each dressed CCA modes according to \ref{['eq:normalSpaceHamiltonian']}; circles and crosses: values extracted from two-tone and single-tone spectroscopy, respectively (error bars from the standard deviation of fitted dressed-mode frequencies), using $\abs{u_m}^2 = \dd \tilde{\omega}_m / \dd \omega_q$. Vertical black dashed line: reference atomic ratio of $0.5$. Horizontal black dashed line: qubit frequency where the atomic ratio of the APBS, $|u_{45}|^2$, is 0.5 (also marked in panel a). Mode labels are indicated in the legend in panel a.
• Figure 2: Steady-state interaction of a giant atom interacting with a structured photonic bath (comparison to a model including disorder)(a) Single-tone transmission of the CCA as a function of bare qubit frequency $\omega_q/2\pi$. The dressed qubit frequency extracted from two-tone spectroscopy is shown above the upper band (purple circles) and inside the middle bandgap (pink circles). Model predictions according to \ref{['eq:normalSpaceHamiltonian']} for the dressed qubit are shown as purple and pink lines, and the bare qubit frequency as a red dashed line. Crosses indicate the dressed CCA modes analyzed in panel b. Inset: zoom-in from $\omega_p/2\pi = 7.7GHz$ to 8GHz. The orange lines in the inset and orange dashed lines in the main panel show the eigenvalues of the fitted model according to \ref{['eq:normalSpaceHamiltonian']}, including resonant frequency disorder with standard deviation $\sigma = 21.8MHz$. (b) Atomic participation ratio of each dressed CCA modes, $|u_m|^2$. Continuous lines: expected atomic participation ratio, $|u_m|^2$, of each dressed CCA modes according to \ref{['eq:normalSpaceHamiltonian']}; circles and crosses: values extracted from two-tone and single-tone spectroscopy, respectively (error bars from the standard deviation of fitted dressed-mode frequencies), using $\abs{u_m}^2 = \dd \tilde{\omega}_m / \dd \omega_q$. Mode labels are indicated in the legend in panel a.
• Figure 3: Superstrong dynamics.(a) Pulse sequence: the qubit is excited, non-adiabatically displaced in frequency for a time $\tau$, then returned at its initial frequency for readout. (b) Zoom-in on the spectroscopy of \ref{['fig:fig2']}. Energy spacings between consecutive and next-nearest dressed CCA modes are denoted $\Delta\tilde{\omega}_n^{(1)}/2\pi$ (purple arrows) and $\Delta\tilde{\omega}_n^{(2)}/2\pi$ (orange arrows), respectively. (c) Measured qubit excited-state population versus $\tau$ and $\omega_q/2\pi$. The black dot marks the bare qubit frequency at $\tau=0$, corresponding to a dressed frequency $\tilde{\omega}_q/2\pi = 7.43GHz$. (d) Fast Fourier transform of the data in panel c. Purple (orange) lines indicate $\Delta\tilde{\omega}_n^{(1)}/2\pi$ ($\Delta\tilde{\omega}_n^{(2)}/2\pi$). The intensity of the lines is proportional to $|u_i|^2|u_j|^2$. Red dots mark $G_n/\pi$, the expected Rabi rate between the qubit and CCA mode $n$. (e) Hamiltonian $H_k$ in the CCA mode basis [see \ref{['methods']}], with bare eigenmodes of frequency $\Omega_n/2\pi$, coupling rates $G_n/2\pi$, and the bare qubit at $\omega_q/2\pi$. Just three modes are shown. (f) Corresponding effective Hamiltonian $H_{\rm eff}$ from perturbation theory [see \ref{['methods']}], featuring effective eigenmodes of frequency $\Omega_n^{\rm eff}/2\pi$ and induced mode--mode couplings $G_{n,n^\prime}/2\pi$, between modes $n$ and $n^\prime$. (g) Comparison between expected and measured Rabi rates versus mode index. Red dots: $G_n/\pi$. Purple squares: $\Delta\tilde{\omega}_n^{\star(1)}/2\pi$, the nearest-neighbor mode frequency spacing $\Delta\tilde{\omega}_n^{(1)}$ at which $|u_n|^2|u_{n+1}|^2$ is maximum. Green crosses: $\Delta\tilde{\omega}_{n, \rm eff}^{\star(1)}/2\pi$, the effective nearest-neighbor mode frequency spacing $\Delta\tilde{\omega}_{n, \rm eff}^{(1)}/2\pi$ at which $|u_n|^2|u_{n+1}|^2$ is maximum $H_{\rm eff}$. (h) Zoom-in of the red frame in panel d, the markers and lines as previously defined in panel d and g. Vertical dashed lines: bare qubit frequencies at which $|u_n|^2|u_{n+1}|^2$ is maximum.