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arXiv:2502.09901 · Laser & Photonics Review

Floquet Engineering and Harnessing Giant Atoms in Frequency‐Comb Emission and Bichromatic Correlations in Waveguide QED

Qing‐Yang Qiu, Lili Zheng, Ying Wu, Xin‐You Lü

Published Feb 13, 2025• 5 citations
arXivHTMLPDF

Abstract

Abstract The capability to design spectrally controlled photon emission is not only fundamentally interesting for understanding frequency‐encoded light–matter interactions, but also is essential for realizing the preparation and manipulation of quantum states. Here, a dynamically modulated qubit array is considered, and realize frequency‐controlled single‐photon emission focusing on the generation of a frequency comb constituted solely of even‐parity or anti‐Stokes sidebands. This system also offers parity‐dependent bunching and antibunching in frequency‐filtered quantum correlations. In particular, the waveguide quantum electrodynamics (QED) setup is extended to include chiral and non‐local coupling architectures, thereby enhancing its versatility in Floquet engineering. This proposal also supports the predictable generation of high‐dimensional entangled quantum states, where the corresponding effective Hilbert space dimension is well controlled by energy modulation. Moreover, the utilisation of sophisticated numerical tools, such as the matrix product states (MPSs) and the discretization approach, enables the efficient simulation of multi‐photon dynamics, in which the non‐Markovian Floquet steady states emerge. This work fundamentally broadens the fields of collective emission, and has wide applications in implementing frequency‐encoded quantum information processing and many‐body quantum simulation.

DOI
10.1002/lpor.202401395

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Abstract The capability to design spectrally controlled photon emission is not only fundamentally interesting for understanding frequency‐encoded light–matter interactions, but also is essential for realizing the preparation and manipulation of quantum states. Here, a dynamically modulated qubit array is considered, and realize frequency‐controlled single‐photon emission focusing on the generation of a frequency comb constituted solely of even‐parity or anti‐Stokes sidebands. This system also offers parity‐dependent bunching and antibunching in frequency‐filtered quantum correlations. In particular, the waveguide quantum electrodynamics (QED) setup is extended to include chiral and non‐local coupling architectures, thereby enhancing its versatility in Floquet engineering. This proposal also supports the predictable generation of high‐dimensional entangled quantum states, where the corresponding effective Hilbert space dimension is well controlled by energy modulation. Moreover, the utilisation of sophisticated numerical tools, such as the matrix product states (MPSs) and the discretization approach, enables the efficient simulation of multi‐photon dynamics, in which the non‐Markovian Floquet steady states emerge. This work fundamentally broadens the fields of collective emission, and has wide applications in implementing frequency‐encoded quantum information processing and many‐body quantum simulation.
We develop a general theoretical framework to dynamically engineer quantum correlations and entanglement in the frequency-comb emission from an array of superconducting qubits in a waveguide, rigorously accounting for the temporal modulation of the qubit resonance frequencies. We demonstrate that when the resonance frequencies of the two qubits are periodically modulated with a π phase shift, it is possible to realize simultaneous bunching and antibunching in cross-correlations as well as Bell states of the scattered photons from different sidebands. Our approach, based on the dynamical conversion between the quantum excitations with different parity symmetry, is quite universal. It can be used to control multiparticle correlations in generic dynamically modulated dissipative quantum systems.
We propose and analyze a general scheme to engineer programmable and nonreciprocal interactions in an array of atoms coupled to a photonic waveguide. By subjecting each atom to a local harmonic frequency modulation with a defined phase ${\ensuremath{\theta}}_{i}$, we demonstrate the emergence of effective long-range couplings whose parameters are dynamically controllable. For atoms coupled to a conventional waveguide, the modulation dresses the atomic operators, leading to effective interactions governed by the Bessel function J0{\mathcal{J}}_{0}J0​ whose argument depends on the phase differences $\mathrm{\ensuremath{\Delta}}{\ensuremath{\theta}}_{ij}$. For atoms coupled to a photonic crystal waveguide near its band edge, where the density of states is sharply varying, the modulation can be tuned to selectively activate the J12{\mathcal{J}}_{1}^{2}J12​ term, which simultaneously scales both the coherent and dissipative components of the complex coupling strength ${\mathrm{\ensuremath{\Gamma}}}_{ij}$. Crucially, the spatial profile of the local modulation phases imprints a factor $exp(\mathrm{i}\mathrm{\ensuremath{\Delta}}{\ensuremath{\theta}}_{ij})$ onto the waveguide-mediated coupling strength ${\mathrm{\ensuremath{\Gamma}}}_{ij}$, enabling the synthesis of nonreciprocal quantum interactions. Our approach thus provides a flexible toolbox for simulating a wide range of non-Hermitian Hamiltonians on waveguide-QED platforms.
Radiative coupling between quantum emitters leads to a range of spectacular emission phenomena. Dicke studied the foundations of collectively enhanced and suppressed decay, commonly referred to as super- and subradiance. Collective effects can further result in directionality of the emission, thus offering a complimentary implementation of chiral quantum optics. Waveguide quantum electrodynamics (QED) allows coupling between spatially separated emitters, enabling selective driving. In this work, we control the emission direction for a pair of quantum dots embedded in a bidirectional photonic crystal waveguide offering independent electrical tuning. Notably the emitters are 13 \micro m apart, which corresponds to 26 effective wavelengths, but are nevertheless radiatively coupled. The directionality arises from a dispersive dipole-dipole interaction, which shifts the energy of the collective states, so that the emitter pair effectively forms an artificial molecule. We show that the emission direction can be switched from left- to rightwards by manipulating the relative driving phase while collectively exciting the emitters. In addition, we observe directional photon statistics under continuous driving, with, for example, single photons detected on one output port, and photon pairs on the other. With pulsed excitation, both emitters are fully inverted and correlated photon pairs are observed in time-resolved intensity correlation measurements. This work demonstrates a novel implementation of chiral quantum optics using quantum dots coupled via a non-chiral waveguide, and reports key steps for scaling up as a multi-emitter waveguide QED platform.
-type atom coupled to a T-shaped waveguide. By controlling local coupling phases to engineer quantum interference, perfect directional frequency conversion is achieved without an engineered chiral waveguide structure. The multi-path interference of the giant atom, combined with local phase tuning, enables flexible control over photon transmission direction and frequency, supporting multiple directional conversion channels. In the Markovian limit, the cavity-mediated structure realizes two fully efficient directional channels, while under non-Markovian conditions, retardation effects open several distinct frequency conversion windows. This phase-controlled, multi-frequency directional architecture provides a versatile platform for frequency-multiplexed quantum routing and networking.
Nonlocal light-matter interactions with giant atoms in high-dimensional environments are not only fundamentally intriguing for testing quantum electrodynamics beyond the dipole approximation but also crucial for building high-dimensional quantum networks and engineering multipartite entangled states. Given the enigmatic and largely uncharted collective signatures exhibited by multiple giant atoms within two-dimensional optical baths, we delve into their nonperturbative collective dynamics within the single-excitation subspace, focusing on the case where they are coupled to a common two-dimensional photonic reservoir and employing a resolvent operator approach. We demonstrate that precisely engineered atomic arrangements lead to unconventional quantum dynamics, featuring non-Markovianity-induced beats and long-lived bound states in the continuum, thereby providing a versatile platform for implementing two-dimensional quantum memory. Phenomenologically, we observe the emergence of exotic photon emission patterns in both two- and three-dimensional (3D) baths. The emission directions are shown to be precisely controllable on demand through exact phase engineering of the coupling parameters, enabling a highly efficient chiral light-matter interface. Moreover, our generalization to a 3D bath reveals that coherent dipole-dipole interactions can survive despite the coupling to a continuum of modes, a finding that challenges conventional wisdom regarding decoherence.
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.