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EMISSION DYNAMICS OF A QUBIT IN PHOTONIC LATTICES WITH SYNTHETIC POTENTIALS

PINTO, Marcel Augusto

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

Engineering the on-site frequencies of a photonic lattice provides a powerful route to endow emitted photons with non-trivial dynamical and topological properties, reshaping the way a coupled qubit decays. This thesis investigates the emission dynamics of a qubit weakly coupled to photonic lattices hosting such synthetic potentials, showing how the resulting band structure dictates qualitatively distinct regimes of light-matter interaction.In the first part, we study a qubit coupled to a one-dimensional coupled-cavity array with a linear gradient in the cavity frequencies, which acts on photons as a synthetic force $F$. For strong $F$, emission becomes reversible and is captured by an effective Jaynes--Cummings model, producing a chiral, time-periodic excitation of an extended region of the array, either to the right or to the left of the qubit depending on its frequency. For weak $F$, the decay is non-Markovian and exhibits revivals reminiscent of atoms between mirrors, even though no mirrors are present: the finite bandwidth confines the emitted photon, and the dynamics is well described by a delay differential equation in which the amplitude and period of Bloch oscillations play the role of cavity length and round-trip time.In the second part, we move to two dimensions and couple a giant atom, a qubit with multiple, spatially separated coupling points, non-locally to a honeycomb lattice of resonators with detuned sublattice frequencies. By suitably arranging the coupling points, the giant atom selectively addresses a single valley, a capability unattainable with a local emitter. This valley-selective coupling endows the emitted photons with an effective valley-polarized Berry curvature, giving rise to valley-polarized edge modes at domain walls between regions of opposite sublattice detuning. As a consequence, a giant atom placed near such a domain wall exhibits chiral emission of valley-polarized photons without breaking time-reversal symmetry, suggesting a natural implementation in circuit QED.Together, these results establish synthetic potentials in photonic lattices as a versatile tool for controlling qubit emission, linking waveguide QED to Bloch-oscillation physics and to valleytronics.

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Engineering the on-site frequencies of a photonic lattice provides a powerful route to endow emitted photons with non-trivial dynamical and topological properties, reshaping the way a coupled qubit decays. This thesis investigates the emission dynamics of a qubit weakly coupled to photonic lattices hosting such synthetic potentials, showing how the resulting band structure dictates qualitatively distinct regimes of light-matter interaction.In the first part, we study a qubit coupled to a one-dimensional coupled-cavity array with a linear gradient in the cavity frequencies, which acts on photons as a synthetic force FFF. For strong FFF, emission becomes reversible and is captured by an effective Jaynes--Cummings model, producing a chiral, time-periodic excitation of an extended region of the array, either to the right or to the left of the qubit depending on its frequency. For weak FFF, the decay is non-Markovian and exhibits revivals reminiscent of atoms between mirrors, even though no mirrors are present: the finite bandwidth confines the emitted photon, and the dynamics is well described by a delay differential equation in which the amplitude and period of Bloch oscillations play the role of cavity length and round-trip time.In the second part, we move to two dimensions and couple a giant atom, a qubit with multiple, spatially separated coupling points, non-locally to a honeycomb lattice of resonators with detuned sublattice frequencies. By suitably arranging the coupling points, the giant atom selectively addresses a single valley, a capability unattainable with a local emitter. This valley-selective coupling endows the emitted photons with an effective valley-polarized Berry curvature, giving rise to valley-polarized edge modes at domain walls between regions of opposite sublattice detuning. As a consequence, a giant atom placed near such a domain wall exhibits chiral emission of valley-polarized photons without breaking time-reversal symmetry, suggesting a natural implementation in circuit QED.Together, these results establish synthetic potentials in photonic lattices as a versatile tool for controlling qubit emission, linking waveguide QED to Bloch-oscillation physics and to valleytronics.
Valleytronics and valley photonics exploit the valley degree of freedom to encode and manipulate information. Here we show that photonic valleys can be selectively addressed in quantum optics using a simple two-level emitter, provided it is coupled nonlocally to the field, thereby realizing a so-called giant atom. Specifically, we consider a qubit coupled at multiple points to an engineered honeycomb lattice of resonators with detuned sublattice frequencies. By tailoring the geometry of the coupling points, the giant atom can be made to emit selectively into a single valley. The emitted photons thereby acquire a well-defined valley character and inherit the associated Berry curvature. By placing the qubit near a domain wall between regions of opposite sublattice detuning, whose interface supports valley-polarized edge modes, emission becomes chiral along the domain wall. This provides a promising route toward implementation of single-photon disorder-robust chiral emission without breaking time-reversal symmetry of the electromagnetic medium in platforms such as circuit QED.
In this paper we investigate the non-Markovian dynamics of a giant atom coupled to a one-dimensional photonic lattice with synthetic gauge fields. By engineering a complex-valued hopping amplitude, we break reciprocity and explore how chiral propagation and phase-induced interference affect spontaneous emission, bound-state formation, and atom–field entanglement. The giant atom interacts with the lattice at multiple, spatially separated sites, leading to rich interference effects and decoherence-free subspaces. We derive an exact expression for the self-energy and perform real-time Schrödinger simulations in the single-excitation subspace, for the atomic population, von Neumann entropy, field localization, and asymmetry in emission. Our results show that the hopping phase ϕ governs not only the directionality of emitted photons but also the degree of atom–bath entanglement and photon localization. Remarkably, we observe robust bound states inside the photonic band and directional asymmetry, due to interference from spatially separated coupling points. These findings provide a basis for engineering non-reciprocal, robust, and entangled light–matter interactions in structured photonic systems.
We investigate the entanglement dynamics of two giant atoms coupled to a one-dimensional photonic lattice with synthetic chirality. The atoms are connected to multiple lattice sites in a braided configuration and interact with a structured photonic reservoir featuring direction-dependent hopping phases. By tuning the atomic detuning and the synthetic gauge phase, we identify distinct dynamical regimes characterized by decoherence-free population exchange, damped oscillations, long-lived revivals, and excitation trapping. Using a combination of time-domain simulations and resolvent-based analysis, we show how interference and band structure effects lead to the emergence of bound states, quasi-bound states, and phase-dependent entanglement dynamics. We compare the initial states with localized and delocalized atomic excitations, demonstrating that pre-existing entanglement can enhance the robustness against decoherence or accelerate its loss, depending on the system parameters. These results highlight the utility of synthetic photonic lattices and nonlocal emitter configurations in tailoring quantum coherence, entanglement, and information flows in structured environments.
Abstract We investigate qubits coupled to the boundary of a two-dimensional photonic lattice that supports dispersionless edge modes—unlike conventional edge modes that sustain propagating photons. As a case study, we consider a honeycomb lattice ( photonic graphene ) of coupled resonators with a zigzag edge, where the edge modes form a flat band defined only over a restricted region of momentum space. We show that light–matter interactions are effectively captured by a dissipative cavity-QED model, wherein the emitter coherently couples to a localized mode emerging as a superposition of edge modes. This mode has support on only one sublattice and displays an unconventional power-law localization around the qubit—yet remaining normalizable in the thermodynamic limit—with a spatial range that can be tuned by introducing lattice anisotropy. We predict the occurrence of vacuum Rabi oscillations and state transfer between distant emitters. An experimental demonstration using superconducting circuits is proposed.
We explore the spontaneous emission dynamics of a giant atom coupled to a photonic Creutz ladder, focusing on how flat-band frustration and synthetic gauge fields shape atom–photon interactions. The Creutz ladder exhibits perfectly flat bands, Aharonov–Bohm caging, and topological features arising from its nontrivial hopping structure. By embedding the giant atom at multiple spatially separated sites, we reveal interference-driven emission control and the formation of nonradiative bound states. Using both spectral and time-domain analyses, we uncover strong non-Markovian dynamics characterized by persistent oscillations, long-lived entanglement, and recoherence cycles. The emergence of bound-state poles in the spectral function is accompanied by spatially localized photonic profiles and directionally asymmetric emission, even in the absence of band dispersion. Calculations of von Neumann entropy and atomic purity confirm the formation of coherence-preserving dressed states in the flat-band regime. Furthermore, the spacetime structure of the emitted field displays robust zig-zag interference patterns and synthetic chirality, underscoring the role of geometry and topology in photon transport. Our results demonstrate how flat-band photonic lattices can be leveraged to engineer tunable atom–photon entanglement, suppress radiative losses, and create structured decoherence-free subspaces for quantum information applications.
Synthetic dimensions provide a powerful approach for simulating condensed matter physics in cold atoms and photonics, whereby a set of discrete degrees of freedom are coupled together and reinterpreted as lattice sites along an artificial spatial dimension. However, atomic experimental realizations have been limited so far by the number of artificial lattice sites that can be feasibly coupled along the synthetic dimension. Here, we experimentally realize for the first time a very long and controllable synthetic dimension of atomic harmonic trap states. To create this, we couple trap states by dynamically modulating the trapping potential of the atomic cloud with patterned light. By controlling the detuning between the frequency of the driving potential and the trapping frequency, we implement a controllable force in the synthetic dimension. This induces Bloch oscillations in which atoms move periodically up and down tens of atomic trap states. We experimentally observe the key characteristics of this behavior in the real-space dynamics of the cloud, and verify our observations with numerical simulations and semiclassical theory. The Bloch oscillations thus act as a smoking-gun signature of the synthetic dimension, and allow us to characterize the effective band structure. Our methods provide an efficient approach for the manipulation and control of highly excited trap states, and set the stage for the future exploration of topological physics in higher dimensions through the use of a tunable artificial gauge field and finite-range interactions.