In this work we study the quantum dynamics emerging when quantum emitters exchange excitations with a two-dimensional bosonic bath with a Dirac cone dispersion. We show that a single quantum emitter spectrally tuned in the vicinity of the Dirac point relaxes following a logarithmic law in time. Moreover, when several emitters are coupled to the bath at that frequency, long-range coherent interactions between them appear which decay inversely proportional to their distance without exponential attenuation. We analyze both the finite and infinite system situation using both perturbative and nonperturbative methods.
In this work we study the quantum dynamics emerging when quantum emitters exchange excitations with a two-dimensional bosonic bath with a Dirac cone dispersion. We show that a single quantum emitter spectrally tuned in the vicinity of the Dirac point relaxes following a logarithmic law in time. Moreover, when several emitters are coupled to the bath at that frequency, long-range coherent interactions between them appear which decay inversely proportional to their distance without exponential attenuation. We analyze both the finite and infinite system situation using both perturbative and nonperturbative methods.
We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which cannot be captured by standard perturbative treatments. In particular, for a single quantum emitter with its transition frequency in the middle of the band, we predict an exponential relaxation at a rate different from that predicted by Fermi's golden rule, followed by overdamped oscillations and slow relaxation decay dynamics. This is accompanied by directional emission into the reservoir. This directionality leads to a modification of the emission rate for few emitters and even perfect subradiance, i.e., suppression of spontaneous emission, for four quantum emitters.
The interaction of quantum emitters with structured baths modifies both their individual and collective dynamics. In A. Gonz\'alez-Tudela and J. I. Cirac, Phys. Rev. Lett. 119, 143602 (2017), we show how exotic quantum dynamics emerges when quantum emitters are spectrally tuned around the middle of the band of a two-dimensional structured reservoir, where we predict the failure of perturbative treatments, anisotropic non-Markovian interactions, and remarkable superradiant and subradiant behavior. In this work, we provide further analysis of that situation, together with a complete analysis for the quantum emitter dynamics in spectral regions different from the center of the band.
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.
The exchange of off-resonant propagating photons between distant quantum emitters induces coherent interactions among them. The range of such interactions, and whether they are accompanied by dissipation, depends on the photonic energy dispersion, its dimensionality, and/or the light-matter couplings. We characterize the limits of photon-mediated interactions for the case of generic one-dimensional photonic baths under the typical assumptions, i.e., finite range hoppings for the photonic bath plus local and rotating-wave light-matter couplings. In that case, we show how, irrespective of the system's parameter, the coherent photon-mediated interactions can always be written as a finite sum of exponentials and thus cannot display a power-law asymptotic scaling. As an outlook, we show how by relaxing some of these conditions, e.g., going beyond local light-matter couplings (e.g., giant atoms) or with longer-range photon hopping models, power-law interactions can be obtained within certain distance windows or even in the asymptotic regime for the latter case.
The dynamics of a two-level system coupled to a particle bath with the Dirac dispersion relation is studied. We analytically show that closing the Dirac gap results in a transition of the survival probability of the two-level system from non-exponential to exponential decay in the long-time regime, while the short-time regime remains exponential. The exact time-evolving state is also calculated. With the Dirac gap closing smoothly, the time-evolving state converges to a time-evolving resonant state, which is normalizable due to causality. We numerically show that introducing a finite cutoff to the Dirac dispersion relation leads to a transition from exponential to non-exponential decay both in short- and long-time regimes, with the time-evolving resonant state resolved to a time-evolving state. Furthermore, we propose several experimental setups that act as a particle bath with the Dirac dispersion relation. We give a detailed calculation for one of them, namely an optical array in the Su-Schrieffer-Heeger configuration. In this case, we show that our theoretical results can be observed experimentally with realistic parameters in an existing experimental setup of an optical waveguide array.
We investigate the exact dynamics of first-order system--bath coherence induced by excitation exchange in bilinear bosonic models. By solving the linear Heisenberg equations, we obtain the exact evolution of system and bath operators and evaluate the first-order coherence between the system mode and the collective bath mode directly coupled to it. We analyze how this coherence depends on initial occupations, coupling strength, spectral width, and detuning, showing that its buildup and oscillatory behavior are closely related to excitation exchange and reservoir memory. We further examine controlled coherence dynamics under leakage-elimination-operator inspired modulation of the system frequency. The results show that random modulation can suppress excitation leakage and maintain finite and relatively stable coherence fluctuations at long times. These results clarify the evolution and control of first-order system--bath coherence in settings where a localized bosonic mode is coupled to a structured bosonic reservoir.