Quantum Emitters in Two-Dimensional Structured Reservoirs in the Nonperturbative Regime

Abstract

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 can not 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 the 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 (QEs) with propagating bosonic particles, e.g., photons, lies at the core of Quantum Optics [1]. This interaction leads, for example, to collective interactions between QEs [2, 3] which can be harnessed for both quantum information and simulation applications. New avenues in the integration of QEs with nanophotonic structures [4][5][6][7][8][9][10][11][12][13][14] provide us with systems in which the QEs interact with low dimensional bosonic modes, with complicated energy dispersions in the case of engineered dielectrics [6][7][8][9][10][11][12]. Despite originally the main motivation of such implementations was to exploit the small sizes to enhance light-matter interactions, it was soon realized that intriguing phenomena arise because of the reduced dimensionality. One particular aspect is the possibility of realizing chiral emission [15][16][17], which can display very uncommon features [18,19]. Another one is the possibility of exploiting the phenomena of sub and superradiance [11,12,[20][21][22], e.g., to enhance the coupling to the emitter [23], to generate QE entanglement [18,24], to produce non-classical light [25,26], or even to perform quantum computation [27].The dynamics of QEs in 1D reservoirs is relatively simple, specially when their transition frequency, ω e , lies within a band. Perturbative treatments predict that a single QE initially excited decays at a rate, Γ, given by the Fermi's Golden Rule (FGR), i.e. proportional to the density of states of the bath at ω e . The emission mostly occurs in the bath modes that are resonant with that frequency. Typically, there are two such modes of associated momentum ±k e , leading to a symmetric left/right emission. When two (or more) QEs are present, the existence of only two such modes leads to super/subradiant states, where the emission is enhanced or suppressed by interference. In higher dimensions for structureless baths, a single QE will also decay at a rate given by the FGR. However, the emission takes place in different directions as there are many resonant modes in the bath. For two QEs, the interference in the emission cannot occur in all those modes at the same time [28] and thus, the phenomena of sub and superradiance are generically absent.In this manus...

Effective many-body Hamiltonians of qubit-photon bound states

“…Finally, we numerically characterize the ground state in the many excitation sector of these quantum optical models, and show how the ground state can undergo an optically driven Mott-superfluid phase transition controlled by the localization length of the bound states. An interesting research direction is to apply the theoretical toolbox developed in the manuscript to study higher dimensional structured baths [32][33][34].…”

Markovian and non-Markovian dynamics of quantum emitters coupled to two-dimensional structured reservoirs

“…In this work, we focus on the coupling of QEs to two-dimensional baths (2D). In particular, we consider the structured 2D reservoir of bosonic modes with square symmetry that we studied in the main manuscript [1], and focus on the situation where the QE transition frequency lies within the band. Apart from the long range character of the interactions expected from the reduced dimensionality, we analyze several effects such as non-perturbative relaxation of a single QE which is accompanied by directional emission into the bath, as also predicted for a classical source of light [63] and sound [64].…”

Non-Markovian Collective Emission from Macroscopically Separated Emitters

“…Delay-induced non-Markovian dynamics has been previously studied in the context of the spontaneous emission of single atoms [4,15,[17][18][19][20][21][22][23], bound states in continuum (BIC) of the EM field [24][25][26][27], and entanglement generation in emitters coupled to waveguides [4,28]. The effects of non-Markovianity have also been investigated in collective atomic states in the context of structured reservoirs [29][30][31][32][33] and in the strongcoupling regime [34]. However, the non-Markovian dynamics emerging from retardation effects in macroscopically delocalized collective systems is yet unexplored.…”

“…A key parameter in the characterization of the non-Markovian dynamics is the emitter separation relative to the photon coherence length η ≡ dγ/v g . It captures the combined physical origin of non-Markovian behavior, as an appreciable value of η can be achieved by increasing the emitter separation d, but also by increasing the system-environment coupling as in [28] or by exploiting slow group velocities achievable in the presence of a band gap or near a band edge [33]. Importantly, as η is increased to near or past η ∼ 1 the description of the system dynamics requires keeping track of field correlation functions of increasing order.…”