The speed at which the magnetic interaction propagates along a chain of classic dipoles is discussed here. While in the quantum information counterpart for long-range interacting spins, where the speed of propagation of the information plays a paramount role, it is not strictly clear whether a light cone exists or not, here we provide numerical evidence that interacting dipoles do posses a linear light cone shortly after a perturbation takes place. Specifically, a power-law expansion occurs which is followed by a linear propagation of the associated interaction. As opposed to the quantum case, and in analogy with the so-called speed of gravity problem, we find that the speed of propagation of information can be arbitrarily large in the classic context. In order to agree with special relativity, we propose the derivation of a frame-independent Landau-Lifshitz equation.
We study the collective radiation properties of cold, trapped ensembles of atoms. We consider the high density regime with the mean interatomic distance being comparable to, or smaller than, the wavelength of the resonant optical radiation emitted by the atoms. We find that the emission rate of a photon from an excited atomic ensemble is strongly enhanced for an elongated cloud. We analyze collective single-excitation eigenstates of the atomic ensemble and find that the absorption/emission spectrum is broadened and shifted to lower frequencies as compared to the non-interacting (low density) o…
We address memory effects in the dynamics of a two-level open quantum system interacting with a classical fluctuating field via dipole interaction. In particular, we study the backflow of information for a field with a Lorentzian spectrum, and reveal the existence of two working regimes, where memory effects are governed either by the energy gap of the two-level system, or by the interaction energy. Our results shows that non-Markovianity increases with time, at variance with the results obtained for dephasing and despite the dissipative nature of the interaction, thus suggesting that the corr…
We develop a methodology for performing approximate optimal control simulations for quantum systems with multiple interacting degrees of freedom. The quantum dynamics are modeled using the first-order Magnus approximation in the interaction picture, where the interactions between different degrees of freedom are treated as the perturbation. We present a numerical procedure for implementing this approximation, which leverages the separability of the zeroth-order time evolution operator and the pairwise nature of common interactions for a reduced computational cost. This formulation of the first…
We consider a pair of dipoles for which direct electrostatic dipole-dipole interactions may be significantly larger than the coupling to transverse radiation. We derive a master equation using the Coulomb gauge, which naturally enables us to include the inter-dipole Coulomb energy within the system Hamiltonian rather than the interaction. In contrast, the standard master equation for a two- dipole system, which depends entirely on well-known gauge-invariant S-matrix elements, is usually derived using the multipolar gauge, wherein there is no explicit inter-dipole Coulomb interaction. We show u…
A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such …
We investigate the effect of degenerate atomic states on the exciton delocalization of dipole-dipole interacting Rydberg assemblies. Using a frozen gas and regular one-, two-, and three-dimensional lattice arrangements as examples, we see that degeneracies can enhance the delocalization compared to the situation when there is no degeneracy. Using the Zeeman splitting provided by a magnetic field, we controllably lift the degeneracy to study in detail the transition between degenerate and non-degenerate regimes.
Resonant laser excitation of multiple Rydberg atoms are prohibited, leading to Rydberg blockade, when the long-range van der Waals interactions are stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e. simultaneous excitation of more than one Rydberg atoms, by off-resonant laser excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise to strongly correlated many-body dynamics and spin-orbit coupling, and also finds quantum computation applications. Instead of commonly used van der Waals interactions, we investigate antiblockade dynamics of two Ryd…
We establish, within the second quantization method, the general dipole-dipole Hamiltonian interaction of a system of $n$-level atoms. The variational energy surface of the $n$-level atoms interacting with $\ell$-mode fields and under the Van Der Waals forces is calculated with respect the tensorial product of matter and electromagnetic field coherent states. This is used to determine the quantum phase diagram associated to the ground state of the system and quantify the effect of the dipole-dipole Hamiltonian interaction. By considering real induced electric dipole moments, we find the quantu…
We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension $d$ and the exponent $α$ governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for $α\ge d+1/2$. We also provide a Lévy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1d long-range spin models with 200 sites.
We develop an analytic formalism to describe dipole radiation near the Dirac cone of a two-dimensional photonic crystal slab. In contrast to earlier work, we account for all polarization effects and derive a closed-form expression for the dyadic Green's function of the geometry. Using this analytic Green's function, we demonstrate that the dipolar interaction mediated by the slab exhibits winding phases, which are key ingredients for engineering topological systems for quantum emitters, as discussed in detail in J. Perczel et al., (2018), arXiv:1810.12299. As an example, we study the coherent …
QED-based Optical Bloch Equations without electric dipole approximation: A model for a two-level atom interacting with a monochromatic X-ray laser beam
The advantage of optical bistability (OB) using three-level electromagnetically induced transparency (EIT) atomic system over the two-level system is its controllability, as absorption, dispersion, and optical nonlinearity in one of the atomic transitions can be modified considerably by the field interacting with nearby atomic transitions. This is due to induced atomic coherences generated in such EIT system. The inclusion of near dipole-dipole (NDD) interaction among atoms further modifies absorption, dispersion, and optical nonlinearity of three-level EIT system and the OB can also be contro…
Periodic-Pulse Control of Collective Emission and Photon Statistics in Interacting Quantum Emitters
Middle Tennessee State University（中田纳西州立大学）；Quantum Research, Interdisciplinary Science, and Education (QRISE) Center, Middle Tennessee State University（中田纳西州立大学量子研究、跨学科科学与教育中心）
Quantum state localization in dipole-dipole interacting disordered networks
Weizmann Institute of Science（魏茨曼科学研究所）；The Institute of Mathematical Sciences, HBNI（印度数学科学研究院，HBNI）；Indian Institute of Technology (ISM)（印度技术学院（ISM））；Institute of Electronic Structure and Laser, FORTH（电子结构与激光研究所，FORTH）；Alikhanyan National Laboratory (YerPhI)（阿利哈尼扬国家实验室（耶尔皮））；Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国家研究所）
In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When systems have long-range interactions, it is highly nontrivial whether such a linear light cone exists. Herein, we consider generic long-range interacting systems with decaying interactions, such as $R^{-α}$ with distance $R$. We prove the existence of the linear light cone for $α>2D+1$ ($D$: the spatial dimension), where we obtain the Lieb--Robinson bound as $\|[…
In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation may occur. We focus on a specific but experimentally natural situation in which the number of bosons at any one site in the unperturbed initial state is approximately limited. We rigorously prove the existence of an almost-linear information-propagation light-cone, thus establishing a Lieb--Robinson bound: the wave-front grows at most as $t\log^2 (t)$. We pro…
