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Non-adiabatic processes near conical intersections are rooted in the stronger coupling between electronic and nuclear degrees of freedom. Using a system of two trapped Rydberg ions, their high polarizability and strong dipolar interactions allow to form a conical intersection, where dynamics takes place on a microsecond time scale. Rydberg lifetimes are typically from a few to tens of microseconds, which could affect the conical dynamics. We study the effect of the finite lifetime of the Rydberg state on the vibronic dynamics around the conical intersection via analyzing the master equation. Through mean field and numerical calculations, damping dynamics are found in both the phonon populations and electronic states depending on the initial states. It is found that oscillatory vibronic dynamics can be seen clearly within the Rydberg lifetime, permitting to observe the conical effect in the trapped Rydberg ion system. [ABSTRACT FROM AUTHOR]

Dense atom ensembles with Rydberg excitations display intriguing collective effects mediated by their strong, long-range dipole–dipole interactions. These collective effects, often modeled using Rydberg superatoms, have gained significant attention across various fields due to their potential applications in quantum information processing and quantum optics. In this review article, we delve into the theoretical foundations of Rydberg interactions and explore experimental techniques for their manipulation and detection. We also discuss the latest advancements in harnessing Rydberg collective effects for quantum computation and optical quantum technologies. By synthesizing insights from theoretical studies and experimental demonstrations, we aim to provide a comprehensive overview of this rapidly evolving field and its potential impact on the future of quantum technologies. [ABSTRACT FROM AUTHOR]

We studied signatures of quantum chaos in dynamics of Rydberg-dressed bosonic atoms held in a one-dimensional triple-well potential. Long-range nearest-neighbor and next-nearest-neighbor interactions, induced by laser dressing atoms to strongly interacting Rydberg states, drastically affect mean-field and quantum many-body dynamics. By analyzing the mean-field dynamics, classical chaos regions with positive and large Lyapunov exponents were identified as a function of the potential well tilting and dressed interactions. In the quantum regime, it was found that level statistics of the eigen-energies gain a Wigner–Dyson distribution when the Lyapunov exponents are large, giving rise to signatures of strong quantum chaos. We found that both the time-averaged entanglement entropy and survival probability of the initial state have distinctively large values in the quantum chaos regime. We further showed that population variances could be used as an indicator of the emergence of quantum chaos. This might provide a way to directly probe quantum chaotic dynamics through analyzing population dynamics in individual potential wells. [ABSTRACT FROM AUTHOR]

We study the population dynamics in a two-atom setup in which each atom is driven independently by different light fields, but coupling the same Rydberg state. In particular, we look at how an offset in the Rabi frequencies between two atoms affects the dynamics. We find novel features such as amplifying the Rabi frequency of one atom, together with strong Rydberg-Rydberg interactions freezes the dynamics in the second atom. We analyze this Rydberg-biased freezing phenomenon in detail, with effective Hamiltonians obtained for various limits of the system parameters. In the absence of Rabi-offset, the doubly excited state population exhibits a Lorentzian profile as a function of interaction, whereas for very small offsets it shows splitting and thus peaks. Using an effective Hamiltonian, as well as the perturbation theory in the weak interaction limit, we show that the peak arises from a competition between Rabi-offset and Rydberg-Rydberg interactions when both are sufficiently small, together with the Rydberg blockade at large interactions. The effective Hamiltonians provide us with analytical results for long time dynamics, which are in an excellent agreement with exact numerical solutions. Also, we analyze the growth and the dynamics of quantum correlations such as entanglement entropy/quantum discord for the coherent dynamics. Finally, we extend our studies to the dissipative case in which the spontaneous emission from the Rydberg state is taken into account and in particular, we look at how the Rabi-offset modifies the purity and quantum discord in the steady states. We conclude that the local manipulation of an atom by introducing a Rabi-offset can be a useful tool to control the quantum correlations and in general, the quantum states of the composite two-qubit systems. [ABSTRACT FROM AUTHOR]

We develop a theoretical framework for the dissipative propagation of quantized light under conditions of electromagnetically induced transparency in atomic media involving strongly interacting Rydberg states. The theory allows us to determine the peculiar spatiotemporal structure of the output of the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. In addition to being crucial for applications of these and other optical quantum devices, the theory opens the door to the study of exotic dissipative many-body dynamics of strongly interacting photons in nonlinear nonlocal media. [ABSTRACT FROM AUTHOR]

We study trapped 2D atomic Bose-Einstein condensates with spin-independent interactions in the presence of an isotropic spin-orbit coupling, showing that a rich physics results from the nontrivial interplay between spin-orbit coupling, confinement and interatomic interactions. For low interactions two types of half-vortex solutions with different winding occur, whereas strong-enough repulsive interactions result in a stripe-phase similar to that predicted for homogeneous condensates. Intermediate interaction regimes are characterized for large enough spin-orbit coupling by an hexagonally-symmetric phase with a triangular lattice of density minima similar to that observed in rapidly rotating condensates. [ABSTRACT FROM AUTHOR]

We study the chaos and hyperchaos of Rydberg-dressed Bose–Einstein condensates (BECs) in a one-dimensional optical lattice. Due to the long-range, soft-core interaction between the dressed atoms, the dynamics of the BECs are described by the extended Bose-Hubbard model. In the mean-field regime, we analyze the dynamical stability of the BEC by focusing on the ground state and localized state configurations. Lyapunov exponents of the two configurations are calculated by varying the soft-core interaction strength, potential bias, and length of the lattice. Both configurations can have multiple positive Lyapunov exponents, exhibiting hyperchaotic dynamics. We show the dependence of the number of the positive Lyapunov exponents and the largest Lyapunov exponent on the length of the optical lattice. The largest Lyapunov exponent is directly proportional to areas of phase space encompassed by the associated Poincaré sections. We demonstrate that linear and hysteresis quenches of the lattice potential and the dressed interaction lead to distinct dynamics due to the chaos and hyperchaos. Our work is relevant to current research on chaos as well as collective and emergent nonlinear dynamics of BECs with long-range interactions. [ABSTRACT FROM AUTHOR]

We show how a broad class of lattice spin-1/2 models with angular- and distance-dependent couplings can be realized with cold alkali atoms stored in optical or magnetic trap arrays. The effective spin-1/2 is represented by a pair of atomic ground states, and spin-spin interactions are obtained by admixing van der Waals interactions between fine-structure split Rydberg states with laser light. The strengths of the diagonal spin interactions as well as the "flip-flop," and "flip-flip" and "flop-flop" interactions can be tuned by exploiting quantum interference, thus realizing different spin symmetries. The resulting energy scales of interactions compare well with typical temperatures and decoherence time scales, making the exploration of exotic forms of quantum magnetism, including emergent gauge theories and compass models, accessible within state-of-the-art experiments. [ABSTRACT FROM AUTHOR]

We analyze the physics of self-bound droplets in a doubly dipolar Bose-Einstein condensate composed by particles with both electric and magnetic dipole moments. Using the particularly relevant case of dysprosium, we show that the anisotropy of the doubly dipolar interaction potential is highly versatile and nontrivial, depending critically on the relative orientation and strength between the two dipole moments. This opens novel possibilities for exploring intriguing quantum many-body physics. Interestingly, by varying the angle between the two dipoles we find a dimensional crossover from quasi-one-dimensional to quasi-two-dimensional self-bound droplets. This opens a so far unique scenario in condensate physics, in which a dimensional crossover is solely driven by interactions in the absence of any confinement. [ABSTRACT FROM AUTHOR]

An array of single Rydberg atoms driven by a temporally modulated atom-field detuning is studied. The periodic modulation effectively modifies the Rabi coupling, leading to unprecedented dynamics in the presence of Rydberg-Rydberg interactions, in particular, blockade enhancement, antiblockades, and state-dependent population trapping. Interestingly, the Schrieffer-Wolf transformation reveals a fundamental process in Rydberg gases, correlated Rabi coupling, which stems from the extended nature of the Rydberg-Rydberg interactions. Also, the correlated coupling provides an alternative depiction for the Rydberg blockade, exhibiting a nontrivial behavior in the presence of periodic modulation. The dynamical localization of a many-body configuration in a driven Rydberg lattice is discussed. [ABSTRACT FROM AUTHOR]