A Rydberg molecule is composed of an outer electron that collides on the residual ionic core. Typical states of Rydberg molecules display entanglement between the outer electron and the core. In this work, we quantify the average entanglement of molecular eigenstates and further investigate the time evolution of entanglement production from initially unentangled states. The results are contrasted with the underlying classical dynamics, obtained from the semiclassical limit of the core-electron collision. Our findings indicate that entanglement is not simply correlated with the degree of classical chaos, but rather depends on the specific phase-space features that give rise to inelastic scattering. Hence mixed phase-space or even regular classical dynamics can be associated with high entanglement generation.
A Rydberg molecule is composed of an outer electron that collides on the residual ionic core. Typical states of Rydberg molecules display entanglement between the outer electron and the core. In this work, we quantify the average entanglement of molecular eigenstates and further investigate the time evolution of entanglement production from initially unentangled states. The results are contrasted with the underlying classical dynamics, obtained from the semiclassical limit of the core-electron collision. Our findings indicate that entanglement is not simply correlated with the degree of classical chaos, but rather depends on the specific phase-space features that give rise to inelastic scattering. Hence mixed phase-space or even regular classical dynamics can be associated with high entanglement generation.
PACS. 03.67.Mn – Entanglement production, characterization, and manipulation. PACS. 05.45.Mt – Quantum chaos; semiclassical methods. PACS. 34.60.+z – Scattering in highly excited states (e.g., Rydberg states). Abstract. – The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). En-tanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence, regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition, quan-tum effects also come into play: for example, partial revivals, which are expected to persist in the semiclassical limit, affect the long-time behaviour of the reduced linear entropy. These results suggest that entanglement may not be a pertinent universal signature of chaos. Entanglement, i.e. the nonseparability intrinsic to composite systems, is one of the most peculiar features of the quantum world. In its most popular form, found for example in the original EPR proposal [1], the entanglement is of geometrical nature. However any usual
The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). Entanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence, regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition, quantum effects also come into play: for example, partial revivals, which are expected to persist in the semiclassical limit, affect the long-time behaviour of the reduced linear entropy. These results suggest that entanglement may not be a pertinent universal signature of chaos.
The dynamical properties of quantum entanglement in the Dicke model without rotating-wave approximation are investigated in terms of the reduced-density linear entropy. The characteristic time of decoherence process in the early-time evolution is numerically obtained and it is shown that the characteristic time decreases as the coupling parameter increases. The mean entanglement, which is defined to be averaged over time, is employed to describe the influences of both quantum phase transition and corresponding classical chaos on the behavior of entanglement. For a given energy, initial conditions are taken to be minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. It is shown that the entanglement has a distinct change at the quantum phase transition, and that the entanglement for regular initial conditions is smaller than that for chaotic ones in the case of weak coupling, while it fluctuates with small amplitude in strong coupling and for chaotic initial conditions.
Rydberg atoms occupy a central role in quantum science; their loosely bound outer electron gives rise to properties that enable quantum information processing1 or the formation of exotic molecular bonds2. Beyond these roles, they have been proposed as a neutral platform for the observation of quantum effects in collisions and reactions of the ionic core with neutral particles3, 4, a long-standing goal of ion-based chemistry and physics. However, all of the experimental results so far could be explained using a classical description of the internuclear motion5. Here we demonstrate cold collisions inside a Rydberg helium atom, achieved by merging helium Rydberg and ground-state helium beams and imaging individual scattering events. We resolve the fully quantum-coherent motion and observe matter-wave diffraction and tunnelling-driven shape resonances down to collision energies of 90 mK. In the case of identical helium nuclei, we demonstrate a new regime of identical-particle Mott interference6, where quantum statistics begin to govern the total scattering cross section. For distinct isotopes, we show the breakdown of the Born-Oppenheimer approximation and benchmark parameter-free, state-of-the-art theory. We directly measure the helium isotope ionization-energy difference to be 15.0 +/- 0.1 K. Our experiments establish Rydberg atoms as a platform for the direct observation of quantum dynamics with a general class of ions, atoms and molecules.
We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled tops, where chaos and entanglement arise from the same physical mechanism. The long-time-averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section--it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudorandom states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time-averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble.
The relationship between classically chaotic dynamics and the entanglement properties of the corresponding quantum system is examined in the semiclassical limit. Numerical results are computed for a modified kicked top, keeping the classical dynamics constant while investigating the entanglement for several versions of the corresponding quantum system characterized by a different value of the effective Planck constant ℏ eff. Our findings indicate that as ℏ eff → 0, the apparent signatures of classical chaos in the entanglement properties, such as characteristic oscillations in the time-dependence of the linear entropy, can also be obtained in the regular regime. These results suggest that entanglement is not a universal marker of chaotic dynamics of the corresponding classical system.