We present analytic expressions describing generation of the entanglement in collisions of initially uncorrelated quantum solitons. The results, obtained by means of the Born's approximation (for fast solitons), are valid for both integrable and non-integrable quasi-one-dimensional systems supporting soliton states.
Abstract We predict hyper-entanglement generation by binary scattering of mesoscopic bound states, considering solitary waves in Bose–Einstein condensates containing thousands of identical Bosons. For it to occur, the underlying many-body Hamiltonian must not be integrable, and the pre-collision quantum state of the solitons needs to be fragmented. Under these conditions, we show that the post-collision state will be hyper-entangled in spatial degrees of freedom and atom number within solitons, for realistic parameters. The effect links aspects of non-linear systems and quantum-coherence and the entangled post-collision state challenges present entanglement criteria for identical particles. Our results are based on simulations of colliding quantum solitons in a quintic interaction model beyond the mean-field, using the truncated Wigner approximation.
Two simple schemes for generating macroscopic (many-photon) continuous-variable entangled states by means of continuous interactions (rather than collisions) between solitons in optical fibers are proposed. First, quantum fluctuations around two time-separated single-component temporal solitons are considered. Almost perfect correlation between the photon-number fluctuations can be achieved after passing a certain distance, with a suitable initial separation between the solitons. The photon-number correlation can also be achieved in a pair of vectorial solitons with two polarization components. In the latter case, the photon-number-entangled pulses can be easily separated by a polarization beam splitter. These results offer possibilities to produce entangled sources for quantum communication and computation.
The study of many-body quantum systems, that fail to thermalize in the presence of disorder, has recently attracted lots of interests. This is due to the appearance of the many-body localized phase and breakdown of eigenstate thermalization hypothesis in such systems which can be described by the local integrals of motion. In this paper, we consider a disordered spin chain in the many-body localized phase and try to study the dynamics of entanglement generation in this system using the local integrals of motion. To this end, we, first, solve the non-interacting system analytically to describe the mechanism of entanglement generation for different kinds of initial states, exactly. Then, we generalize this approach to the interacting system to learn the dynamics of entanglement generation. Finally, we discuss the physical meaning of different behaviors in the dynamics of entanglement generation in the presence and absence of interaction.
In this thesis we investigate the properties of ultra-cold quantum gases in reduced dimension and the effects of harmonic confinement on soliton-like properties. We study regimes of agreement between mean-field and many-body theories the generation of entanglement between initially independent finite sized atomic systems. Classical solitons are non-dispersing waves which occur in integrable systems, such as atomic Bose-Einstein condensates in one dimension. Bright and dark solitons are possible, which exist as peaks or dips in density. Quantum solitons are the bound-state solutions to a system satisfying quantum integrability, given via the Bethe Ansatz. Such integrability is broken by the introduction of harmonic confinement. We investigate the equivalence of the classical field and many-body solutions in the limit of large numbers of atoms and derive numerical and variational approaches to examine the ground state energy in harmonic confinement and the fidelity between a Hartree-product solution and a quantum soliton solution. Soliton collisions produce no entanglement between either state and result only in an asymptotic position and phase shift, however external potentials break integrability and thus give the possibility of entangling solitons. We investigate the dynamical entanglement generation between two atomic dimers in harmonic confinement via exact diagonalisation in a basis of Harmonic oscillator functions, making use of the separability of the centre-of-mass component of the Hamiltonian. We show repulsive states show complex dynamics, but with an overall tendency towards states of larger invariant correlation entropy, whereas attractive states resist entanglement unless a phase matching condition is satisfied. This phase matching condition could in theory be used to generate states with highly non-Poissonian number superpositions in atomic systems with controlled number.