Entanglement in Ensembles of Large Spins – EELS

Our proposal is to study the growth of entanglement in ensembles of large spin atoms loaded in optical lattices. We aim at developing new methods and concepts to investigate the dynamical generation of correlations and entanglement in ensembles composed of many particles, which is relevant in the context of the development of quantum technologies. Our project addresses three crucial needs: the necessity of experimental methods to generate entanglement; the need for new theoretical methods to describe out-of-equilibrium many-body quantum dynamics; the need for theoretical and experimental research on how to measure quantum correlations on many-body systems.

Our investigations will focus on two independent physical systems, corresponding to two atomic species which strongly differ by the nature of the interatomic interactions. For 52Cr atoms, there are strong long-range and anisotropic dipole-dipole interactions; For 87Sr atoms, interactions are short range and spin-independent – driving magnetism with SU(N) symmetry, where N is the number of spin states.

Our approach is to first engineer pure separable many-body states, using coherent spin manipulations within the lattice; then to study the dynamical evolution under the effect of interactions. For Cr, the manipulation techniques are straightforward (homogeneous or inhomogeneous magnetic fields, radio-frequency fields). For Sr, we suggest to employ the tensor light shift associated with the narrow 1S0-3P1 transition in order to create artificial magnetic fields with negligible dissipation. We propose a scheme to deterministically engineer an array of 4 atom plaquettes, each containing a SU(4) singlet.

We will set up a number of experimental protocols to investigate the dynamics, and compare to theoretical simulations (obtained via a spin-wave approach to the real-time dynamics, as well as via the unitary evolution of strongly correlated variational wavefunctions). The focus will be on the growth of entanglement due to interatomic interactions. We propose a bipartite measurement of a globally conserved observable. Measurements will be performed on two separate and complementary parts of the sample, making use of a superlattice, where selective band excitation will be performed to isolate every other site. To experimentally prove that local fluctuations are associated to the propagation of entanglement, it is necessary to assert that the many-body system remains pure. To do so, we propose in the case of Cr an experiment consisting in realizing a Loschmidt echo. Using NMR techniques, the sign of dipole-dipole interactions can be changed. Reversing the Hamiltonian allows to verify the reversibility of dynamics, and to probe the Hamiltonian character of the evolution. We also propose measurements of the collective spin length, its fluctuations, and of the spin structure factor. At low energy, the latter gives access to the spectrum of excitations.

Theory and experimental research will allow pinpointing which preparation protocols best prepare low energy states, close to the Hamiltonian ground state, after dynamics under the effect of interactions has occurred. We will investigate the approach towards equilibrium of such isolated quantum systems, and explore whether magnetic ordering is reached.