Related papers: High-dimensional SO(4)-symmetric Rydberg manifolds…
Precision measurements of transitions between singlet ($S=0$) Rydberg states of H$_2$ belonging to series converging on the $\mathrm{X}^+\,^2\Sigma_g^+(v^+=0,N^+=0)$ state of H$_2^+$ have been carried out by millimetre-wave spectroscopy…
The 1+1D O(3) non-linear {\sigma}-model is a model system for future quantum lattice simulations of other asymptotically-free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction can make efficient use…
We present a general theoretical treatment and calculations of the fine and hyperfine structures in the spectra of high-$n$ molecular Rydberg states in static uniform electric fields. The treatment combines (i) multichannel quantum-defect…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…
Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
We study the classical and quantum phase transitions of Sp(4) spin systems on three dimensional stacked square and triangular lattices. We present general Ginzburg-Landau field theories for various types of Sp(4) spin orders with different…
Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a…
Let group generators having finite-dimensional representation be realized as Hermitian linear differential operators without nhomogeneous terms as takes place, for example, for the SO(n) group. Then orresponding group Hamiltonians…
Superconducting quantum symmetries in extended single-band 1-dimensional Hubbard models are shown to originate from the classical (pseudo-)spin SO(4) symmetry of a class of models of which the standard Hubbard model is a special case.…
Quantum simulation holds the promise of improving the atomic simulations used at EDF to anticipate the ageing of materials of interest. One simulator in particular seems well suited to modeling interacting electrons: the Rydberg atoms…
Synthetic dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a…
Exploiting inherent symmetries is a common and effective approach to speed up the simulation of quantum systems. However, efficiently accounting for non-Abelian symmetries, such as the $SU(2)$ total-spin symmetry, remains a major challenge.…
We show that combination of a linearly polarized resonant microwave field and a parallel static electric field may be used to create a non-dispersive electronic wavepacket in Rydberg atoms. The static electric field allows for manipulation…
The ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point,…
Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase…
High-dimensional quantum information processing has emerged as a promising avenue to transcend hardware limitations and advance the frontiers of quantum technologies. Harnessing the untapped potential of the so-called qudits necessitates…
We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, $|nS_{1/2}, m_J\rangle$ and $|(n+1)S_{1/2}, m_J\rangle$. In this setting, the effective spin-1/2 Hamiltonian takes the form of an {\it XXZ} model. We…
This contribution to the present Workshop Proceedings outlines a general programme for identifying geometric structures--out of which to possibly recover quantum dynamics as well--associated to the manifold in Hilbert space of the quantum…
Rydberg-atom quantum simulators are of keen interest because of their possibilities towards high-dimensional qubit architectures. Here we report three-dimensional conformation spectra of quantum-Ising Hamiltonian systems with programmed…