Browsing by Author "Mukherjee, Rick"
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Item Accessing Rydberg-dressed interactions using many-body Ramsey dynamics(American Physical Society, 2016) Mukherjee, Rick; Killian, Thomas C.; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsWe demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions in a many-body system well within experimentally measured lifetimes, in contrast to previous research, which either focused on interactions near Förster resonances or on few-atom systems. We build a spin-12 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, which we demonstrate can be used to characterize the Rydberg-dressed interactions. Furthermore, the dynamics can differ significantly from that observed in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results also apply to bare (undressed) Rydberg states as a special case, for which we quantitatively reproduce recent ultrafast experiments without fitting.Item Geometric representation of spin correlations and applications to ultracold systems(American Physical Society, 2018) Mukherjee, Rick; Mirasola, Anthony E.; Hollingsworth, Jacob; White, Ian G.; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsWe provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics using a Bloch vector—e.g., a magnetic field causes it to precess and dissipation causes it to shrink—one can reason similarly about the shapes we use to visualize correlations. This visualization demonstrates its usefulness by unveiling the hidden structure in the correlations. For example, seemingly complex correlation dynamics can be described as simple motions of the shapes. We demonstrate the simplicity of the dynamics, which is obscured in conventional analyses, by analyzing several physical systems of relevance to cold atoms.Item Thermodynamics and magnetism in the two-dimensional to three-dimensional crossover of the Hubbard model(American Physical Society, 2020) Ibarra-García-Padilla, Eduardo; Mukherjee, Rick; Hulet, Randall G.; Hazzard, Kaden R.A.; Paiva, Thereza; Scalettar, Richard T.; Rice Center for Quantum MaterialsThe realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using the determinant quantum Monte Carlo method, a simple realization of anisotropy in the three-dimensional (3D) Hubbard model in which the tunneling between planes, t⊥, is unequal to the intraplane tunneling t. This model interpolates between the three-dimensional isotropic (t⊥=t) and two-dimensional (2D; t⊥=0) systems. We show that at fixed interaction strength to tunneling ratio (U/t), anisotropy can enhance the magnetic structure factor relative to both 2D and 3D results. However, this enhancement occurs at interaction strengths below those for which the Néel temperature TNˊeel is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal U/t. We characterize the 2D-3D crossover in terms of the magnetic structure factor, real space spin correlations, number of doubly occupied sites, and thermodynamic observables. An interesting implication of our results stems from the entropy's dependence on anisotropy. As the system evolves from 3D to 2D, the entropy at a fixed temperature increases. Correspondingly, at fixed entropy, the temperature will decrease going from 3D to 2D. This suggests a cooling protocol in which the dimensionality is adiabatically changed from 3D to 2D.Item Ultracold Nonreactive Molecules in an Optical Lattice: Connecting Chemistry to Many-Body Physics(American Physical Society, 2016) Doçaj, Andris; Wall, Michael L.; Mukherjee, Rick; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsWe derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.