## Quantum Magnetism

We use the lowest two hyperfine states of Li 7 at high magnetic field to realize the 2-component Bose-Hubbard model. We are interested in studying phenomena in Quantum Magentism: the ordered phases which arise when the dominant interaction between particles on a lattice is superexchange. In particular, the 2-component Bose Hubbard Hamiltonian can be directly mapped onto the Heisenberg spin Hamilitonan. In the context of the Bose Hubbard model, superexchange is a second order tunneling process, characterized by a matrix element "t^{2}/U." Here "t" is the hopping and "U" is the on-site interaction. The phase diagram of this Hamiltonian includes feromagnetic and anti-ferromagnetic phases aligned either with the quantization axis "z" or with a line in the the "xy"-plane. The main limitations so far for observing the full phase diagram of this model have been the slow rate of the superexchange process compared to the lifetimes of cold atoms in optical lattices and the very low critical temperatures required for superexchange to be the dominant interactions. Li 7 promises to make improvements on both fronts. Its light mass leads to faster tunneling, compared to other atoms, such as Rb, commonly used in Quantum Simulation experiments, so "t^{2}/U" is large. In addition, the critical temperature for magnetic ordering is also on the order of "t^{2}/U," so it can be reached more easily with Li.

## Spin 1/2

Starting from an n=1 Mott insulator, we can simulate the s=1/2 Hubbard model.

## Spin 1

Starting from an n=2 Mott insulator, we can simulate the s=1 Hubbard model.

## Interaction Spectroscopy

https://arxiv.org/abs/1809.06891

We would like to realize a Spin 1 model with the lowest two hyperfine states of Li 7 by going into a Mott insulator with two atoms per site. We call the lowest two hyperfine states "a" and "b."

Interaction spectroscopy relies on the fact that the interactions between two atoms on a site depend on the spin configuration of the two atoms. For example, the interactions between two "a" atoms, U_{aa} are in principle different from the interactions between an "a" and a "b" atom, U_{ab}. The RF transition frequency between two "a" atoms on a site and an "a" and a "b" atom on a site is shifted from the bare transition between a single "a" and a single "b" atom on a site by the interaction difference U_{ab}-U_{aa}. We can flip only one of the two atoms per site when the interaction differences are not degenerate, i.e. U_{ab}-U_{aa} is not equal to U_{bb}-U_{ab}. If the interaction differences are degenerate, we can drive a transition from "bb" all the way to "aa."

We prepare a Mott insulator of "b" atoms and drive a spin flip transition from "b" to "a." We measure the number of spin flipped atoms (the number of "a" atoms) and we observe two peaks: One corresponding to the transition of the n=1 shell of the Mott insulator at the bare transition frequency, and one of the n=2 shell at a frequency shifted by the interaction difference $U_{ab}-U_{aa}.

We use interaction spectroscopy to map out the interaction differences across the Feshbach resonances of Li 7. In addition, we use amplitude modulation spectroscopy to measure the absolute value of the interactions.

Finally, we find a point at which the interactions are degenerate and drive a full Rabi oscillation between "bb" and "aa"

## New Superradiant Regimes in a BEC

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.051603

We study superradiance with two non-interacting counterpropagating beams along the long axis of a BEC. We find that there are two regimes in which the system behaves qualitatively differently. At low Rayleigh scattering rates, the stimulated emission from the two beams cancel. At large Rayleigh scattering rates, we see evidense of a formation of a different phase. Such a phase has been predicted in [S. Ostermann, F. Piazza, and H. Ritsch, Phys. Rev. X 6, 021026 (2016)]. It consists of a stationary density modulation and a standing optical wave. See our results here: https://arxiv.org/abs/1709.02028

Superradiance with a single pump beam: moving density modulation

Two non-interfering pump beams:

## Noise in Optical Lattices

We have studied noise and heating in optical lattices extensively.

## Li 7 BEC

Here is a graph showing the cooling steps we take to make a Li 7 BEC.

## Posters

__NSF visit poster (MIT, April 28, 2014)__