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# 2013 Cs Experiment

**Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice**

Optical lattices serve as a work horse for ultracold atomic systems simulating the condensed matter systems with versatile control, e.g. changing the lattice depth and the on site interaction strength. Shaking the optical lattice provide another degree of freedom which allows us to change the tunneling of atoms in the optical lattice.

In this work, we load ultracold Cs in a 3D trap with an additional one dimensional optical lattice. We phase modulate the optical lattice to couple the ground band and the first excited band. Depending on the modulation strength, we engineer the admixed band structure to let it evolve from one single minimum to double minima.

Due to the penalty of the interaction energy, atoms prefer to condense in one well instead of both wells in momentum space. We label the two wells as spin up and spin down which allows us to realize an effective ferromagnetic system without an internal degree of freedom. With the high resolution in situ imaging system, we observe domain formation and extract the correlation function of the ferromagnetic sample.

Our new paper was selected as the research highlight of the James Frank Institute.

**Strongly Interacting Two-Dimensional Bose Gases**

Interacting Bose gases in two dimensions provide a platform to study the interplay between interactions, quantum statistics and fluctuations. In this work, we prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezenskii-Kosterliz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. By tuning the scattering length and loading the sample into an optical lattice, a wide range (almost two orders of magnitude) of the two-body interaction strength is covered.

Based on the equations of state measurements, we extract the coupling constants as well as critical thermodynamic quantities in different regimes. In the superfluid and the BKT transition regimes, the extracted coupling constants show significant down-shifts from the mean-field and perturbation calculations when g approaches or exceeds one. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength, a tendency confirmed by the extended classical-field and renormalization calculations.

Below are the measured equation of state of 2D Bose gases at different interaction strengths.

Equations of state for 2D Bose gases in the weak and strong coupling regimes. The filled and open circles represent experimental measurements of 2D gases and 2D lattice gases. The upper blue shaded area is the superfluid regime, and the red boundary corresponds to the BKT transition regime. The inset compares the equations of state of a 2D gas and a 2D lattice gas with an almost identical coupling constant g ~ 0.4.

#### Explore links listed below for past results and proposals archived in chronicle order.

### Group members

Li-Chung Ha (PhD student)

Eric Hazlett (postdoc)

Shih-Kuang Tung (postdoc)

Ulrich Eismann (visiting scholar, now postdoc at Observatoire de Paris-Meudon)

Xibo Zhang (PhD student, now postdoc at JILA)

Chen-Lung Hung (PhD student, now postdoc at Caltech)

Nathan Gemelke (postdoc, now professor at Penn state)

Cheng Chin (PI)