Time-of-Flight Imaging Method to Observe Signatures of Antiferromagnetically Ordered States of Fermionic Atoms in an Optical Lattice

We propose a simple method to detect the antiferromagnetic (AF) state of fermionic atoms in an optical lattice by combining a time-of-flight (TOF) imaging method and a Feshbach resonance. In this scheme, the nontrivial dynamics of fermionic atoms during the imaging process works as a probe with respect to the breaking of the translational symmetry in the AF state. Precise numerical simulations demonstrate that the characteristic oscillatory dynamics induced by the scattering process that transfers an AF ordering vector appears in TOF images, which can be easily observed experimentally.

Figure 1

Number of atoms with $\uparrow$ pseudospin $⟨n_{\mathbf{r}\uparrow }⟩$ at (a) $T/W\sim 0.8$ and (b) $T/W\sim 0.3$. Time-of-flight image obtained after 2 ms linear lattice ramping down at (c) $T/W\sim 0.8$ and (d) $T/W\sim 0.3$.

Figure 2

(a) Schematic diagram of the sequence of the TOF imaging to detect the AF state. TOF images taken by the present sequence for (b) the PM state (obtained at $T/W\sim 0.8$) and (c) the AF state ($T/W\sim 0.3$). The image size is $240\mu \mathrm{m}$ square.

Figure 3

(a),(b) Fraction of atoms in the 2nd RBZ, $F=I_{2\mathrm{nd}}/(I_{1\mathrm{st}}+I_{2\mathrm{nd}})$, as a function of $t$. The inset shows the definition of the 1st and 2nd RBZs. (c) Time evolution of the quasimomentum distribution of atoms with $\mathbf{k}=(0,0)$ and ($\pi$, $\pi$) for the AF and PM states.

Figure 4

Fraction of atoms in the 2nd RBZ $F$ as a function of $t$ for the PM and AF states. The increase rate of the scattering length is changed as $R_{\mathrm{SC}}=5$, 1, and 0.