Quantum Many Particle Systems in Ring-Shaped Optical Lattices

In the present work we demonstrate how to realize a 1D closed optical lattice experimentally, including a tunable boundary phase twist. The latter may induce “persistent currents,” visible by studying the atoms’ momentum distribution. We show how important phenomena in 1D physics can be studied by physical realization of systems of trapped atoms in ring-shaped optical lattices. A mixture of bosonic and/or fermionic atoms can be loaded into the lattice, realizing a generic quantum system of many interacting particles.

Figure 1

The optical potential resulting from the interference of a plane wave with an LG mode with $L=14$, $p=0$. For $p\ne 0$ the potential is virtually unaltered.

Figure 2

Interference pattern for condensates released by the lattice (1), obtained resorting to the analog of light diffraction from a circular grating [19]. The figures show the square of the order parameter $|\psi (k_x,k_y){|}^2=|{\psi }_0(k_x,k_y){\Sigma }_{j=0}^{L-1}\cos \{i[k_x\cos (2\pi j/L)+k_y\sin (2\pi j/L)+{\varphi }_j]\}{|}^2$. On the left ${\varphi }_j=0$ for all the condensates; on the right the atoms move along the ring with velocity $\propto \nabla \varphi$; the interference pattern reflects a loss of matter at the trap center caused by centrifugal effects.

Figure 3

The zero temp. momentum distribution for fermions with Hubbard dynamics is presented: $|\Psi (k_x,k_y){|}^2\propto |w(k_x,k_y){|}^2{\Sigma }_{i,j}{e}^{i\mathbf{k}·({\mathbf{x}}_i-{\mathbf{x}}_j)}{\Sigma }_{k_{\varphi }}{e}^{i{k}_{\varphi }({\varphi }_i-{\varphi }_j)}⟨n_{k_{\varphi }}⟩$; $\mathcal{N}/L=32/16$ ($\mathcal{N}/L=1$ is the less advantageous case to discern the effects of $\Phi$ at finite size, since the metal-insulator transition strongly suppresses $D_c$ [34]); $⟨n_{k_{\varphi }}⟩$ is calculated perturbatively at second order in $U/t$. For $\Phi =0$ (left), $k_{\varphi }=\{-\pi (\mathcal{N}-1)/L\dots \pi (\mathcal{N}-1)/L\}$. For $\Phi \ne 0$, $k_{\varphi }=\{-\pi (\mathcal{N}-1)/L+\Phi /L\dots \pi (\mathcal{N}-1)/L+\Phi /L\}$; the asymmetry in $|\Psi (k_x,k_y){|}^2$ is due to the offset of $⟨n_{k_{\varphi }}⟩$ caused by $\Phi$.