Two-dimensional network of atomtronic qubits

Through a combination of laser beams, we engineer a two-dimensional optical lattice of Mexican hat potentials able to host atoms in its ring-shaped wells. When tunneling can be ignored (at high laser intensities), we show that a well-defined qubit can be associated with the states of the atoms trapped in each of the rings. Each of these two-level systems can be manipulated by a suitable configuration of Raman laser beams imprinting a synthetic flux onto each Mexican hat cell of the lattice. Overall, we believe that the system has the potential to form a scalable architecture for atomtronic flux qubits.

Figure 1

The triangular optical lattice of Mexican hats obtained from the structure function $v\left(\vec{r}\right)$, Eq. (1), with $\gamma =0.98$ and $\varphi =\pi /25$ (top panel). Sufficiently cold atoms would accumulate in the ring-shaped minima obtained for $v\left(\vec{r}\right)=0$ (white rings in the middle panel). By increasing the potential strength $U_0$, tunneling between adjacent cells can be strongly suppressed and the different cells become independent. Each of them is able to store a single “flux” qubit. Bottom panel: Contour plot of the slightly distorted ring-shaped potential well within a unit cell of the Mexican hat lattice.

Figure 2

Logarithmic plot of the gap $\mathrm{\Delta }E$ (in units of the recoil energy $E_R$) between the two lowest bands of the Mexican hat lattice and their respective widths $W_1$ and $W_2$ (in units of $E_R$) for different values of $U_0/E_R$. All plots are obtained with $\gamma =0.98$ and $\varphi =\pi /25$. For $U_0\ge 50E_R$, the bandwidths are smaller than the band gap by at least four orders of magnitude. From a numerical fit we find the value of the effective action $S$ to be around 3.4 (see text).

Figure 3

Top panel: The five lowest zero-flux energy levels of the lattice band structure at zero Bloch wave vector (in units of the recoil energy $E_R$) as a function of imbalance $\gamma$ when $\varphi =0$. By departing $\gamma$ from unity, one can separate the two lowest levels from all others. Middle panel: The three lowest single-particle energy levels (in units of the recoil energy $E_R$) obtained for $\gamma =0.98$ and $\varphi =0$ within a single unit Bravais cell (with open boundary conditions) as a function of the synthetic flux $\mathrm{\Phi }$. The two lowest levels cross at some flux ${\mathrm{\Phi }}_0=2.525\pi$. Bottom panel: Same as the middle panel but with $\varphi =\pi /25$. As one can see, the degeneracy at ${\mathrm{\Phi }}_0$ is lifted. The qubit is encoded in the two lowest states dubbed $|0\rangle$ and $|1\rangle$. For all panels, $U_0=50E_R$.

Figure 4

Top panels: Spatial density distributions $|\psi \left(\vec{r}\right){|}^2$ of qubit states $|0\rangle$ (left) and $|1\rangle$ (right) at zero flux $\mathrm{\Phi }=0$. Bottom panels: Logarithm of the momentum density distributions $log\left[{\left|\psi \left(\vec{k}\right)\right|}^2\right]$ of the same states at zero flux. Since states $|0\rangle$ and $|1\rangle$ are respectively even and odd with respect to $x\to -x$, so are their Fourier transforms with respect to $k_x\to -k_x$. Potential parameters are $U_0=50E_R$, $\gamma =0.98$, and $\varphi =\pi /25$.