Many-body atomic speed sensor in lattices

We study the properties of transmissivity of a beam of atoms traversing an optical lattice loaded with ultracold atoms. The transmission properties as a function of the energy of the incident particles are dependent on the quantum phase of the atoms in the lattice. In fact, in contrast to an insulator regime, the absence of an energetic gap in the spectrum of the superfluid phase enables the atoms in the optical lattice to adapt to the presence of the beam. This induces a backaction process that has a strong impact on the transmittivity of the atoms. Based on the corresponding strong dependency we propose the implementation of a speed sensor with an estimated sensitivity of ${10}^8–{10}^9(\mathrm{m}/\mathrm{s})/\sqrt{\mathrm{Hz}}$. We point out that the velocity sensitivity improves when the interaction term in the optical lattice increases. Applications of the presented scheme are discussed.

Figure 1

Scheme of the speed sensor. A focused beam of test atoms (blue spheres) impacts a one-dimensional optical lattice in superfluid regime (red spheres). The transmission rate of the colliding atoms depends on their speed with respect to the lattice.

Figure 2

Behavior of $T\left(v\right)$ (top) and FI $I\left(v\right)$ (center). Black dashed line (empty black circles): Mott-insulator-like phase. Red dash-dotted solid line (red empty squares): superfluid phase. (Bottom) Average occupancy $n_i\left(v\right)=\langle {\widehat{n}}_i\rangle$ of the optical lattice sites in the superfluid regime for several different sites: red circle/dashed line, $i=i_0$; black square/dotted line, $i=i_0\pm 1$; green up triangle/solid line, $i=i_0\pm 2$; blue down triangle/dot dashed line, $i=i_0\pm 3$; orange diamond/dashed line, $i=i_0\pm 4$. All quantities are plotted as functions of the velocity of the test atoms in the reference system in which the optical lattice is at rest. Simulations were performed fixing ${\omega }_{\perp }=5$ kHz, $a=266$ nm, and $V_0=7E_r$. The lattice is loaded with ${}^{87}\mathrm{Rb}$ with an average 2.5 atoms per site and $a_{bb}=100a_0$. Beam atoms are ${}^7\mathrm{Li}$ with $r={\ell }_t/{\ell }_z=10$ and $a_{bt}=200a_0$. For these values $v_R=8.63$ mm/s. Gray vertical lines: position of local peaks of the FI.

Figure 3

Maximum of FI as a function of the $\langle {\widehat{n}}_{\text{test}}\rangle a_{bt}$ for different values of $r={\ell }_t/{\ell }_z$ (top) and of the lattice depth $V_0$ (bottom). Lines: superfluid phase. Dots: Mott-insulator-like phase. (Top) Lattice depth $V_0=7E_r(t/u\simeq 0.29)$ for $r=2$ (red solid line/red empty circles); $r=10$ (black dotted line/black empty squares); $r=15$ (blue dashed line/blue empty diamonds). (Bottom) We fix $r=10$ and vary $V_0$: $V_0=6E_r$ ($u=0.048E_r,t/u\simeq 0.42$) (black dotted line/black empty squares); $V_0=7E_r$ ($u=0.050E_r,t/u\simeq 0.29$) (red solid line/red empty circles); $V_0=10E_r$ ($u=0.054E_r,t/u\simeq 0.11$) (green dot-dashed line/green empty diamonds); $V_0=13E_r$ ($u=0.058E_r,t/u\simeq 0.04$) (blue dashed line/blue empty triangles). Other parameters as in Fig. 2.