Coherent transport by adiabatic passage on atom chips

Adiabatic techniques offer some of the most promising tools for achieving high-fidelity control of the center-of-mass degree of freedom of single atoms. Because the main requirement of these techniques is to follow an eigenstate of the system, constraints on timing and field strength stability are usually low, especially for trapped systems. In this paper we present a detailed example of a technique to adiabatically transport a single atom between different waveguides on an atom chip. To ensure that all conditions are fulfilled, we carry out fully three-dimensional simulations of the system, using experimentally realistic parameters. We also detail our method for simulating the system in very reasonable time scales on a consumer desktop machine by leveraging the power of graphics-processing-unit computing.

Figure 1

Schematic of the suggested setup for observing the CTAP process in a system of waveguides. Note that the asymmetric approach of the outer wires to the middle wire is exaggerated, so that the counterintuitive arrangement is visible. The atom is initially located in the left guide and, due to the presence of a harmonic oscillator potential $V_z$ in the $z$ direction, travels along the direction indicated by the red solid arrow. We also show the expected position of the atom at $t=\pi /{\omega }_z$ in the right-hand-side guide and indicate the orientation of the bias field, $B_b$, and the applied field, $B_{ip}$ (purple dashed arrows).

Figure 2

Isosurfaces of the waveguides created on an atom chip with the direction of propagation indicated by the blue solid arrow (for clarity $V_z=0$ in this plot). The dimensions of the interesting area on the chip we simulate are $20\mu$m $\times 1000\mu$m ($x\times z$) and we take a height ($y$ direction) above the chip of $4\mu$m into account. The three wires are initially equally separated by $7\mu$m and their distance at the position of closest approach is $4.3\mu$m. The left wire remains straight initially for a distance of $50\mu$m, which produces an asymmetry in the point of closest approach of the left and right wires to the middle wire as indicated by $\xi$. The bias and applied fields (indicated by the green dashed arrows) are $B_b=140\times {10}^{-4}$ T and $B_{ip}=300\times {10}^{-4}$ T. In (a) the currents of the left, middle, and right wires are $I_L=I_M=I_R=0.1$ A, respectively, and in (b) the currents of the left and right wires are $I_L=I_R=0.1$ A and the middle wire current is reduced to $I_M=0.07$ A.

Figure 3

Contour plot of the waveguides at 500 $\mu \mathrm{m}$ along the -axis. Panel (a) shows the deformation of the waveguides when all currents are equal, $I_L=I_M=I_R=0.1$ A, and panel (b) shows how this effect can be mitigated by using a reduced middle-wire current of $I_M=0.07$ A, while the current in the outer wires remain at $I_L=I_R=0.1$ A.

Figure 4

The population in the left (blue dashed line), middle (green dot-dash line) and right (red solid line) waveguides as a function of time for (a) the counter-intuitive waveguide arrangement and (b) the intuitive, direct tunneling one. The current in the middle wire is reduced to $I_M=0.07A$.

Figure 5

The density of the atomic state at $t=0.048$ for (a) the counterintuitive setup and (b) the intuitive one. The current in the middle wire is $I_M=0.07$ A in both cases.

Figure 6

The final population in the target waveguide for both the CTAP (red solid line) and intuitive (blue dashed line) processes, for values of $I_M=0.0672$ A to $I_M=0.0761$ A in steps of $0.001$ A.