Quantum Tweezer for Atoms

We propose a quantum tweezer for extracting a desired number of neutral atoms from a reservoir. A trapped Bose-Einstein condensate is used as the reservoir, taking advantage of its coherent nature, which can guarantee a constant outcome. The tweezer is an attractive quantum dot, which may be generated by red-detuned laser light. By moving at certain speeds, the dot can extract a desired number of atoms from the condensate through Landau-Zener tunneling. The feasibility of our quantum tweezer is demonstrated through realistic and extensive model calculations.

Figure 1

A quantum dot (tweezer) moves out of a trapped BEC (reservoir) with the speed of $v$. The inset illustrates that a resonance occurs as the dot moves further away from the trap center such that the energy of the atoms matches the chemical potential $\mu$ of the condensate. If one of the atoms is tunneled into the BEC, the energy level of the dot is lowered, due to the absence of repulsion from the lost atom. Thus, no other atom has a chance of leaking back to the condensate at this position.

Figure 2

The probability of extracting a single atom as a function of the speed of the dot. The calculation was performed for a one-dimensional BEC with $N=10000$ atoms in a harmonic trap with frequency $\omega =0.005$. The dot is a square well with depth $U_0=8$ and width $a=1$, and the effective coupling constant is $g=8$. The units for all these parameters are defined in the text. For sodium, speed is measured in units of $2.75\mathrm{m}\mathrm{m}/\mathrm{s}$, so that for many speeds shown it takes a fraction of a second to extract one atom. The plateau exhibited extends several orders of magnitude.

Figure 3

Energy levels as a function of position for different numbers of atoms in the dot (bottom panel). In the top panel, the energy levels $E_n$ (ignoring the off-diagonal terms) are plotted for comparison. The dotted line represents the edge of the condensate. The parameters used are the ones of Fig. 2.

Figure 4

Probability of finding no atoms (dashed), one atom (dotted), and two atoms (solid line) inside the dot as a function of position for three different speeds. The top panel is the adiabatic result ($v\to 0$), the middle panel is for $v=1$, and the bottom panel for $v=50$.

Figure 5

Energy levels as a function of position (bottom panel) for a one-dimensional condensate with $\omega =0.005$, $N=10000$ atoms, potential depth $U_0=13.5$, and width $a=1$, and the effective coupling constant is $g=10$. The dotted line represents the edge of the condensate. The average energy $E_n$ of states $|n⟩$ are plotted in the top panel for comparison.

Figure 6

The probability of extracting one (black) and two atoms (gray) as a function of speed for the case described in Fig. 5. In this case, we can see two different plateaus, showing that the quantized output depends strongly on the speed of the dot.