Entanglement Interferometry for Precision Measurement of Atomic Scattering Properties

We report on a matter wave interferometer realized with entangled pairs of trapped ${}^{87}\mathrm{Rb}$ atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.

Figure 1

Ramsey interferometer sequence (shaded bars). Ramsey fringes are obtained by varying the phase $\alpha$ of the last microwave $\pi /2$ pulse. The magnetic field can be ramped to different magnetic field values in order to change the interaction properties of the atoms.

Figure 2

Measurement of total atom number versus magnetic field in a 2D optical lattice. The solid line is a Lorentzian fit to the data with center at 9.121(9) G and a width of 20(5) mG. The hold time at the various magnetic field values is 1 ms.

Figure 3

Time resolved measurement of the total atom number at the measured Feshbach resonance in a 3D lattice potential. Sites with more than one atom are emptied within 3 ms, whereas sites with only one atom are protected from loss. The solid line is a fit to an exponential decay with offset, from which we find to have a ratio $N_1/N_2\approx 1.1$.

Figure 4

Measured visibility dynamics due to entanglement in the system for a magnetic field value of 9.081 G. The solid line is a fit using Eq. (1) yielding a revival time $t_R=2\pi t_{\mathrm{hold}}/{\varphi }_{\chi }=9.5(2)\mathrm{ms}$, $V_0=0.82(4)$, $n_2=0.5$, ${\tau }_1=41(13)\mathrm{ms}$, and ${\tau }_2=20(5)\mathrm{ms}$. The inset is a measurement of the Ramsey sequence for a constant magnetic field $B=8.63\mathrm{G}$, away from the Feshbach resonance, and the solid line is a fit describing an exponential decay of the fringe visibility.

Figure 5

Measured absolute value of the change of elastic scattering length for magnetic field values around the Feshbach resonance (dots). Both sides were fitted separately to a dispersive curve with a common center [9.128(9) G] and width [15(4) mG]. In order to illustrate the dispersive behavior of $\Delta a_{s,\chi }$ (dashed line), the fitted branch above the resonance is flipped to negative values according to the sign determined by the TOF measurement.