Spin-entanglement of an atomic pair through coupling to their thermal motion

Abstract

The spin-dynamics of two alkali atoms in an optical tweezer is driven by spin-changing collisions that couple the spin-state of the atoms to their relative motion. This paper experimentally studies the resulting spin-states when the relative motion is in a thermal state with k B T much larger than the energies of the spin-states that take part in the dynamics. We find that an initially unentangled spin-state can evolve into an entangled state. This is contrary to the common case when coupling a quantum system to hot degrees of freedom leads to loss of entanglement and not its generation. Moreover, we show that the generated entanglement is technologically useful as it, in principle, can enhance the sensitivity of measurements beyond the standard quantum limit. This may provide a promising avenue for robust entanglement generation for future technologies.

Figures (4)

• Figure 1: Experimental procedure for entanglement generation and investigation. a: Two atoms are initially loaded and prepared in the $F=2, m_F=0$ state in separate optical tweezers. By merging the tweezers, both atoms end up in the same tweezer. This allows the spin-changing collisions illustrated in b. A Raman pulse (also illustrated in b) couples $|-1\rangle$ and $|1\rangle$. Finally, atoms in $|1\rangle$ are ejected (see c) and the remaining atom number distribution is determined. b: Two atoms initially in $|0,0\rangle$ couple to the states $|\chi_1\rangle$ (dark yellow arrows) and $|\chi_2\rangle$ (light yellow arrows) by spin-changing collisions. Red arrows illustrate the Raman pulse. c: The atoms in $|1\rangle$ are ejected using a Raman pulse and push beam.
• Figure 2: a: Idealized calculation of probabilities for finding 1 (red), or 2 (green) atoms in the $F=2$, $m_F=-1$ state as a function of Raman-pulse duration. The probability for finding 0 is identical to that of finding 2. Solid and dashed curves represent entangled and unentangled states, respectively. b: Experimental populations of 0-atom (blue), 1-atom (red), and 2-atom (green) as a function of Raman-pulse duration $\tau$ from 0 to $\pi$ pulse. Solid and dashed curves show the corresponding theoretical expectations for entangled and unentangled states.
• Figure 3: a: Data taken with the entanglement destruction procedure, showing agreement with the unentangled model. b: The same experimental procedure as in Fig. \ref{['fig:Entanglement_data']}b, but with the data taken interleaved with that of a. Symbols and curves are the same as in Fig. \ref{['fig:Entanglement_data']}b.
• Figure 4: Results of the $\pi/2-T-\pi/2$ Ramsey-type experiment: The top panel presents Ramsey fringe obtained with the entangled stateDashed line: The expected signal for two entangled atoms (Eq. 17 in supplementary) with a fitted offset and fringe contrast. A $\chi^2$-test accept the model. Bottom panel: The result from two unentangled atoms. The dashed line is Eq. 18 in supplementary with fitted offset and fringe contrast.