Coherent Collisional Spin Dynamics in Optical Lattices

We report on the observation of coherent, purely collisionally driven spin dynamics of neutral atoms in an optical lattice. For high lattice depths, atom pairs confined to the same lattice site show weakly damped Rabi-type oscillations between two-particle Zeeman states of equal magnetization, induced by spin-changing collisions. Moreover, measurement of the oscillation frequency allows for precise determination of the spin-changing collisional coupling strengths, which are directly related to fundamental scattering lengths describing interatomic collisions at ultracold temperatures.

Figure 1

(a) Two atoms localized in the vibrational ground state of a common lattice well can change their spin orientation while preserving total magnetization. The atoms remain in the lowest vibrational state at all times. (b) The process can be described as a coherent coupling between two-particle Zeeman states $|{\varphi }_i⟩$, $|{\varphi }_f⟩$, and $|{\varphi }_{f^{\prime }}⟩$, where the coupling strength ${\Omega }_{if}$ depends on the choice of initial and final state, and the detunings ${\delta }_{if}$, ${\delta }_{f{f}^{\prime }}$ can be varied by the second order Zeeman shift.

Figure 2

Spin dynamics of atom pairs localized in an optical lattice at a magnetic field of $B=0.8\mathrm{G}$. The atoms are initially prepared in $|0,0⟩$ and can evolve into $|+1,-1⟩$. Shown are the populations in $m_f=0$ (○) and $m_f=\pm 1$ (●) together with a fit to a damped sine yielding an oscillation frequency of ${\Omega }_{if}^{\prime }=2\pi \times 278(3)\mathrm{Hz}$.

Figure 3

Oscillation frequency (inset: amplitude) of spin dynamics vs magnetic field for the case $|0,0⟩\leftrightarrow |+1,-1⟩$ (○) and $|-1,-1⟩\leftrightarrow |0,-2⟩$ (●). The diamonds are results of a Fourier transform for the coupled three-level case. The solid lines are fits to the expected behavior of the Rabi model. The upper curve has been offset by 300 Hz (inset: 0.2) for clarity. The error bars are typically on the order of a few percent. As comparison the calculated curves [based on 22 ] are shown as dashed lines. The shaded regions mark the range of frequencies consistent with an error of $0.2a_B$ in the scattering lengths and an uncertainty of 10% (as upper bound) in the lattice depth, where both errors have been added.

Figure 4

High contrast spin oscillations between $|0,0⟩$ (○) and $|+1,-1⟩$ (●) at 0.6 G and $40E_r$. Here, atoms in sites with unity filling are selectively discarded from the measurement (see text).

Figure 5

Damping rate of spin oscillations vs lattice depth for $|0,0⟩\leftrightarrow |+1,-1⟩$. The solid line is a fit to $\alpha J/h+{\gamma }_0$ with ${\gamma }_0=37(3){\mathrm{s}}^{-1}$ (illustrated as dashed line). The inset shows atom loss vs hold time at a 10 G magnetic field, where spin dynamics is suppressed. The fast loss rate of ${\gamma }_1\approx 35(5){\mathrm{s}}^{-1}$ coincides with the offset ${\gamma }_0$ of the damping rate even at high lattice depths.