Spin dynamics in a two-dimensional quantum gas

We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimposed angular density modulations. The density distributions depend on the applied magnetic field and are well explained by a simple Bogoliubov model. We show that the two clouds are anticorrelated in momentum space. The observed momentum correlations pave the way towards the creation of an atom source with nonlocal Einstein-Podolsky-Rosen entanglement.

Figure 1

(a) Absorption image after Stern-Gerlach separation and time of flight for $q=-330\mathrm{Hz}$ and 8 ms evolution time. (b) Time evolution of relative population in $|\pm 1\rangle$. The data have been fitted with an exponential function for the first 8 ms; the statistical uncertainty of each point is on the order of the symbol size. (c) Mean relative population in $|\pm 1\rangle$ after 8 ms evolution time; the solid line is a guide to the eye.

Figure 2

(a) Absorption images for several values of $q$; the gray scale was adjusted for different settings of $q$ to enhance visibility. The schematic for $q=-382$ Hz illustrates momentum conservation in a spin-changing collision. (b) Simulated time-of-flight density distributions for the same values of $q$.

Figure 3

(a) (Solid line) Effective potential experienced by $|\pm 1\rangle$ and (red dashed line) the cylindrical box approximation. (b) Instability rates $E_{nl}^{\pm }/h$ for $n=1,l=0,1,\cdots ,9$. The peak instability rate is that of the $n=1,l=0$ mode; the peak rate decreases monotonically with increasing $l$. (c) Instability rates in the range $q=0$ to $-500$ Hz. (d) A closeup of (c) showing the instability rates at $q=-400$ Hz.

Figure 4

(a) Cloud radius after 20 ms time of flight. Black points: experimental data; red squares: simulations; blue line: ballistic expansion model (offset to begin at the average value of the mean field repulsion across the populated lattice sites). (b) Density correlation function at $q=-297$ Hz (mean of 54 realizations for both simulations and experimental data). Black line: cross-correlation for $|\pm 1\rangle$ clouds; blue dash-dotted line: mean autocorrelation function for $|\pm 1\rangle$ clouds; red dotted line: autocorrelation for simulations.