Cavity-Enhanced Light Scattering in Optical Lattices to Probe Atomic Quantum Statistics

Different quantum states of atoms in optical lattices can be nondestructively monitored by off-resonant collective light scattering into a cavity. Angle resolved measurements of photon number and variance give information about atom-number fluctuations and pair correlations without single-site access. Observation at angles of diffraction minima provides information on quantum fluctuations insensitive to classical noise. For transverse probing, no photon is scattered into a cavity from a Mott insulator phase, while the photon number is proportional to the atom number for a superfluid.

Figure 1

Setup. A lattice is illuminated by a probe at the angle ${\theta }_0$ which is scattered into a cavity at ${\theta }_1$.

Figure 2

Intensity angular distributions for two traveling waves. (a) Intensity of classical diffraction; (b) noise quantity $R$ (5) for coherent atomic state (constant 1, line A), SF with all sites illuminated $K=M$ (curve B), and MI state (constant 0, line C); (c) the same as in (b) but for partially illuminated SF with $K=M/2$. $N=M=30$, ${\theta }_0=0$.

Figure 3

Intensity angular distributions for two standing-wave modes. (a) Intensity of classical diffraction; (b) noise quantity for the coherent state; and (c) for SF (curve A) and MI (constant 0, line B). $N=M=K=30$, ${\theta }_0=0.1\pi$.