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.
We investigate how the antiferromagnetic Mott insulator evolves into the
d-wave BCS superconductor through hole doping. Allowing spin fluctuations in the strong-coupling approach, we find a spin-gapped incoherent metal with preformed pairing as an intermediate phase between the antiferromagnetic Mott insulator and
d-wave superconductor. This non-Fermi-liquid metal is identified with an infrared stable fixed point in the spin-decomposition gauge theory, analogous to the spin liquid insulator in the slave-boson gauge theory. We consider the single particle spectrum and dynamical spin susceptibility in the anomalous metallic phase, and discuss physical implications.
We propose a method to probe states in the Mott insulator regime produced from a condensate in an optical lattice. We consider a system in which we create time-dependent number fluctuations in a given site by turning off the atomic interactions and lowering the potential barriers on a nearly pure Mott state to allow the atoms to tunnel between sites. We calculate the expected interference pattern and number fluctuations from such a system and show that one can potentially observe a deviation from a pure Mott state. We also discuss a method in which to detect these number fluctuations using time-of-flight imaging.