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arXiv:quant-ph/0610073 · Physical Review Letters

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

Igor B. Mekhov, Christoph Maschler, Helmut Ritsch

Published Mar 7, 2007• 96 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.98.100402

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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.
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Light transmission or diffraction from different quantum phases of cold atoms in an optical lattice has recently come up as a useful tool to probe such ultracold atomic systems. The periodic nature of the optical lattice potential closely resembles the structure of a diffraction grating in real space but is loaded with a strongly correlated quantum many-body state which interacts with the incident electromagnetic wave, a feature that controls the nature of light transmission or dispersion through such quantum media. In this paper we show that, as one varies the relative angle between the cavity mode and the optical lattice, the peak of the transmission spectrum through such cavities also changes, which reflects the statistical distribution of the atoms in the illuminated sites. Consequently, the angle-resolved transmission spectrum of such quantum diffraction gratings can provide a plethora of information about the Fock-space structure of the many-body quantum state of ultracold atoms in such an optical cavity that can be explored in current state-of-the-art experiments.