Noise Correlations in one-dimensional systems of ultra-cold fermions

Time of flight images reflect the momentum distribution of the atoms in the trap, but the spatial noise in the image holds information on more subtle correlations. Using Bosonization, we study such noise correlations in generic one dimensional systems of ultra cold fermions. Specifically, we show how pairing as well as spin and charge density wave correlations may be identified and extracted from the time of flight images. These incipient orders manifest themselves as power law singularities in the noise correlations, that depend on the Luttinger parameters, which suggests a general experimental technique to obtain them.Comment: 5 pages, 3 figures. Added discussion on the visibility of noise correlation features for realistic condition

Noise Correlations in low-dimensional systems of ultracold atoms

We derive relations between standard order parameter correlations and the noise correlations in time of flight images, which are valid for systems with long range order as well as low dimensional systems with algebraic decay of correlations. Both Bosonic and Fermionic systems are considered. For one dimensional Fermi systems we show that the noise correlations are equally sensitive to spin, charge and pairing correlations and may be used to distinguish between fluctuations in the different channels. This is in contrast to linear response experiments, such as Bragg spectroscopy, which are only sensitive to fluctuations in the particle-hole channel (spin or charge). For Bosonic systems we find a sharp peak in the noise correlation at opposite momenta that signals pairing correlations in the depletion cloud. In a condensate with true long range order, this peak is a delta function and we can use Bogoliubov theory to study its temperature dependence. Interestingly we find that it is enhanced with temperature in the low temperature limit. In one dimensional condensates with only quasi-long range (i.e. power-law) order the peak in the noise correlations also broadens to a power-law singularity.Comment: 14 pages, 7 figure

Noise Correlations of Hard-core Bosons: Quantum Coherence and Symmetry Breaking

Noise correlations, such as those observable in the time of flight images of a released cloud, are calculated for hard-core bosonic (HCB) atoms. We find that the standard mapping of HCB systems onto spin-1/2 XY models fails in application to computation of noise correlations due to the contribution of multiply occupied virtual states in HCB systems. Such states do not exist in spin models. An interesting manifestation of such states is the breaking of particle-hole symmetry in HCB. We use noise correlations to explore quantum coherence of strongly correlated bosons in the fermionized regime with and without external parabolic confinement. Our analysis points to distinctive new experimental signatures of the Mott phase.Comment: 17 pages, 6 figures. This is a detailed revised version of quant-ph/0507153. It has been submitted to Journal of Physics B: the special edition for the Cortona BEC worksho