Abstract
We apply the atom counting theory to strongly correlated Fermi systems and spin models, which can be realized with ultracold atoms. The counting distributions are typically sub-Poissonian and remain smooth at quantum phase transitions, but their moments exhibit critical behavior, and characterize quantum statistical properties of the system. Moreover, more detailed characterizations are obtained with experimentally feasible spatially resolved counting distributions.
Highlights
II, we briefly describe the models of the 1D optical lattice that we consider, and the Jordan-Wigner transformation that can be used to diagonalize them
In order to understand the properties of counting distributions better, we look at the mean and variance, which can be calculated from the following recurrences: mM+1 = mM + 2κvM 2 +1, varM+1 = m2M+1 − mM+12 = varM + 4κ2vM 2 +1(1 − vM 2 +1)
The recurrences imply that the mean mN ≤ κN ; we find typical value of mN of order of κN
Summary
Particle-wave duality is one of the most spectacular, and at the same time intriguing phenomena of quantum mechanics. Atomic fluctuations leave an imprint on the quantum fluctuations of the light, and vice versa This idea was recently extended to ultra-cold spinor gases [8], where it can be used to detect, manipulate, and even engineer various states of such systems. FERMI GAS IN AN 1D OPTICAL LATTICE one should introduce tunneling assisted with a laser or microwave induced double spin flip For this aim, one should make use of the resonance between onsite two atom “up-up” and “down-down” states, without disturbing “up-down” configurations. One way to realize such Hamiltonian with ultracold atoms is to use a Fermi-Bose mixture in the strong coupling limit In this limit, the low energy physics is well described by fermionic composites theory [13], in which fermions form composite objects with 0, 1, .
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