Collective modes in Ising lattices

J.-i. Igarashi

Kush Saha, Subhasis Sinha, K. Sengupta

We chart out the possible phases of laser-driven Rydberg atoms in the presence of a hypercubic optical lattice. We define a pseudospin degree of freedom whose up (down) components correspond to the excited (ground) states of the Rydberg atoms and use them to demonstrate the realization of a canted Ising antiferromagnetic (CIAF) Mott phase of the atoms in these systems. We also show that, on lowering the lattice depth, the quantum melting of the CIAF and density-wave Mott states (which are also realized in these systems) leads to supersolid phases of the atoms. We provide analytical expressions for the phase boundaries and collective excitations of these phases in the hard-core limit within mean-field theory and discuss possible experiments to test our theory.

I. R. Yukhnovskii, Ihor V. Pylyuk, Mykhailo P. Kozlovskii

The behaviour of a three-dimensional Ising-like system at temperatures above the critical value of T c is studied in the approximation of the sextic distribution for modes of spin density oscillations (ρ 6 model). The original collective variables method is developed in this higher non-Gaussian approximation for calculating the thermodynamic characteristics of the system near T c taking into account the first confluent correction. The calculations are illustrated by an example of a simple cubic lattice and an exponentially decreasing interaction potential. The main distinctive feature of the method is the separate inclusion of the contributions to the thermodynamic functions from the short-wave and long-wave spin density oscillation modes. The dependences of the phase transition temperature, leading critical amplitudes, and correction-to-scaling amplitudes for the specific heat and susceptibility on the microscopic parameters of the system are investigated.

H. S. Green

B. A. Men'

Zlatko G. Koinov

We derive the Bethe-Salpeter (BS) equations for the collective-mode spectrum of superfluid Fermi gases of equal mixture of atomic Fermi gas of two hyperfine states loaded into a moving optical lattice. In a moving lattice the superfluid state is unstable due to spontaneous emission of the short-wavelength rotonlike excitations which appear in the spectrum of the collective modes. It is shown that the spectrum obtained by the BS equations is in an excellent agreement with the collective-mode dispersion calculated by the perturbation approach, while there are some differences between the results obtained by density response function method and by the BS approach. The difference increases with increasing the lattice velocity, which can be seen in the analytical approximations for the dispersion relation in the long-wavelength limit in a weak-coupling regime.