The susceptibility of a quantum coherent gas is derived near resonance and the effect of dipole-dipole interactions are assessed for a three-level system using mean-field theory. It is shown that the gas exhibits an ultralarge index effect with no absorption with the dipole effects included, but that for large N (number of atoms per unit volume) the dipole interactions have a marked effect. These results imply that the dipole interactions of a coherent gas near resonance do not destroy the ultralarge absorption-free index effect.
We present analysis of a system of three two-level atoms interacting with each other through the dipole-dipole interaction. The interaction manifests between excited state of one of the atoms and the ground state of its nearest neighbour. Steady state populations of the density matrix elements are presented and are compared with a situation when only two atoms are present. It can be noticed that the third atom modifies the behaviour of the three atoms. Two configurations are analysed, one in which the three atoms are in a line, with no interaction between atoms at the end points and the other in which the atoms form a closed loop with each atom interacting with both its neighbours.
We investigate how the long-range tail of dipole-dipole interactions modifies the dynamics of strongly interacting hard-core bosons in a one-dimensional lattice. In the nearest-neighbour model, large interactions generate an emergent Hilbert-space fragmentation into manifolds labelled by the number of nearest-neighbour bonds
NNN. The dipolar tail has a non-monotonic effect on this fragmented dynamics as the interaction-to-tunnelling ratio
V/t is increased. At intermediate
V/t, it enhances delocalisation relative to the nearest-neighbour model by reducing the energetic detuning between neighbouring
NNN manifolds and sustaining their hybridisation by hopping. At larger
V/t, the same tail lifts degeneracies within each manifold, beginning with the splitting associated with the next-nearest-neighbour bond number
NNNN, and promotes intra-manifold localisation and Hilbert-space shattering. The competition between these two effects produces a crossover from a delocalising to a localising role of the dipolar tail, visible in the late-time spatial inhomogeneity. This crossover occurs for nearly all initial states considered and persists at different fillings. Transverse confinement strengthens the short-range part of the dipolar tail and shifts the crossover to lower
V/t, bringing it into the regime relevant to current experiments with magnetic atoms and polar molecules.
The theory of pressure broadening by foreign atoms is formulated within the framework of an adiabatic representation (which we distinguish from the adiabatic approximation). This allows us to treat all the electrons in the gas as indistinguishable, and thus include the possibility of electron exchange between atoms; this effect, which is responsible for much of the interatomic interaction, is neglected in all previous theories, apart from the adiabatic and 'nearest neighbor' theories which are of limited applicability. By means of projection operators, we define a spectral matrix, whose dimension is equal to the number of distinct frequencies characteristic of the isolated radiator. The spectrum is equal to the sum of all the elements of the spectral matrix; the diagonal elements correspond to the different lines of the spectrum, and the off diagonal elements represent quantum interference between overlapping lines. The Fourier transform of the spectral matrix is the correlation matrix, whose elements time correlate components of the dipole moment operator responsible for different lines of the spectrum. The time evolution of the zero perturber correlation matrix is given by eiΩτ, where Ω is a diagonal matrix whose elements are the different frequencies characteristic of the radiator. The perturbing gas causes the 'reduced Liouvillian' Ω to acquire a time dependent or frequency dependent non-Hermitian nondiagonal part. To obtain low density approximations, we treat that non-Hermitian 'perturbation' to first order in the gas density.