Bose-Hubbard model with attractive interactions

We consider the Bose-Hubbard model of atoms in an optical lattice potential when the atom-atom interactions are attractive. If the lowest energy lattice sites are degenerate (such as in the homogeneous case), then, at a critical value of the interaction strength, a phase-coherent condensate becomes unstable to a quantum superposition such that the number distribution of each of the degenerate sites becomes double peaked. In the limit when the interaction dominates, the superposition becomes macroscopic and has the form $|\psi>\propto\sum_{j} e^{i\phi_{j}}\hat{b}^{\dagger N}_{j}|{\rm vac}>$, where $N$ is the total number of atoms and the sum ranges over the energy-degenerate sites.Comment: 4 pager, 5 figures, accepted for publication in PR

Maximal entanglement of two spinor Bose-Einstein condensates

Starting with two weakly-coupled anti-ferromagnetic spinor condensates, we show that by changing the sign of the coefficient of the spin interaction, $U_{2}$, via an optically-induced Feshbach resonance one can create an entangled state consisting of two anti-correlated ferromagnetic condensates. This state is maximally entangled and a generalization of the Bell state from two anti-correlated spin-1/2 particles to two anti-correlated spin$-N/2$ atomic samples, where $N$ is the total number of atoms.Comment: 5 pages, 3 figures, accepted for publication in PR

On-demand single-photon state generation via nonlinear absorption

We propose a method for producing on-demand single-photon states based on collision-induced exchanges of photons and unbalanced linear absorption between two single-mode light fields. These two effects result in an effective nonlinear absorption of photons in one of the modes, which can lead to single photon states. A quantum nonlinear attenuator based on such a mechanism can absorb photons in a normal input light pulse and terminate the absorption at a single-photon state. Because the output light pulses containing single photons preserve the properties of the input pulses, we expect this method to be a means for building a highly controllable single photon source.Comment: 5 pages, 2 figures, to appear in PRA. To be published in PR

Tax evasion and exchange equity: a reference-dependent approach

The standard portfolio model of tax evasion with a public good produces the perverse conclusion that when taxpayers perceive the public good to be under-/overprovided, an increase in the tax rate increases/decreases evasion. The author treats taxpayers as thinking in terms of gains and losses relative to an endogenous reference level, which reflects perceived exchange equity between the value of taxes paid and the value of public goods supplied. With these alternative behavioral assumptions, the author overturns the aforementioned result in a direction consistent with the empirical evidence. The author also finds a role for relative income in determining individual responses to a change in the marginal rate of tax