Algebraic solution for a two-level atom in radiation fields and the Freeman resonances

Journal ArticleUsing techniques of complex analysis in an algebraic approach, we solve the wave equation for a two-level atom interacting with a monochromatic light field exactly. A closed-form expression for the quasienergies is obtained, which shows that the Bloch-Siegert shift is always finite, regardless of whether the original or the shifted level spacing is an integral multiple of the driving frequency ω. We also find that the wave functions, though finite when the original level spacing is an integral multiple of ω, become divergent when the intensity-dependent shifted energy spacing is an integral multiple of the photon energy. This result provides an ab initio theoretical explanation for the occurrence of the Freeman resonances observed in above-threshold ionization experiments

High-precision quasienergies for a driven two-level atom at the two-photon preresonance

Journal ArticleA computation with unprecedented precision is presented for quasienergies of a two-level atom in a monochromatic radiation on the basis of a recently obtained exact expression [D.-S. Guo et al., Phys. Rev. A 73,023419 (2006)]. We start with the proof of an expression theorem. With this theorem the quasienergies for any two-level atom can be expressed in terms of the quasienergies for only those with the original energy spacing (per field photon energy) being an integer (preresonances). Then we carry out a numerical evaluation of the quasienergies at the two-photon preresonance, which involves computing an infinite determinant, up to the 18th power of the coupling strength. The theoretical prediction presents an experimental challenge for highprecision tests of quantum mechanics and could be exploited for precise calibration of high laser intensities

Negative entanglement measure for bipartite separable mixed states

We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. In the 1D Bose-Hubbard model, the NEM as a function of $t/U$ changes from zero to negative on approaching the critical point of quantum phase transition.Comment: 6 pages, 3 figure

Calculating the relative entropy of entanglement

We extend Vedral and Plenio's theorem (theorem 3 in Phys. Rev. A 57, 1619) to a more general case, and obtain the relative entropy of entanglement for a class of mixed states, this result can also follow from Rains' theorem 9 in Phys. Rev. A 60, 179.Comment: 2 pages, RevTex, an important reference adde