Bloch vector formalism in the problem of nonlinear resonant response of a quasi-two-dimensional supercrystal

Taking into account the ideas of the generalized two-level scheme, within the framework of the semiclassical approach to the consideration of the resonant interaction of the light field with matter, an analytical solution to the problem of the evolution of superradiance in a quasi-two-dimensional supercrystal formed by quantum dots is obtained. The calculation was carried out for the physical parameters of a semiconductor structure with quantum-well effects in the presence of resonant nonlinearity and intraband relaxation.

Measurement of Purity, the Simplest Nonlinear Functional of the Density Matrix

After reviewing the earlier ideas to measure the purity of a quantum system, a new scheme for the measurement of purity is presented, which aims at providing a simple, direct and efficient procedure without resorting to quantum state tomography. The scheme is also illustrated in the Bloch-vector representation for a two-level quantum system (qubit) and for a general D-level quantum system. As a variant, a simple example implemented in a one-dimensional scattering process to measure the purity of the target qubit is also given.

Qubit purification speed-up for three complementary continuous measurements

We consider qubit purification under simultaneous continuous measurement of the three non-commuting qubit operators , , . The purification dynamics is quantified by (i) the average purification rate and (ii) the mean time of reaching a given level of purity, 1− ε . Under ideal measurements (detector efficiency η =1), we show in the first case an asymptotic mean purification speed-up of 4 when compared with a standard (classical) single-detector measurement. However, by the second measure—the mean time of first passage of the purity—the corresponding speed-up is only 2. We explain these speed-ups using the isotropy of the qubit evolution that provides an equivalence between the original measurement directions and three simultaneous measurements, one with an axis aligned along the Bloch vector and the other with axes in the two complementary directions. For inefficient detectors, η =1− δ <1, the mean time of first passage increases because qubit purification competes with an isotropic qubit dephasing. In the asymptotic high-purity limit ( ε , δ ≪1), we show that the increase possesses a scaling behaviour : is a function only of the ratio δ / ε . The increase is linear for small arguments, but becomes exponential for δ / ε large.