Optical manipulation of a single Mn spin in a CdTe-based quantum dot

A system of two coupled CdTe quantum dots, one of them containing a single Mn ion, was studied in continuous wave and modulated photoluminescence, photoluminescence excitation, and photon correlation experiments. Optical writing of information in the spin state of the Mn ion has been demonstrated, using orientation of the Mn spin by spin-polarized carriers transferred from the neighbor quantum dot. Mn spin orientation time values from 20 ns to 100 ns were measured, depending on the excitation power. Storage time of the information in the Mn spin was found to be enhanced by application of a static magnetic field of 1 T, reaching hundreds of microseconds in the dark. Simple rate equation models were found to describe correctly static and dynamical properties of the system.Comment: 4 pages, 3 figure

Single spin optical read-out in CdTe/ZnTe quantum dot studied by photon correlation spectroscopy

Spin dynamics of a single electron and an exciton confined in CdTe/ZnTe quantum dot is investigated by polarization-resolved correlation spectroscopy. Spin memory effects extending over at least a few tens of nanoseconds have been directly observed in magnetic field and described quantitatively in terms of a simple rate equation model. We demonstrate an effective (68%) all-optical read-out of the single carrier spin state through probing the degree of circular polarization of exciton emission after capture of an oppositely charged carrier. The perturbation introduced by the pulsed optical excitation serving to study the spin dynamics has been found to be the main source of the polarization loss in the read-out process. In the limit of low laser power the read-out efficiency extrapolates to a value close to 100%. The measurements allowed us as well to determine neutral exciton spin relaxation time ranging from 3.4 +/- 0.1 ns at B = 0 T to 16 +/- 3 ns at B = 5 T.Comment: to appear in Phys. Rev.

Certified Knowledge Compilation with Application to Verified Model Counting

Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision-decomposable, negation normal form (dec-DNNF) . Knowledge compilation is the process of converting a formula into such a form. Unfortunately existing knowledge compilers provide no guarantee that their output correctly represents the original formula, and therefore they cannot validate a model count, or any other computed value. We present Partitioned-Operation Graphs (POGs), a form that can encode all of the representations used by existing knowledge compilers. We have designed CPOG, a framework that can express proofs of equivalence between a POG and a Boolean formula in conjunctive normal form (CNF). We have developed a program that generates POG representations from dec-DNNF graphs produced by the state-of-the-art knowledge compiler D4, as well as checkable CPOG proofs certifying that the output POGs are equivalent to the input CNF formulas. Our toolchain for generating and verifying POGs scales to all but the largest graphs produced by D4 for formulas from a recent model counting competition. Additionally, we have developed a formally verified CPOG checker and model counter for POGs in the Lean 4 proof assistant. In doing so, we proved the soundness of our proof framework. These programs comprise the first formally verified toolchain for weighted and unweighted model counting