I will discuss our research on 2D magnetic materials and heterostructures. After a short introduction, I will present results on atomically thin multilayers of different magnetic semiconductors such as CrI3, CrCl3 (layered antiferromagnets), MnPS3 (antiferromagnetic within individual layers), and CrBr3 (ferromagnetic semiconductors). Using atomically thin, exfoliated crystals, we form tunnel barriers that enable magnetism to be probed by magnetotransport measurements. Examples of observed phenomena include: i) a giant tunneling magnetoresistance in CrI3; ii) a full characterization of the magnetic phase diagram of CrCl3 multilayers; iii) the observation of a spin-flop transition in MnPS3 persisting to the ultimate thickness of an individual monolayer, and iv) the demonstration that the tunneling magnetoresistance of ferromagnetic CrBr3 barriers depends on magnetic field and temperature only through the magnetization (from well above to well below the Curie temperature). We conclude that measurements of the temperature and magnetic field dependence of the tunneling magnetoresistance allow precise information about the magnetic state of atomically thin crystals to be obtained, something impossible to do with most conventional experimental techniques, not sufficiently sensitive when used on such a small amount of material.

The security of public key cryptography is based on the hardness of certain algorithmic problems. Schemes we use today rely on the hardness of factoring and computing discrete logarithms in elliptic curve groups. Unfortunately, these are no longer secure once a large-scale quantum computer is built. Thus we have to switch (not instantly but gradually) our currently used protocols (e.g., TLS) to ensure quantum resistance. In this talk I will describe how the abelian hidden subgroup problem relates to factoring and discrete logarithms and will present hard algorithmic problems that we presume are intractable even for a quantum computer

We will first discuss fundamental concepts of phase transition phenomenology in the context of cavity QED systems. A short introduction to cavity QED will be presented. This includes the description of our laboratory setup at Wigner RCP. Then we will describe two recent experiments where first-order phase transitions have been observed with laser cooled and trapped atoms in an optical cavity. Besides the time-resolved observation of the dynamical transmission blockade breakdown phase transition, the system allows for the quantification of enhanced fluctuations in the critical region and for performing finite size scaling measurements.