Exfoliated chromium triiodide (CrI3) is a layered van der Waals (vdW) magnetic insulator that consists of ferromagnetic layers coupled through antiferromagnetic interlayer exchange [1][2][3] . The resulting permutations of magnetic configurations combined with the underlying crystal symmetry produces tunable magneto-optical phenomena that is unique to the two-dimensional (2D) limit [4][5][6][7] . Here, we report the direct observation of 2D magnons through magneto-Raman spectroscopy with optical selection rules that are strictly determined by the honeycomb lattice and magnetic states of atomically thin CrI3. In monolayers, we observe an acoustic magnon mode of ~0.3 meV with cross-circularly polarized selection rules locked to the magnetization direction. These unique selection rules arise from the discrete conservation of angular momentum of photons and magnons dictated by threefold rotational symmetry in a rotational analogue to Umklapp scattering 8 . In bilayers, by tuning between the layered antiferromagnetic and ferromagnetic-like states, we observe the switching of two magnon modes. The bilayer structure also enables Raman activity from the optical magnon mode at ~17 meV (~4.2 THz) that is otherwise Raman-silent in the monolayer. From these measurements, we quantitatively extract the spin wave gap, magnetic anisotropy, intralayer and interlayer exchange constants, and establish 2D magnets as a new system for exploring magnon physics.

Optimizing open quantum system evolution is an important step on the way to achieving quantum computing and quantum thermodynamic tasks. In this article, we approach optimisation via variational principles and derive an open quantum system variational algorithm explicitly for Lindblad evolution in Liouville space. As an example of such control over open system evolution, we control the thermalisation of a qubit attached to a thermal Lindbladian bath with a damping rate γ. Since thermalisation is an asymptotic process and the variational algorithm we consider is for fixed time, we present a way to discuss the potential speedup of thermalisation that can be expected from such variational algorithms. * sai@phy.iitb.ac.in arXiv:1711.08776v1 [quant-ph]

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