Raman fingerprints on the Bloch sphere of a spinor Bose–Einstein condensate

Abstract

We explore the geometric interpretation of a diabatic, two-photon Raman process as a rotation on the Bloch sphere for a pseudo-spin-1 /2 system. The spin state of a spin-1 /2 quantum system can be described by a point on the surface of the Bloch sphere, and its evolution during a Raman pulse is a trajectory on the sphere determined by properties of the optical beams: the pulse area, the relative intensities and phases, and the relative frequencies. We experimentally demonstrate key features of this model with a 87 Rb spinor Bose-Einstein condensate, which allows us to examine spatially dependent signatures of the Raman beams. The two-photon detuning allows us to precisely control the spin density and imprinted relative phase profiles, as we show with a coreless vortex. With this comprehensive understanding and intuitive geometric interpretation, we use the Raman process to create and tailor as well as study and characterize exotic topological spin textures in spinor BECs.

Topological atom optics and beyond with knotted quantum wavefunctions

“…The optical fields including the Raman beams and the imaging beam all propagate along the long axis of the cloud, which is also the atomic quantization axis. The experimental configuration is described in more detail in previous publications 35,44,45,47 .…”

“…is the vector of Pauli matrices, ϕ is the relative phase between the Raman fields, and the parameters Ω and α are related to the total and relative intensities of the optical fields (see "Methods") 46,47 . When one of the Raman beams has a Laguerre-Gaussian mode, this beam carries OAM.…”

Creating full-Bloch Bose–Einstein condensates with Ramanq-plates

“…Our Raman technique has been described in detail previously [52,54,56]. Briefly, we create a spin polarized 87 Rb BEC of » 6.5 10 6 atoms in…”

“…Since all spatial points in the cloud begin at one pole of the Bloch sphere, we adjust the Raman q-plate beams such that the antipodal point of the Bloch sphere is then mapped to the perimeter of the atomic cloud. Although this could be done by changing the size of the Raman beams relative to the atomic cloud, it can more easily be accomplished through changing any one of the other parameters [54] such as the pulse area (Wt) or the detuning Δ.…”

20 years of Bose–Einstein condensates: current trends and applications of ultracold quantum gases

“…This Special Issue of Journal of Modern Optics showcases a few of the directions that research and scientific developments, indebted to the BEC machinery, have taken. These include systems where the internal quantum states come into play [1,2] as well as the study of ultracold fermions [3] and particles with dipolar interactions [4]. Such diverse and rich systems have become of more than academic interest due to an ever-increasing technical ability to harness and manipulate multiple atomic species, simultaneously [5].…”