Justin T. Schultz

Singular atom optics with spinor Bose–Einstein condensates

Spinor Bose–Einstein condensates (BECs) and singular optical systems have both recently served as sandboxes to create and study analogs of phenomena from other fields of physics that are otherwise difficult to create and control experimentally. Interfacing singular optics and spinor BECs allows us to take advantage of and build on the foundations of singular optics to create and describe complex spin textures in BECs that serve as analogs of other systems. Here, the complete BEC wavefunctions are precisely engineered via a two-photon Raman interaction to contain π-symmetric (lemon, star) or 2π-symmetric (saddle, spiral) C-point singularities. The optical Raman beams are singular optical beams that contain these singularities and transfer them to the condensate, thereby creating vector-vortex spin textures—the spinor counterparts to scalar vortices—in pseudo-spin-1/2 BECs. With a version of atom-optic polarimetry, we can measure the Stokes parameters of the atomic cloud and characterize the singularities by the patterns present in their ellipse fields or by the C-point index. In the low density limit, these spin textures are analogs of optical vector vortices and should have dynamics driven by a matter-wave Gouy phase. With precise tuning of Raman beam parameters, we can create full Bloch BECs that contain every possible superposition between two states in the atomic cloud. Full Bloch BECs are similar to topologically stable magnetic skyrmions such as those created in thin metal films and nanowires, which may prove useful for atom-spintronics and topological quantum processes.

Measuring the Gouy Phase of Matter Waves Using Full Bloch Bose-Einstein Condensates

We propose and demonstrate experimental steps towards a new method for directly measuring the Gouy phase in a matter wave (Bose-Einstein condensate) system via an atomic analogy of full Poincare optical beams.

Spin Textures and Topological Excitations in Spinor 87-Rb Bose-Einstein Condensates

We engineer a variety of topological excitations in a BEC using a two-photon Raman process. Structures such as coreless vortices, fractional vortices, skyrmions, and monopoles can be created.

Imaging Stokes Parameters of Spinor BECs

We present two methods to image the spin density and relative phases of states in spinor BECs. In a psuedo-spin-1/2 system, these measurements are analogous to the Stokes parameters used to describe polarization in optics.

Let π Be a Function

Summary In the plane, the ratio of the circumference of a circle to its diameter is always π. On a sphere, however, this ratio (which we denote Π) takes on other values, provided the diameter is measured along a great circle on the sphere. In this article, we explore Π as a function of radius on surfaces of revolution. We also consider the inverse problem—we begin with a function and, under certain conditions, find a surface or Riemannian manifold with Π equal to that function.