Topological Spin Textures in Spinor BECs

BECs in cold atomic gases allow researchers to study diverse phenomena common to seemingly disparate fields -- our work on vortex spin textures in spinor BECs is connected to quantum optics, superfluidity, topology, condensed matter physics, nuclear physics, and more. 

We control the phase and amplitude of each spin state of a BEC using a coherent two-photon stimulated Raman imprinting technique. This allows us to create complex non-equilibrium spin textures with specific spin and orbital (vortex) angular momenta to study various phenomena, each connecting to a different field of physics. We can create fractional vortices, Skyrmions, spin monopoles, non-Abelian vortices, and various ground state phases in our BEC. We are currently working on generating another topologically unique spin texture, known as knots, in the BEC.

One of our experimental tracks involves determining the symmetry properties of the ground state of rubidium-87, and therefore what types of spin textures, topological defects, and other phenomena may exist in equilibrium. The possible phases are analogous to those studied in superfluids and solid state physics, and depend on the s-wave spin state-dependent scattering lengths. These fundamental properties vary between atomic species and are difficult to calculate precisely. They are also challenging to measure directly in the lab. Our Raman process allows us to create non-equilibrium spin textures with arbitrary vortex winding number, relative populations and spatial distribution across spin states. Thus, we can imprint the required spin texture onto the BEC, and then let it evolve in time. The rate of evolution and final population distribution among the spin states indicates the symmetry of the ground state.

Another series of experiments are on quantum simulation using magnetic monopole analogs. Unlike electric charges, which commonly exist in isolation, Maxwell’s equations prohibit the existence of isolated magnetic charge (magnetic monopoles). If you break an everyday magnet apart, each piece becomes a smaller complete magnet instead of separate north and south poles. You can continue breaking these magnets in half and you will never, as far as we know, end up with a separate north (positive monopole) and south pole (negative monopole). It’s possible that quantum mechanics modifies Maxwell’s equations so that monopoles can exist. Despite extensive searches in meteorites, polar volcanic rock, and particle colliders, a naturally-occurring monopole has not been found. This makes the question of magnetic monopoles a major mystery in physics. We have made magnetic monopole analog spin textures in the BEC as the first step in exploring this mystery. We engineer the spin states, vortex states, and relative phases in the BEC to generate monopole, anti-monopole, and synthetic monopole field spin textures. The vortices and spins in the BEC behave as if there were a magnetic monopole present. We can measure the evolution and interaction of these monopole structures to test theoretical predictions on their properties and connections to naturally occurring magnetic monopoles. 

We are also working on generating knots in a spinor BEC. Using the coherent spatially-dependent Raman imprinting process developed by our group, we can transfer a 3D knot in a laser beam into a 3D knot in the condensate. The stability of such knots depends on their topological processes as well as the symmetry properties of the choice of BEC state. By writing different knots and watching them evolve in time, we can study fundamental symmetry properties of the BEC. Generating 3D knots in the spatial mode of a BEC is also interesting in itself. Recently, we proposed an experimental protocol to imprint torus knots and lemniscate knots in a pseudo-spin-1/2 BEC using a Raman process technique that is similar to the method for imprinting 2D topological defects such as vortices and 2D skyrmions. Instead of using Raman beams with a single spatial mode, we use more complicated structured Raman laser fields. Apart from 3D knots, we are also interested in imprinting other types of 3D topological defects in a BEC. One example would be imprinting a 3D skyrmion and studying its evolution. We are looking forward to experimentally imprinting 3D topological defects in our new experimental platform under development.