Current Research
Synthetic magnetic fields in Fock space
My current research has been focused on showing how synthetic magnetic fields can be created in Fock space by periodically driving simple many-body systems. Similarly to magnetic fields in real materials, the magnetic fields in Fock space result in topological features such as symmetry protected edge states and chiral currents.
Topological edge currents
We have shown [Phys. Rev. A 106, 033317 (2022)] that by periodically driving the interactions between two two-mode Bose gases one can generate a synthetic magnetic field in the Fock space of the two gases. In real materials a 2D surface has x and y coordinates, however, in Fock space we label the coordinates as half the occupation number difference between the two modes of each gas: n = (N1-N2)/2 and m = (M1-M2)/2.
cyclo.aviLike with magnetic fields in real materials, synthetic magnetic fields in Fock space lead to insulator behavior in the bulk where the initial Gaussian distribution stays in place and rotates which is analogous to cyclotron motion of charged particles.
edge.aviThe synthetic magnetic field also leads to conductor behavior along the edges of the Fock space which is similar to edge currents found in topological materials. In Fock space, the flow of the probability distribution plays the role of electric currents in real materials.
Meissner-vortex phase transition
We have also periodically driven the interactions between a single two-mode Bose gas and a spin-1/2 particle to generate a synthetic magnetic field. In this system we showed [Phys. Rev. A 106, 043325 (2022)] that a quantum phase transition takes place that is analogous to the Meissner-vortex transition in type-II superconductors when a magnetic field is applied. Instead of the Fock space being a square like in the above videos, it has the shape of a strip because the spin-1/2 particle has two states. In real materials this shape of lattice is often referred to as a ladder lattice due to it being long in one direction and short in the other.
The top shows the expected Meissner vortex transition in a type-II superconductor ladder lattice where below a critical magnetic field there is a current in the material (blue) expelling the applied magnetic field. Above the critical magnetic field, vortices form (green loops) where the magnetic field punctures the material.
The bottom shows the ground state probability distribution of the Fock space formed by a two-mode Bose gas and a spin-1/2 particle. When the synthetic magnetic field is below the critical value the ground state is solid, however, above the critical value it is broken up into strips. The holes are where vortices form in the Fock space just like in the type-II superconductor.