PhD Research Projects

Mott insulator and supersolid phases in different Gauss law sectors of a 1D Z2 lattice gauge theory

We analyze the ground state phases of a 1D Z2 lattice gauge theory in different Hilbert Space sectors. In a lattice gauge theory, the Hilbert space splits into disconnected sectors corresponding to values of a local conserved quantity on each site, termed as a 'Gauss law'. In different such 'Gauss law' sectors, we find that the ground state can form interesting many-body phases like mott insulator states, supersolid states alongwith novel pairing phenomena.

Paper: Currently in progress

Subsystem symmetry, spin glass order and criticality from random measurements in a 2D Bacon-Shor circuit

We study a 2D measurement-only random circuit motivated by the Bacon-Shor error correcting code. We find a rich phase diagram as one varies the relative probabilities of measuring nearest neighbor Pauli XX and ZZ check operators. In the Bacon-Shor code, these checks commute with a group of stabilizer and logical operators, which therefore represent conserved quantities. Described as a subsystem symmetry, these conservation laws lead to a continuous phase transition between an X-basis and Z-basis spin glass order. The two phases are separated by a critical point where the entanglement entropy between two halves of an L X L system scales as L ln L, a logarithmic violation of the area law. We generalize to a model where the check operators break the subsystem symmetries (and the Bacon-Shor code structure). In tension with established heuristics, we find that the phase transition is replaced by a smooth crossover, and the X- and Z-basis spin glass orders spatially coexist. Additionally, if we approach the line of subsystem symmetries away from the critical point in the phase diagram, some spin glass order parameters jump discontinuously

Paper: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.024205

https://arxiv.org/abs/2303.02187

Rotating Bose gas dynamically entering the lowest Landau level

Motivated by recent experiments, we model the dynamics of a condensed Bose gas in a rotating anisotropic trap, where the equations of motion are analogous to those of charged particles in a magnetic field. As the rotation rate is ramped from zero to the trapping frequency, the condensate stretches along one direction and is squeezed along another, becoming long and thin. When the trap anisotropy is slowly switched off on a particular timescale, the condensate is left in the lowest Landau level. We use a time dependent variational approach to quantify these dynamics and give intuitive arguments about the structure of the condensate wavefunction. This preparation of a lowest Landau level condensate can be an important first step in realizing bosonic analogs of quantum Hall states.

Paper: journals.aps.org/pra/abstract/10.1103/PhysRevA.105.023310

arxiv.org/abs/2111.10415

Driven-dissipative control of cold atoms in tilted optical lattices

We present a sequence of driven-dissipative protocols for controlling cold atoms in tilted optical lattices. These experimentally accessible examples are templates that demonstrate how dissipation can be used to manipulate quantum many-body systems. We consider bosonic atoms trapped in a tilted optical lattice, immersed in a superfluid bath, and excited by coherent Raman lasers. With these ingredients, we are able to controllably transport atoms in the lattice and produce self-healing quantum states: a Mott insulator and the topologically ordered spin-1 AKLT state.

Paper: journals.aps.org/pra/abstract/10.1103/PhysRevA.103.043322

https://arxiv.org/abs/2101.00547

Dynamics of Bose-Einstein recondensation in higher bands

Motivated by recent experiments, we explore the kinetics of Bose-Einstein condensation in the upper band of a double well optical lattice. These experiments engineer a non-equilibrium situation in which the highest energy state in the band is macroscopically occupied. The system subsequently relaxes and the condensate moves to the lowest energy state. We model this process, finding that the kinetics occurs in three phases: The condensate first evaporates, forming a highly non-equilibrium gas with no phase coherence. Energy is then redistributed among the noncondensed atoms. Finally the atoms recondense. We calculate the time-scales for each of these phases, and explain how this scenario can be verified through future experiments.

Paper: journals.aps.org/pra/abstract/10.1103/PhysRevA.101.033609

https://arxiv.org/abs/1911.05111