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Please find below popular summaries of some of my latest research projects in a level accessible to undergraduate students or physics enthusiasts (last update 2022). For a more basic introduction to my works and research topics see Public Outreach.
Fractons in hard-core Bose-Hubbard models
Fractons in hard-core Bose-Hubbard models
Phys. Rev. Research 4, 023151 (2022)
arXiv: 2107.06786
Symmetry is a fundamental concept which appears in a variety of contexts ranging from art to natural sciences. In everyday use it refers to a sense of a perfect balance and harmony. In physics, the study of symmetries proves to be of the utmost importance as the symmetries of physical equations can be related to the conservation laws. Recently it has become clear that certain symmetries leading to the conservation of charge and dipole moments in particle distributions entail the existence of exotic excitations, dubbed fractons, which lack the ability to move, either completely or partially. Unfortunately, fracton models are usually complicated and hence they are unlikely to be realised in a laboratory. To resolve this issue we propose a simple lattice model of fracton defects which can not only be efficiently studied theoretically but also is feasible experimentally in recently proposed quantum simulator platforms with big time crystals.
Specifically, we construct an extended Bose-Hubbard model with hopping terms involving four lattice sites, where in the hard-core regime the low energy excitations have fracton properties. While isolated fracton defects are completely immobile, neighboring defect pairs compose lineons which can propagate only in one dimension. What is interesting, we find that two lineons can form a bound state without mobility restrictions. We confirm the robustness of our results against symmetry breaking perturbations.
Our construction provides a clear path towards understanding many-body dynamics with restricted mobility. Further studies can shed light onto fracton interactions, fracton entanglement as well as exotic fractonic superfluids which go beyond the mean-field treatment.
Fig. The lowest energy excitations of extended Bose-Hubbard models with four-site hopping terms can have fracton properties with restricted mobility.
Inseparable 2D time crystal lattices
Inseparable 2D time crystal lattices
Phys. Rev. Lett. 127, 263003 (2021)
arXiv: 2103.03778
This work deals with a two dimensional (2D) gravitational bouncer model, where ultracold atoms are bouncing between a pair of oscillating mirrors in the presence of the gravitational field. One of the greatest advantages of this model is that it allows for a drastic breaking of the discrete time translation symmetry, giving rise to robust big time crystals and big time crystalline structures. The latter supports quantum solid state phenomena in a time dimension.
In the Letter we introduce a new methodology for the systematic engineering of arbitrary two dimensional (2D) inseparable temporal lattices. The presentation is focused on an example of the Lieb lattice with the Möbius strip geometry, whose flat band hosts complex interaction induced dynamics. Tunability of long range interactions and exotic long distance simultaneous hopping of particles provide a versatile platform for quantum simulations of exotic many-body physics in a time dimension.
Fig. Possible geometries of effective 2D time crystal lattices. Blue colors represents areas around maxima of the effective potential which correspond to the lowest energies of a particle with a negative effective mass.
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