#### Degree

Doctor of Philosophy (PhD)

#### Department

Department of Physics & Astronomy

#### Document Type

Dissertation

#### Abstract

We present a study of analog cosmological models in Bose-Einstein condensates (BEC) and in graphene, and superfluidity in a box-shaped traps. We start by examining the dynamics of a Bose-Einstein condensate (BEC) trapped inside an expanding toroid that can realize an analog inflationary universe. The expanding condensate forces phonons to undergo redshift and damping due to quantum pressure, owing to the thinness of the ring. We predict that such expanding BECs can exhibit spontaneous phonon creation from the vacuum state and show how it would manifest in the atom density and density correlations and discuss connections with the inflationary theory. We then extend this work to study entanglement of the spontaneously generated phonon pairs, for which we use the techniques of quantum continuous variables. We then develop a protocol to experimentally measure the correlations entering the covariance matrix, allowing an experimental quantification of the entanglement properties of the inflationary BEC. We then present a of how a spatially-varying quasiparticle velocity in honeycomb lattices, achievable using strained graphene or in engineered cold-atom optical lattices that have a spatial dependent tunneling amplitude, can yield the Rindler Hamiltonian embodying an observer accelerating in Minkowski spacetime. Within this setup, a sudden switch-on of the spatially-varying strain yields a spontaneous production of electron-hole pairs, an analog version of the Unruh effect characterized by the Unruh temperature. We discuss how this thermal behavior, along with Takagi's statistics inversion, can manifest themselves in photo-emission and scanning tunneling microscopy experiments. We show that the electronic conductivity grows linearly with frequency $\omega$, vanishing in the DC limit. Finally, we find that the total electronic energy at zero environment temperature looks like Planck's blackbody result for photons due to the aforementioned statistics inversion, whereas for an initial thermally excited state of fermions, the total internal energy undergoes stimulated particle reduction. Finally, we study ultracold Fermi gases trapped inside a three-dimensional box with vanishing boundary conditions, with interactions modeled using the Fermi-Huang pseudopotential. Taylor expanding the pairing to linear order in position, solves the gap equation yielding the transition temperature and local pairing amplitude that vanishes at the edges.

#### Date

4-2-2023

#### Recommended Citation

Bhardwaj, Anshuman, "Analog Cosmology and Superfluidity in Atomic Gases and Electronic Materials" (2023). *LSU Doctoral Dissertations*. 6077.

https://digitalcommons.lsu.edu/gradschool_dissertations/6077

#### Committee Chair

Sheehy, Daniel

#### DOI

10.31390/gradschool_dissertations.6077

#### Included in

Atomic, Molecular and Optical Physics Commons, Condensed Matter Physics Commons, Cosmology, Relativity, and Gravity Commons, Quantum Physics Commons