McCormack, Gary
(2022)
Mean-field Dynamics of Rydberg-Dressed Bosonic Atoms in Free-Space and Optical Lattices.
PhD thesis, University of Nottingham.
Abstract
In the past several decades, cold atom experiments have provided physicists with copious amounts of new discoveries, none more important than that of Bose-Einstein condensation, where laser-cooled bosonic gases `condense' into the lowest available energy state of the system. While playing a pivotal role in ultracold experiments, atoms within a Bose Einstein condensate interact very weakly with one another. A major dichotomy to this is interaction experienced by Rydberg atoms, where the interaction strength between atoms are orders of magnitude larger than standard atom-atom interactions.
In this thesis we examine the dynamical properties of Rydberg-dressed Bose-Einstein condensates under different forms of trapping potentials. The study of the out-of-equilibrium dynamics of Bose-Einstein condensates has lead to a plethora of novel and interesting features. We aim to expand on this already lucrative field by inducing dynamics via Rydberg-dressing, which creates an effective soft-core interaction between the dressed states.
The work chapters will be divided into two main parts. First we study the excitation of roton and maxon modes in a three-dimensional free space model, where the dynamics is induced via an instantaneous quench of the interaction parameters in Chapter 3. The Bogoliubov eigenspectrum develops maxon and roton modes, which are respectively the local maximum and minimum of the spectrum in momentum space. They lead to exotic dynamics associated with the energy scales of the modes. The maxon modes are found to produce stable oscillations which are unseen in dipole-dipole interacting Bose-Einstein condensates. The simulations examined encapsulate the quantum depletion, density-density correlations, and condensate number fluctuation; all of which display two distinct oscillation frequencies, attributed to the development of maxon and roton modes for strongly interacting systems.
In the second half of this thesis, we examine the dynamics of Rydberg-dressed Bose-Einstein condensates, when confined on periodic lattice potentials. In particular, we focus our attention on a Bose-Hubbard chain, as this will allow us to truly utilise the long-range behaviour of the soft-core interaction. This will be discussed in Chapters 4 and 5. The eigenspectra of such systems develop complex anti- and avoided-level crossings. The resulting dynamics is described by mean-field Gross-Pitaevskii equations. This leads to nonlinear and chaotic dynamics in the adiabatic level crossings, and self-trapping behaviour. We show that the system is highly dependent on the initial state, the zero-energy level bias of the traps, and the nonlinear interaction strength. We then expand on the chaotic nature of the system by examining the energetic stability and the Lyapunov exponents. These show that the self-trapping behaviour arises due to strongly positive exponents, as opposed to the conventional idea of the system being energetically unstable. We finally discuss how the chaotic nature of Rydberg-dressing scales with the size of the system. The findings show that such systems are hyperchaotic, with the number of positive Lyapunov exponents scaling linearly with the number of sites.
The results of this thesis may prove to be highly useful in the creation of stable Rydberg-dressed Bose-Einstein condensates, and in the field of ultracold atoms as a whole.
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