McCormack, Gary
(2022)
Meanfield Dynamics of RydbergDressed Bosonic Atoms in FreeSpace 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 BoseEinstein condensation, where lasercooled 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 atomatom interactions.
In this thesis we examine the dynamical properties of Rydbergdressed BoseEinstein condensates under different forms of trapping potentials. The study of the outofequilibrium dynamics of BoseEinstein condensates has lead to a plethora of novel and interesting features. We aim to expand on this already lucrative field by inducing dynamics via Rydbergdressing, which creates an effective softcore 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 threedimensional 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 dipoledipole interacting BoseEinstein condensates. The simulations examined encapsulate the quantum depletion, densitydensity 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 Rydbergdressed BoseEinstein condensates, when confined on periodic lattice potentials. In particular, we focus our attention on a BoseHubbard chain, as this will allow us to truly utilise the longrange behaviour of the softcore interaction. This will be discussed in Chapters 4 and 5. The eigenspectra of such systems develop complex anti and avoidedlevel crossings. The resulting dynamics is described by meanfield GrossPitaevskii equations. This leads to nonlinear and chaotic dynamics in the adiabatic level crossings, and selftrapping behaviour. We show that the system is highly dependent on the initial state, the zeroenergy 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 selftrapping 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 Rydbergdressing 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 Rydbergdressed BoseEinstein condensates, and in the field of ultracold atoms as a whole.
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