School of Physics - Theses
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ItemDipolar Bose-Einstein Condensates in Time-Dependent Magnetic Fields( 2021)The last 20 years have heralded the synthesis of Bose-Einstein condensates (BECs) of elements with large magnetic dipole moments, such as chromium, erbium and dysprosium, polarised by a magnetic field. These dipolar BECs experience both the dipole-dipole interaction (DDI) and a short-ranged, effectively isotropic interaction, rendering them a robust platform for studying the interplay of such interactions in many-body quantum systems. Thus, it is useful to be able to independently control the two interaction strengths. In this context, it has long been known that the temporal average of the DDI arising from a rapidly rotating magnetic field is simply that of a static field with an interaction strength dependent on the angle between the field and its rotation vector. However, while numerous theoretical studies assumed that the DDI may effectively be tuned by rapidly rotating the dipole polarisation, this assumption had not been rigourously examined when the author’s candidature commenced. In this thesis, we investigate harmonically trapped dipolar BECs in time-dependent magnetic fields via an effective mean-field theory, the dipolar Gross-Pitaevskii equation (GPE). This involves semi-analytically identifying the stationary states in the interaction–dominated Thomas-Fermi (TF) limit and then solving for the corresponding collective modes of the BEC to identify when it is dynamically unstable against the exponential growth of a mode. Initially, we study a nondipolar BEC in a tilted rotating harmonic trap and uncover a dynamical instability above a certain critical rotation frequency that is lower than the transverse trap frequency. Complementary numerical solutions of the GPE demonstrate that this instability results in vortex nucleation and, ultimately, a vortex lattice embedded in a tilted background density. This informs our analysis of a statically harmonically trapped dipolar BEC in a rotating magnetic field. Regardless of the field tilting, we find that at sufficiently high rotation frequencies, the stationary states closely mimic those of the corresponding time-averaged DDI. However, a critical rotation frequency is also uncovered, for any nonzero tilt angle, above which the stationary states are dynamically unstable. In the limit where the field is orthogonal to its rotation axis, these predictions are then compared with numerical simulations of the dipolar GPE. If the rotation frequency exceeds the transverse trap frequency, we find that the dynamical instability induces the turbulent decay of the stationary state, which may explain the unexpectedly short BEC lifetime observed in recent experimental investigations of DDI time-averaging. Conversely, rotation below the transverse trap frequency causes vortex nucleation – as yet unobserved in dipolar BECs – and ultimately a vortex lattice. Finally, a variational formalism for the TF dynamics of dipolar BECs is developed. This allows us to demonstrate the excellent agreement of the dynamics predicted by the time-averaged DDI with those influenced by a rapidly rotating field. Furthermore, we find that large-angle oscillations of the dipole polarisation induces the nonlinear coupling of quadratic collective modes, a phenomenon of long-standing interest. Together, these results suggest that directly rotating the dipole polarisation represents a simple, yet powerful, method to control and induce novel phenomena in dipolar BECs.