Precise engineering of the Bose-Einstein condensate wavefunction using magnetic resonance control

Abstract

To engineer the wavefunction of a Bose–Einstein condensate is to exert control over both the density and phase of the Bose–Einstein condensate order parameter. Having the ability to engineer the condensate order parameter down to the smallest length scale relevant to condensate dynamics—the healing length scale—would enable the study of new combinations of topological defects and may pave the way to using Bose–Einstein condensates as versatile, precise quantum simulators. In this thesis, we present a new wavefunction engineering technique which reaches the sub-optical healing length scale. Influenced by magnetic resonance imaging, we name this technique magnetic resonance control. This technique uses time-varying coupling between internal spin states of a spinor Bose–Einstein condensate within a magnetic field gradient to address spatial regions of the condensate, enabling control over both the phase and the density of the condensate order parameter down to the healing length scale. Techniques already exist to engineer condensate wavefunctions, but not with such a fine degree of control. These techniques primarily rely on either the intensity variation of a laser beam, which limits the resolution to the diffraction limit (larger than the typically sub-optical healing length scale), or the adiabatic inversion of a magnetic trapping potential, which can not be easily changed to produce a variety of structures in the condensate wavefunction. To develop our magnetic resonance control technique, we simulate a spinor condensate in one dimension with time-dependent coupling between spin states and time-dependent external magnetic field gradients using the Gross–Pitaevskii equation. We show that magnetic resonance control can engineer a single black soliton using experimentally feasible parameters. A black soliton is an ideal target state to select for this demonstration because engineering such a state requires control over both the phase and density of the condensate with healing-length resolution. We demonstrate that magnetic resonance control can be extended to engineer more complicated target states by simulating the creation of multiple solitons in a condensate, with control over the initial positions and trajectories of the solitons. When magnetic resonance control is applied to Bose–Einstein condensates in the laboratory, it will be necessary to have an imaging system capable of resolving the fine structures created. As an alternative to high-cost, custom-manufactured lenses, and in-vacuum optical systems, I have designed and bench-tested an objective lens with a high numerical aperture (0.36) and a long working distance (35 mm) consisting of standard catalogue lenses. Using 780 nm light, suitable for imaging rubidium condensates, this objective can achieve a resolution of 1.3 μm across a diffraction-limited field of view of 360 μm through a 5 mm thick glass window of a science cell. By changing the spacing between the lens elements, this objective lens can compensate for the aberrations produced by a glass window up to 15 mm thick, and by changing the aperture size the objective becomes suitable for diffraction-limited monochromatic imaging on the D2 line of all the alkalis. Before performing proof-of-principle magnetic resonance control experiments on real Bose–Einstein condensates, we needed to construct an experimental apparatus capable of producing spinor Bose–Einstein condensates. In this thesis I summarise my main contributions to this group endeavour, including: constructing the ultra-high vacuum system; supervising the bakeout of our vacuum system; designing and aligning the optical systems to produce laser beams of different, tunable frequencies to trap, cool, and image rubidium gas; trapping a cloud of rubidium atoms in a magneto-optical trap; constructing laser beam shutters, photodetectors, and photodetector signal filters; and designing and constructing our side imaging and top imaging systems. Using our spinor Bose–Einstein condensate apparatus, I performed the first proof-of-principle magnetic resonance control experiments. With a pair of condensates side-by-side, separated by 200 μm, we can use magnetic resonance control to invert the spin of one condensate only, while leaving the other condensate unaffected. We anticipate magnetic resonance control being used in the laboratory to engineer the first black soliton in a Bose–Einstein condensate. Looking beyond solitons, magnetic resonance control could have applications to the field of magnon spintronics, and extending the technique to higher dimensions could enable the study of exotic topological defects such as spin knots in a quantum fluid.