Molecules are created from a Bose-Einstein condensate of atomic 87Rb using a Feshbach resonance. A Stern-Gerlach field is applied, in order to spatially separate the molecules from the remaining atoms. For detection, the molecules are converted back into atoms, again using the Feshbach resonance. The measured position of the molecules yields their magnetic moment. This quantity strongly depends on the magnetic field, thus revealing an avoided crossing of two bound states at a field value slightly below the Feshbach resonance. This avoided crossing is exploited to trap the molecules in one dimension.
Abstract Recent advances in the precise control of ultracold atomic systems have led to the realisation of Bose–Einstein condensates (BECs) and degenerate Fermi gases. An important challenge is to extend this level of control to more complicated molecular systems. One route for producing ultracold molecules is to form them from the atoms in a BEC. For example, a two-photon stimulated Raman transition in a 87Rb BEC has been used to produce 87Rb2 molecules in a single rotational-vibrational state1, and ultracold molecules have also been formed2 through photoassociation of a sodium BEC. Although the coherence properties of such systems have not hitherto been probed, the prospect of creating a superposition of atomic and molecular condensates has initiated much theoretical work3, 4, 5, 6, 7. Here we make use of a time-varying magnetic field near a Feshbach resonance8, 9, 10, 11, 12 to produce coherent coupling between atoms and molecules in a 85Rb BEC. A mixture of atomic and molecular states is created and probed by sudden changes in the magnetic field, which lead to oscillations in the number of atoms that remain in the condensate. The oscillation frequency, measured over a large range of magnetic fields, is in excellent agreement with the theoretical molecular binding energy, indicating that we have created a quantum superposition of atoms and diatomic molecules—two chemically different species.
The final stage in the creation of a Bose-Einstein condensate (BEC) is trapping and compressing in a strong magnetic trap. When the spin of an atom changes, it is lost from this magnetic trap. To be able to do experiments with varying atom spin, one can use an optical dipole trap, which traps atoms independent of their spin. This thesis presents a far red-detuned optical dipole trap, which is characterized by trapping BEC's. Furthermore, an approach to rapidly scan this trap is presented, creating a 'quasi-2D' potential. With this potential we attempt to create a horizontal sheet of condensed atoms, where the depth of the sheet of atoms is smaller than the range of the spin dynamics. This would enable a unique visualization of the spin dynamics using spin-dependent imaging.
This thesis presents a novel magnetic resonance imaging (MRI) technique for spinor Bose-Einstein condensates (BEC) with the paramagnetic Faraday effect. This quantum-photon interface couples the spin of the BEC to the polarisation of an off-resonant laser, which in a magnetic field gradient allows a 1D density profile of the BEC to be reconstructed. As opposed to conventional imaging techniques that are destructive or diffraction limited, this technique is minimally destructive to the BEC and not diffraction limited. Multishot in situ imaging of a single condensate is therefore possible, paving the way for time-resolved studies and 2D/3D reconstructions. A theoretical model for Faraday imaging is developed using the tensor polarisability formalism for the atom-light interaction, and the signal-to-noise ratio is derived. Resolution limits induced by Stern-Gerlach separation are considered, encouraging rapid measurements with strong magnetic field gradients. Analysing the trapping potential reveals that the `magic-zero' wavelength 790nm produces no dipole force and enables a tightly focused probe laser to be used without perturbing the trap. Polarisation-maintaining fibers were seen to impart large fluctuations depending on the incident polarisation, which were minimised. The broad diode laser emission background is seen to reduce the lifetime of the BEC, which was corrected with an interference filter. Short-time Fourier transforms are used to process the photodetected signal, showing the evolution of the polarisation rotation frequency and amplitude. Frequency-modulation is observed at the power line frequency, corresponding to magnetic field fluctuations induced by nearby equipment. Birefringence of optical elements results in elliptical polarisation of the probe and an effective magnetic field, which is cancelled using a quarter-waveplate. The quadratic Zeeman effect causes rapid amplitude modulation, and is eliminated by applying a microwave dressing field. Radiative spin echo is achieved in a magnetic field gradient, proving that dephasing is coherent, and that multishot imaging possible. Magnetic resonance imaging (MRI) is performed on a partially-evaporated atom cloud, distinguishing the thermal and condensed fractions. A split dipole trap is used to create two spatially separated BECs, which are individually resolved during MRI. The resolution is only limited by the strength of the applied magnetic field gradient, and is not subject to the diffraction limit. Custom coils will enable MRI of condensates at the sub-micron scale.
More recently, laser cooling of the diatomic radical magnesium monofluoride (
24Mg19F) is being experimentally preformed [Appl. Phys. Express 8, 092701 (2015) and Opt. Express 22, 28645 (2014)] and was also studied theoretically [Phys. Rev. A 91, 042511 (2015)]. However, some important problems still remain unsolved, so, in our paper, we perform further theoretical study for the feasibility of laser cooling and trapping the
24Mg19F molecule. At first, the highly diagonal Franck-Condon factors of the main transitions are verified by the closed-form approximation, Morse approximation, and Rydberg-Klein-Rees inversion methods, respectively. Afterwards, we investigate the lower $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}$ hyperfine manifolds using a quantum effective Hamiltonian approach and obtain the zero-field hyperfine spectrum with an accuracy of less than 30 $\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{K}$ compared with the experimental results, and then find out that one cooling beam and one or two repumping beams with their first-order sidebands are enough to implement an efficient laser slowing and cooling of
24Mg19F. Meanwhile, we also calculate the accurate hyperfine structure magnetic
g factors of the rotational state ($X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+},N=1$) and briefly discuss the influence of the external fields on the hyperfine structure of
24Mg19F as well as its possibility of preparing three-dimensional magneto-optical trapping. Finally we give an explanation for the difference between the Stark and Zeeman effects from the perspective of parity and time reversal symmetry. Our study shows that, besides appropriate excitation wavelengths, the short lifetime for the first excited state $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$, and lighter mass, the
24Mg19F radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.
We describe an approach to quantum control of the quasiparticle excitations in a trapped Bose-Einstein condensate based on adiabatic and diabatic changes in the trap anisotropy. We describe our approach in the context of the Landau-Zener transition at the avoided crossings in the quasiparticle excitation spectrum. We find also that there can be population oscillation between different modes at the specific aspect ratios of the trapping potential at which the mode energies are almost degenerate. These effects may have implications in the expansion of an excited condensate as well as the dynamics of a moving condensate in an atomic waveguide with a varying width.