A simple experimental method is demonstrated to spatially and non-destructively image spin states in a BEC of sodium-23. The birefringeant properties of the spin -1 and spin 0 states of the F=1 ground are used in combination with phase-contrast imaging to create a linear combination of two images taken in quick succession. We show that in the high detuning/low density limit the created linear combination is proportional to the density of either spin -1 or spin 0 states. The technique is used to estimate the spin drag coefficient of a spin -1 and spin 0 domains moving through in FORT under the influence of a spin dependent force.
A simple experimental method is demonstrated to spatially and non-destructively image spin states in a BEC of sodium-23. The birefringeant properties of the spin -1 and spin 0 states of the F=1 ground are used in combination with phase-contrast imaging to create a linear combination of two images taken in quick succession. We show that in the high detuning/low density limit the created linear combination is proportional to the density of either spin -1 or spin 0 states. The technique is used to estimate the spin drag coefficient of a spin -1 and spin 0 domains moving through in FORT under the influence of a spin dependent force.
An imaging system is presented that is capable of far-detuned non-destructive imaging of a Bose-Einstein condensate with the signal proportional to the second spatial derivative of the density. Whilst demonstrated with application to Rb85, the technique generalizes to other atomic species and is shown to be capable of a signal-to-noise of ∼25 at 1 GHz detuning with 100 in-trap images showing no observable heating or atom loss. The technique is also applied to the observation of individual trajectories of stochastic dynamics inaccessible to single shot imaging. Coupled with a fast optical phase locked loop, the system is capable of dynamically switching to resonant absorption imaging during the experiment.
We introduce a novel, non-invasive imaging technique based on spin-dependent off-axis holography (SOAH) for spin-1 Bose-Einstein condensates (BECs). Utilizing a dual reference beam strategy, this method records two orthogonal circular polarization components of a single probe beam. The circular birefringence of spin-polarized atoms induces differing complex phase shifts in the polarization components of the light, which are reconstructed from the interference patterns captured on camera. Our approach enables spin- and density-resolved imaging of both phase and amplitude information \emph{in-situ} on a sub-millisecond time scale with minimal disturbance to the condensate. We explore the technique's efficacy under various background static fields, demonstrating its sensitivity to the quantization axis of the atoms and confirming its effectiveness.
In this thesis, we develop, validate and apply a non-destructive, spin-sensitive probing method for ultracold gases of sodium. By exploiting the polarization dependence of the atom-light interaction, the method combines optical hardware with computational reconstruction to access spin-resolved density and magnetization distributions from a single, minimally destructive exposure. The thesis is structured in three parts; firstly, we describe the experimental platform for making, probing and manipulating sodium spinor Bose–Einstein condensates, including laser cooling, optical and magnetic trapping, and radio-frequency techniques for coherent spin preparation. In the second part, we develop the core measurement technique of spin-dependent off-axis holography is developed, and evaluate its robustness to technical noise and the magnetic field variations. The reconstruction and analysis pipeline is presented in detail, with special emphasis on the background noise suppression using an inpainting technique based on principal component analysis. In the final part, the method is applied to investigate dynamics in spin-1 ultracold atomic sodium. To that end, we introduce the theory of three-level spin systems and propose magnetization-preparation and precise Zeeman-sublevel readout schemes, which are experimentally verified. These tools are then used to investigate spin diffusion and spin mixing dynamics, and the formation and evolution of spin domains. This work establishes spin-dependent off-axis holography as a powerful tool for probing spinor quantum gases. The techniques developed here enable efficient and minimally destructive imaging of spin dynamics, and provide new opportunities for studying non-equilibrium spin phenomena and magnetism in ultracold atomic systems.
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.
The three experiments described in this thesis investigate fundamental properties of ultracold atoms. Using laser cooling and evaporative cooling, a dilute gas of sodium atoms is cooled to ~100 nK. Under these circumstances a Bose-Einstein condensate (BEC) forms, where millions of atoms collapse into the lowest energy state of the system and share a macroscopic wavefunction. The experiments are done in an ultrahigh vacuum and the atoms are manipulated remotely using laser beams, magnetic fields, and RF-fields. Using ultracold atoms allows unprecedented control over the internal and external degrees of freedom of the system, making it very suitable for precision measurements. Ultracold atoms also serve as a model system for more complicated or remote fields such as solid-state physics and cosmology. In the first experiment the refractive index of an ultracold bosonic gas is studied. The atomic clouds are analyzed for temperature and number of particles using nearly non-destructive phase-contrast imaging. After each pulse of probe light a small fraction of the atoms is lost, while the cloud is simultaneously slightly heated. This makes it possible to study the scattering rate as a function of temperature using only a single sample. It is observed that the scattering rate increases below the critical temperature for BEC by more than a factor of 3 compared to the classical value. This enhancement is in good agreement with the predictions by theoretical work that takes two-body correlation and the Lorentz-Lorenz correction into account. The method is also used to perform calorimetry on the Bose gas and directly measure the heat capacity of the BEC. The second chapter deals with magnetism in ultracold gases. When cooling an ultracold gas containing different spin components below the critical temperature for BEC, stable magnetic domains form. The appearance of these domains and the dynamics of the domain walls are studied. The spin mixture is prepared by performing an RF-sweep on ground state atoms in the presence of a magnetic field. Spin dynamics are induced by applying magnetic gradients. Spin drag, which is the transport coefficient responsible for damping spin currents, was measured in a two-component system. Furthermore a new method for spin resolved phase contrast imaging is presented, which is used to study time evolution in situ non-destructively. The last experiment focuses on spontaneous symmetry breaking. When passing a continuous phase transition, spontaneous symmetry breaking causes the development of domains with an independently chosen order parameter. The domains are separated by boundary defects. In this experiment the spontaneous creation of solitons was observed, which are boundary defects in the phase of the condensate, as well as magnetic domain walls, which are the boundary defects in the magnetization. Through the Kibble-Zurek mechanism it is possible to determine the critical exponents that characterize the phase transition. The critical exponents are predicted to be universal, i.e. do not depend on the microphysics of the system, so the results from our ultracold atoms lab can help answer universal questions for example from cosmology and from the early universe.
Spinor Bose Einstein condensates have widely been sought after as perfect emulators of condensed matter phenomena, providing widely tunable and highly controlled systems. Utilizing a novel spin sensitive phase contrast imaging technique, the vector magnetization is measured in-situ with high spatial and temporal resolution and applied to a number of experiments. Using optically trapped F = 1 87Rb spinor condensates, the equilibrium phase diagram of a spin-1 Bose gas is quantitatively explored by observing the evolution of unmagnetized spin textures and their thermal equilibrium properties. Spin domain coarsening and a strong dependence of the spin configuration on the quadratic Zeeman shift is observed, supporting the predicted mean-field equilibrium phase diagram for small values of the quadratic shift. Additionally, spinor Bose gases are demonstrated to be an effective tool in calibrating and characterizing experimental imaging systems. Sinusoidal test patterns of varying pitch are created and used to extract the modulation transfer function and quantify optical aberrations which are of immense importance in systems which claim to have high spatial resolution. Lastly we realize an optical kagome geometry in a two-dimensional optical superlattice with a scalar Bose gases. The optical superlattice can be tuned between various geometries, including kagome, one-dimensional stripe, and decorated triangular lattice. Using atom optics we characterize the various geometries and demonstrate the versatility of this optical superlattice. The kagome geometry presents a new experimental arena for studies of geometrically frustrated systems.