Trapped ultracold gases are highly controllable experimental systems with unique quantum properties, making them a brilliant medium for research in solid state physics, quantum computation, and precision measurements. The standard technique for observing a cold atomic sample is time-of-flight absorption imaging. While this provides valuable information regarding the distribution and quantum state of atoms, the process destroys the sample via spontaneous emission and recoil heating, allowing for acquisition of just one data point per experimental run. In this thesis we develop and implement a complementary hyperfine state sensitive, off-resonant, optical dispersive interrogation system that uses frequency modulation spectroscopy to monitor the temporal dynamics of atomic population during coherent dynamical processes in cold atom systems. The applicability of this robust and powerful tool is expanded to simultaneously measure both the F = 2 hyperfine state population of 87Rb and the F = 9/2 hyperfine state population of 40K. This dual-species probe is used to monitor the sympathetic cooling process, whereby 40K is cooled indirectly via collision with a sample of 87Rb, which itself is undergoing forced RF evaporative cooling. The dispersive probing technique is then used to investigate a range of magnetic Feshbach resonances in 87Rb. Feshbach resonances allow the atomic interaction strength to be precisely tuned via an external magnetic field. Rapid and effcient location and identification of four such resonances were demonstrated between the |F=1, mF=1> and |F=2, mF=0> states. Despite the resonance-induced loss features being <~0.1 G wide, only a small number of experimental runs was sufficient to explore a magnetic field range >18 G. The resonances consist of two known s-wave features in the vicinity of 9 G and 18 G, and two previously unobserved p-wave features near 5 G and 10 G. The dispersive detection approach is further used to monitor the atomic loss in real-time, and directly characterise the two-body loss dynamics for each Feshbach resonance. We further characterise the four observed Feshbach resonances by dispersively measuring the 2-body loss rate coefficient, K21, as a function of magnetic field. Finally, the dispersive probe method is paired with an FPGA-based feedback algorithm and used to perform reliable transfer of 87Rb atoms to a target quantum state in the presence of an unknown, random magnetic field. The algorithm processes off-resonant optical measurements of state populations during a microwave-induced adiabatic rapid passage in real time, and terminates the process when a certain threshold in population transfer is achieved.
Trapped ultracold gases are highly controllable experimental systems with unique quantum properties, making them a brilliant medium for research in solid state physics, quantum computation, and precision measurements. The standard technique for observing a cold atomic sample is time-of-flight absorption imaging. While this provides valuable information regarding the distribution and quantum state of atoms, the process destroys the sample via spontaneous emission and recoil heating, allowing for acquisition of just one data point per experimental run. In this thesis we develop and implement a complementary hyperfine state sensitive, off-resonant, optical dispersive interrogation system that uses frequency modulation spectroscopy to monitor the temporal dynamics of atomic population during coherent dynamical processes in cold atom systems. The applicability of this robust and powerful tool is expanded to simultaneously measure both the F = 2 hyperfine state population of 87Rb and the F = 9/2 hyperfine state population of 40K. This dual-species probe is used to monitor the sympathetic cooling process, whereby 40K is cooled indirectly via collision with a sample of 87Rb, which itself is undergoing forced RF evaporative cooling. The dispersive probing technique is then used to investigate a range of magnetic Feshbach resonances in 87Rb. Feshbach resonances allow the atomic interaction strength to be precisely tuned via an external magnetic field. Rapid and effcient location and identification of four such resonances were demonstrated between the |F=1, mF=1> and |F=2, mF=0> states. Despite the resonance-induced loss features being <~0.1 G wide, only a small number of experimental runs was sufficient to explore a magnetic field range >18 G. The resonances consist of two known s-wave features in the vicinity of 9 G and 18 G, and two previously unobserved p-wave features near 5 G and 10 G. The dispersive detection approach is further used to monitor the atomic loss in real-time, and directly characterise the two-body loss dynamics for each Feshbach resonance. We further characterise the four observed Feshbach resonances by dispersively measuring the 2-body loss rate coefficient, K21, as a function of magnetic field. Finally, the dispersive probe method is paired with an FPGA-based feedback algorithm and used to perform reliable transfer of 87Rb atoms to a target quantum state in the presence of an unknown, random magnetic field. The algorithm processes off-resonant optical measurements of state populations during a microwave-induced adiabatic rapid passage in real time, and terminates the process when a certain threshold in population transfer is achieved.
This thesis describes the use of microwave frequency sweeps across the resonance of a magnetic dipole transition to induce adiabatic rapid passage of an ultracold (<1 μK) atomic ensemble between Zeeman sub-levels of the 87Rb ground state. Atoms begin in the |F = 2, mF = 2> quantum state, and efficient preparation of the sample in the |F = 1, mF = 1> state is demonstrated.\nA dispersive probing system is developed using the technique of frequency modulation spectroscopy, which involves a heterodyne detection scheme. Dispersive probing is implemented in parallel to the state preparation, such that the real-time evolution of coherent transfer processes can be monitored.\nThe dispersive probe is used as a tool to quickly and accurately determine the microwave resonance frequency to within a 30 kHz range. Resonant coherent manipulations (Rabi oscillations) between the |F = 1, mF = 1> and |F = 2, mF = 2> states are then demonstrated and probed dispersively.\nA proof of concept application of the dispersive probing system is also presented. It is used to monitor an RF evaporative cooling sequence, providing a precursor measurement on a trapped atomic cloud. This leads to the ability to terminate the experimental sequence in the case of an unfavourable starting point, and thus a reduction of classical number fluctuations in the final atom number.
Magnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time-consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of 87Rb, between the $|\mathrm{F}=1,{\mathrm{m}}_{\mathrm{F}}=1\ensuremath{\rangle}$ and $|\mathrm{F}=2,{\mathrm{m}}_{\mathrm{F}}=0\ensuremath{\rangle}$ states. Despite the loss features being $\ensuremath{\lesssim}0.1$ G wide, we require only 21 experimental runs to explore a magnetic field range >18 G, where $1\phantom{\rule{0.16em}{0ex}}\mathrm{G}={10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. The resonances consist of two known s-wave features in the vicinity of 9 G and 18 G and two previously unreported p-wave features near 5 G and 10 G. We further utilize the dispersive approach to directly characterize the two-body loss dynamics for each Feshbach resonance.
The research described in this thesis is part of an international effort with the aim of studying ultracold quantum degenerate gas samples like Bose-Einstein condensates and Fermi degenerate systems, consisting of atoms confined in magnetic or optical traps. The behavior of such samples is governed by the inter-atomic interactions and the resulting properties of the atom-atom scattering. At the relevant temperatures of 1nK to 10µK a key property is the atom-atom scattering length a. In chapter 2 a theoretical method is presented which enables one to describe the interaction and scattering of (ultra)cold atoms to unprecedented precision. It is also unparalleled in comprehensiveness: it allows the prediction of a large and varied set of experimental data for all isotopes of the same element. The method relies on the extraction from experiments of a few (phase) parameters which completely summarize the behavior of the atoms in the (ultra)cold regime. In chapter 3 the method is applied to the "workhorses" of cold-atom physics: the atomic species 85Rb and 87Rb. We extract the foregoing parameters to a very high precision from several recent high precision experiments, allowing us to predict e.g. the 87Rb spinor condensate to be ferromagnetic: a prediction for which the scattering length has to be calculated with a precision better than 1%. We also predict Feshbach resonances at experimentally accessible magnetic field strengths; resonances searched for and found by the experimental group of Rempe. In close collaboration with his group we "fine-tune" the interaction parameters found previously, by making use of only one of the observed resonances. We then obtain agreement with 42 out of the observed 43 resonance field strengths and are able to identify bound states inducing the Feshbach resonances at these locations. Chapter 4 describes the results of this research. With a thorough understanding of the rubidium interactions, we then switch to lithium which has a fermionic (6Li) and a bosonic (7Li) isotope. Both are being used in cold-atom experiments. In chapter 5 we evaluate the interaction parameters for lithium allowing us to predict magnetic field strengths for which a sample of fermionic 6Li atoms can be regarded as strongly interacting. Furthermore, a three-level method for measuring mean-field shifts, based on radio-frequency techniques, is introduced. For weak interactions we find proportionality of resonance shifts to interaction strengths. In the strongly interacting regime, however, these shifts become very small reflecting the quantum unitarity limit and many-body effects. Most interesting is the fact that in this regime the shifts are small both for large positive a and for large negative a, likely reflecting the universality of the interaction energy. In chapters 6 and 7 the interactions between lithium atoms are reinvestigated, making use of newly available experimental data and with the updated interaction parameters special attention is paid to locating field strengths at which magnetically tunable Feshbach resonances occur in the scattering of lithium atoms. In chapter 6 scattering events in a gas of (fermionic) 6Li atoms are studied. In chapter 7 we show that a consistent description of the 6Li+6Li system can be given. We discuss theoretical uncertainties for the position of the wide 6Li Feshbach resonance and present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6Li-7Li system, and their importance for different types of crossover superfluidity models is discussed. Molecules created by magnetically sweeping over these resonances will have a fermionic character. One magnetic field strength is predicted at which two different fermionic molecules can be created simultaneously.
Within this work, I put forward my experimental studies of the interactions in ultracold atomic mixtures, and their applications in quantum thermodynamics. I detail the key features and the progress made towards building a system which is capable of cooling quantum gases to absolute zero. In order to quantify the heat exchange of a system, knowledge of its temperature is required. Precise temperature measurements of systems with low numbers of ultracold atoms are of great importance in quantum technologies, but they can be quite resource intensive. We first utilised the experimental system to develop an adaptive Bayesian strategy, which processes data from both real and simulated release-recapture thermometry experiments of a single atom of 41K in an optical tweezer at microkelvin temperatures. By adaptively choosing the release-recapture times, this strategy produces more reliable estimates, while converging faster to the real temperature compared to conventional methods. A simpler, non-adaptive a priori method produced competitive results when applied to real experimental data. In addition to this, the underlying Bayesian framework is not specific to our platform and can be adapted for various experiments. Following this, I move onto the studies of a quantum impurity system, which involved immersing the single atom in a bath of ultracold 87Rb atoms. The K atom is trapped within a species-selective dipole potential, allowing for independent manipulation of the bath and impurity. I explore the characterisation and control of the interactions between the two subsystems. This was performed using Feshbach spectroscopy, where I detected several interdimensional confinement induced Feshbach resonances for the KRb interspecies scattering length. In addition to the underlying free-space s-wave interactions, I detected a series of p-wave resonance features. I further determine how the resonances behave as the temperature of the bath and the dimensionality of the interactions change. Finally, I was able to screen the quantum impurity by tuning the wavelength of the species selective tweezer, which adds another tool for control of the system. These results have a range of applications in quantum simulations of quantum impurity models and quantum thermodynamics.
We have developed a robust interrogation system using frequency modulation spectroscopy to measure the quantum state-dependent phase shift incurred on an off-resonant optical probe when transmitted by an atomic medium. Recently, our focus has been on extending this technique for the detection of Feshbach resonances in 87Rb atoms. Feshbach resonance is a mechanism which allows the atomic interaction strength to be precisely tuned via an external magnetic field. To access a Feshbach resonance atoms must be independently prepared in certain internal states, during which we utilize programmable optical tweezers to perform precise spatial micro-manipulation of the ensemble in laser “test-tubes.” We use our dispersive probing system to identify the resonant magnetic field value in a sample with a dense “ball” geometry. An important design consideration for such a probing scheme is the three-dimensional mode-matching at the interface between light and the atomic sample when coupled by the dispersive interaction. We discuss challenges which dealing with this new geometry compared to the previously used prolate geometry, and consider the possibility of dipole-dipole interactions in our sample leading to cooperative light scattering processes.
We investigate quantum-mechanical interactions between ultracold rubidium and cesium in an optical trap at temperatures of a few microkelvin. Our results provide, on the one hand, an experimental key to understand the collisional properties and, on the other hand, a tool to control the interspecies interactions. By performing loss measurements we locate several Feshbach resonances, which provide insight into the energy structure of weakly bound RbCs molecules near the dissociation threshold and allow for the production of such heteronuclear Feshbach molecules. In the future we will transfer these loosely-bound molecules into the absolute internal ground state. The availability of ultracold heteronuclear ground state molecules will open the door to investigate phenomena associated with ultracold polar quantum gases. In our new experimental set-up we are able to trap and cool rubidium and cesium atoms in their lowest internal states. First we load both species into a two-color magneto-optical trap, having full control over the single-species atom number. We extend the technique of degenerate Raman-sideband cooling to a two-color version, which is able to simultaneously cool and polarize both rubidium and cesium. Thereafter we load the atoms into a levitated crossed optical dipole trap. Because of the presence of the gradient magnetic field the trap is highly state selective and consequently provides perfect spin-polarization of the sample. Furthermore, a coincidence of the magnetic-moment-to-mass ratios of the two species allows for simultaneous levitation of both, which assures an almost perfect spatial overlap between the species. We perform Feshbach spectroscopy in two different spin channels of the mixture within a magnetic field ranging from 20 to 300G. In the lowest spin combination of the species we locate 23 interspecies Feshbach resonances, while in a higher spin mixture we find 2 resonances. The high number of resonances found within this range of magnetic field is unusual for alkali mixtures. The presence of many resonances points to scattering properties of the mixture, which include higher-order coupling mechanisms. The obtained data on the Feshbach spectroscopy provide, on one hand, fundamental experimental input to characterize the Rb-Cs scattering properties and, on the other hand, identification of possible starting points for the association of ultracold heteronuclear RbCs molecules. In addition we show preliminary results on spectroscopy of the binding energy of RbCs dimers, based on a modulation of the magnetic field. The recently obtained Bose-Einstein condensate of Cs atoms, which represents a benchmark for the performance of the present apparatus, will be discussed as well as the potential pathways towards a double-degenerate mixture. We follow two main goals, first the production of a double Bose-Einstein condensate and, second, the transfer of shallow bound Feshbach molecules to the absolute internal ground state. The production of heteronuclear ground state molecules allows to enter the world of ultracold polar quantum systems.