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 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.
An important route toward the preparation of cold molecules is magnetically tunable Feshbach resonances. Here we investigate an inelastic Feshbach resonance between a single pair of 87Rb and 39K atoms confined in an optical tweezer, with both atoms prepared in the |F=1,mF=−1⟩ state. By developing an in-situ imaging scheme for 39K, we directly measure magnetic-field-dependent collisional loss without separating the atoms after the interaction. For weak confinement, the resonance position measured in our experiment differs from the bulk-gas experiments. In contrast, we observe a significant shift of the resonance toward higher magnetic fields as the tweezer trap depth increases. Coupled-channel calculations accounting for finite temperature effects fail to explain the magnitude of this shift, suggesting that it originates from differential optical responses of the open-channel atom pair and the weakly bound molecular state under strong confinement. Our results indicate that optical tweezer light can significantly modify Feshbach resonance properties, opening a pathway toward optical control of atom–atom interactions and weakly bound molecular states in dual-species tweezer platforms.
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 reports on the first observation of optical tuning of interactions in an ultracold atomic gas. To control the elastic interactions, we use optically induced scattering resonances. They are realized by coupling pairs of atoms to a bound molecular state with the help of laser light. In comparison to the well-known magnetic Feshbach resonances, these optical Feshbach resonances allow a very fast switching of interactions in a spatially resolved way. This is because laser light can be switched on and off much faster than magnetic fields and because the light intensity can be spatially structured. Our experiments are performed with a Bose-Einstein condensate (BEC) of Rb atoms, which we produce in our new BEC setup. This apparatus has been constructed in the framework of this thesis and offers excellent optical access to the ultracold atom cloud. To investigate the tunability of atomic interactions with single-frequency laser light, we optically couple pairs of free atoms to an electronically excited molecular state. The coupling is achieved with a laser that is tuned close to the respective free-bound photoassociation transition. By changing the laser detuning we are able to adjust the atomic scattering length to any value between 10 a0 and 190 a0, where a0 denotes the Bohr radius. The atomic scattering length is a single quantity that fully describes ultracold elastic interactions. Since laser induced atom losses restrict the duration of our experiments, Bragg spectroscopy is employed as a fast method to measure the scattering length. We also demonstrate that optical Feshbach resonances can be realized with a two-color Raman coupling scheme. To implement this scheme, a second laser is added that couples the excited molecular state to a weakly bound molecular level in a ground state potential. Tuning the second laser results in a modification of the atomic scattering length similar to the one observed with a single laser. In addition, this scheme allows to control the width of the resonance via the detuning of the first laser. For the one-color and two-color coupling schemes, we investigate how the elastic scattering properties depend on the different available parameters, i.e. the laser detunings and intensities. Our experimental findings can successfully be described with an available theoretical model, which treats ultracold collisions in the presence of laser light. Optical Feshbach resonances have the possibility of becoming a valuable tool for fast switching of interactions. This is of special interest in quantum computation schemes with neutral atoms, where interactions between different atomic qubits need to be controlled.
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.
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.
We theoretically investigate the control of a magnetic Feshbach resonance using a bound-to-bound molecular transition driven by spatially modulated laser light. Due to the spatially periodic coupling between the ground and excited molecular states, there exists a band structure of bound states, which can uniquely be characterized by some extra bumps in radio-frequency spectroscopy. With the increasing of coupling strength, the series of bound states will cross zero energy and directly result in a number of scattering resonances, whose position and width can be conveniently tuned by the coupling strength of the laser light and the applied magnetic field (i.e., the detuning of the ground molecular state). In the presence of the modulated laser light, universal two-body bound states near zero-energy threshold still exist. However, compared with the case without modulation, the regime for such universal states is usually small. A unified formula, which embodies the influence of the modulated coupling on the resonance width is given. The spatially modulated coupling also implies a local spatially varying interaction between atoms. Our work proposes a practical way of optically controlling interatomic interactions with high spatial resolution and negligible atomic loss.