We report on precision measurements of spin-dependent interaction-strengths in the 87 Rb spin-1 and spin-2 hyperfine ground states. Our method is based on the recent observation of coherence in the collisionally driven spin-dynamics of ultracold atom pairs trapped in optical lattices. Analysis of the Rabi-type oscillations between two spin states of an atom pair allows a direct determination of the coupling parameters in the interaction Hamiltonian. We deduce differences in scattering lengths from our data that can directly be compared to theoretical predictions in order to test interatomic potentials. Our measurements agree with the predictions within 20%. The knowledge of these coupling parameters allows one to determine the nature of the magnetic ground state. Our data imply a ferromagnetic ground state for 87 Rb in the f = 1 manifold, in agreement with earlier experiments performed without the optical lattice. For 87 Rb in the f = 2 manifold, the data point towards an antiferromagnetic ground state; however our error bars do not exclude a possible cyclic phase.
We report on precision measurements of spin-dependent interaction-strengths in the 87 Rb spin-1 and spin-2 hyperfine ground states. Our method is based on the recent observation of coherence in the collisionally driven spin-dynamics of ultracold atom pairs trapped in optical lattices. Analysis of the Rabi-type oscillations between two spin states of an atom pair allows a direct determination of the coupling parameters in the interaction Hamiltonian. We deduce differences in scattering lengths from our data that can directly be compared to theoretical predictions in order to test interatomic potentials. Our measurements agree with the predictions within 20%. The knowledge of these coupling parameters allows one to determine the nature of the magnetic ground state. Our data imply a ferromagnetic ground state for 87 Rb in the f = 1 manifold, in agreement with earlier experiments performed without the optical lattice. For 87 Rb in the f = 2 manifold, the data point towards an antiferromagnetic ground state; however our error bars do not exclude a possible cyclic phase.
We report on the observation of coherent, purely collisionally driven spin dynamics of neutral atoms in an optical lattice. For high lattice depths, atom pairs confined to the same lattice site show weakly damped Rabi-type oscillations between two-particle Zeeman states of equal magnetization, induced by spin-changing collisions. Moreover, measurement of the oscillation frequency allows for precise determination of the spin-changing collisional coupling strengths, which are directly related to fundamental scattering lengths describing interatomic collisions at ultracold temperatures.
This thesis reports on the experimental investigation of controlled spin dependent interactions in a sample of ultracold Rubidium atoms trapped in a periodic optical potential. In such a situation, the most basic interaction between only two atoms at one common potential well, forming a micro laboratory for this atom pair, can be investigated. Spin dependent interactions between the atoms can lead to an intriguing time evolution of the system. In this work, we present two examples of such spin interaction induced dynamics. First, we have been able to observe and control a coherent spin changing interaction. Second, we have \nachieved to examine and manipulate an interaction\ninduced time evolution of the relative phase of a spin 1/2-system, both in the case of particle pairs and in the more general case of N interacting particles. The first part of this thesis elucidates the spin-changing interaction mechanism underlying many fascinating effects resulting from interacting spins at ultracold temperatures. This process changes the spin states of two colliding particles, while preserving total magnetization. If initial and final states have almost equal energy, this process is resonant and leads to large amplitude\noscillations between different spin states. The measured coupling parameters of such a process allow to precisely infer atomic scattering length differences, that e.g. determine the nature of the magnetic ground state of the hyperfine states in Rubidium.\nMoreover, a method to tune the spin oscillations at will based on the AC-Zeeman effect has been implemented. This allowed us to use resonant spin changing \ncollisions as a quantitative and non-destructive particle pair probe in the optical lattice. This led to a series of experiments shedding light on the Bosonic superfluid to Mott insulator transition.\nIn a second series of experiments we have been able to coherently manipulate the interaction induced time evolution of the relative phase in an ensemble of spin 1/2-systems. For two particles, interactions can lead to an entanglement oscillation of the particle pair. For the general case of N interacting particles, the ideal time evolution leads to the creation of spin squeezed states and even Schrödinger cat states. In the experiment we have been able to control the underlying\ninteractions by a Feshbach resonance. For particle pairs we could directly observe the entanglement oscillations. For the many particle case we have been able to observe and reverse the interaction induced dispersion of the relative phase.\nThe presented results demonstrate how correlated spin states can be engineered through \ncontrol of atomic interactions. Moreover, the results point towards the possibility to simulate quantum\nmagnetism phenomena with ultracold atoms in optical traps, and to realize and analyze many novel quantum spin states which have not been experimentally realized so far.
Precision measurement of spin-dependent inter-hyperfine scattering lengths in 87Rb
We present precision measurements of the f=1 to f=2 inter-hyperfine scattering lengths in a single-domain 87Rb spinor Bose-Einstein condensate. The inter-hyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a non-interacting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a co-magnetometer strategy to cancel laboratory magnetic noise. We find the scattering length ratios a32(12)/a20(1)=−1.27(15) and a12(12)/a20(1)=−1.31(13), limited by atom number fluctuations. Using better control of atom number, we estimate precisions of ∼0.3% should be possible with this technique.
We study the dynamics of spin-1 atoms in a periodic optical-lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth. The time evolution of the nonequilibrium state shows collective collapse-and-revival oscillations of matter-wave coherence as well as oscillations in the spin populations. We show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many-body ground state. Furthermore, we show that the strengths of the spin-dependent and spin-independent atom-atom interactions can be deduced from the observations. The Hamiltonian that describes the physics of the final deep lattice not only contains two-body interactions but also effective multibody interactions, which arise due to virtual excitations to higher bands. We derive these effective spin-dependent three-body interaction parameters for spin-1 atoms and describe how spin mixing is affected. Spinor atoms are unique in the sense that multibody interactions are directly evident in the in situ number densities in addition to the momentum distributions. We treat both antiferromagnetic (e.g., 23Na) and ferromagnetic (e.g., 87Rb and 41K) condensates.
Quantum mechanical superexchange interactions form the basis of quantum magnetism in strongly correlated electronic media. We report on the direct measurement of superexchange interactions with ultracold atoms in optical lattices. After preparing a spin-mixture of ultracold atoms in an antiferromagnetically ordered state, we measured coherent superexchange-mediated spin dynamics with coupling energies from 5 hertz up to 1 kilohertz. By dynamically modifying the potential bias between neighboring lattice sites, the magnitude and sign of the superexchange interaction can be controlled, thus allowing the system to be switched between antiferromagnetic and ferromagnetic spin interactions. We compare our findings to predictions of a two-site Bose-Hubbard model and find very good agreement, but are also able to identify corrections that can be explained by the inclusion of direct nearest-neighbor interactions.
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.