This dissertation discusses the experimental study of strong fermionic interactions in an optical lattice. Ultracold samples of $^{40}$K are prepared in an intricate experimental platform using the combination of various optical and evaporative cooling techniques. The atoms are adiabatically loaded into an optical lattice to realize isolated pair states. Various tools for the coherent manipulation of spin and orbital degrees of freedom of the atoms in the lattice are developed. The inter-particle interactions between pairs are tuned using magnetic Feshbach resonances. Spectroscopic measurements of resonantly enhanced and controllable s-wave and p-wave interaction energies are reported. The measurements extend to the unitary limit of interactions characterized by diverging scattering lengths and universal observables. These measurements show excellent agreements to an exact solution for two harmonically confined atoms interacting via a pseudopotential and numerical solutions using an \textit{ab initio} interaction potential. For p-wave interactions, exquisite experimental control is demonstrated by measuring Rabi oscillations between non-interacting and strongly interacting atomic pairs, which are used to accurately measure highly sensitive properties such as the two-body wavefunction overlap. With the full suppression of three-body loss processes, the lifetime of p-wave interacting pairs is investigated. The experiments demonstrate that losses of p-wave interacting pairs are limited by the intrinsic lifetime of the free-space molecular dimer, resulting in the observation of lifetimes that are fifty times larger than previous measurements in $^{40}$K. The observation, control, and comprehensive understanding of strong fermionic interactions demonstrated in this thesis illuminate a path towards the assembly of new many-body states of matter.
This dissertation discusses the experimental study of strong fermionic interactions in an optical lattice. Ultracold samples of 40K are prepared in an intricate experimental platform using the combination of various optical and evaporative cooling techniques. The atoms are adiabatically loaded into an optical lattice to realize isolated pair states. Various tools for the coherent manipulation of spin and orbital degrees of freedom of the atoms in the lattice are developed. The inter-particle interactions between pairs are tuned using magnetic Feshbach resonances. Spectroscopic measurements of resonantly enhanced and controllable s-wave and p-wave interaction energies are reported. The measurements extend to the unitary limit of interactions characterized by diverging scattering lengths and universal observables. These measurements show excellent agreements to an exact solution for two harmonically confined atoms interacting via a pseudopotential and numerical solutions using an \textit{ab initio} interaction potential. For p-wave interactions, exquisite experimental control is demonstrated by measuring Rabi oscillations between non-interacting and strongly interacting atomic pairs, which are used to accurately measure highly sensitive properties such as the two-body wavefunction overlap. With the full suppression of three-body loss processes, the lifetime of p-wave interacting pairs is investigated. The experiments demonstrate that losses of p-wave interacting pairs are limited by the intrinsic lifetime of the free-space molecular dimer, resulting in the observation of lifetimes that are fifty times larger than previous measurements in 40K. The observation, control, and comprehensive understanding of strong fermionic interactions demonstrated in this thesis illuminate a path towards the assembly of new many-body states of matter.
In this thesis, we observe and characterize both s-wave and p-wave interactions of fermionic 40K atoms in deep optical lattices. The p-wave interactions especially draw our attention, as they have a well understood connection to topological properties. The discovery of p-wave interactions in ultracold-atom systems is promising, as the systems are tunable and controllable, but the experimental efforts have been severely limited by the short lifetime of atoms due to the three-body loss mechanism. The deep lattice potential applied in our study ensures near-zero tunneling, such that we are able to directly measure the on-site interaction energies of isolated pairs of atoms, and this isolation especially helps to suppress three-body losses for p-wave interacting pairs.For s-wave interactions between two lowest spin states in the ground hyperfine manifold, the binding energies of the s-wave molecular dimers have been studied pre- viously. However, in our study, we also measure the repulsive interaction energies via the radio-frequency (RF) spectroscopy. The obtained energy eigenspectrum for the atom pairs can be well explained by the theory based on two atoms in a harmonic trap interacting via a pseudopotential. Another experimental technique to measure the s-wave interaction energies is developed as well using Raman excitation. By cou- pling both spin and motional degrees of freedom, we obtain an energy spectrum that agrees well to the one using RF spectroscopy. To study p-wave interactions between two identical atoms in a spin triplet state, we prepare an initial non-interacting triplet state with a motional excitation via Raman excitation, and then directly measure the p-wave interaction energies by RF coupling the initial state to the final interacting one. The resulting universal energy spectra obtained at various conditions are well characterized by an exact solution for two harmonically confined atoms interacting via a p-wave pseudopotential with anharmonic corrections. We also measure the Rabi oscillations of the p-wave interacting pairs, and take the first steps towards the coher- ent control of the oscillations. Finally, we set up an experiment to test the lifetime of the p-wave interacting pairs, and find that losses are limited by the intrinsic lifetime of the molecular dimer. The lifetimes are measured to be much longer than observed for free-space dimers, and are predicted well by calculating the short-range fraction of the wavefunctions. Another theory based on an ab initio interaction potential is applied as well, which gives similar results to the pseudopotential theory, and again proves their validity.
This dissertation summarizes my recent work regarding systems of strongly interacting fermionic atoms in optical lattices. This work addresses the combination of two experimental techniques that have been the subject of much recent research in ultracold atom physics. One is the use of optical lattices, which provide a means to realize diverse interaction configurations within a clean, controllable system. The other is the use of magnetically tunable Feshbach resonances to control the strength of the interatomic interaction. Together, these techniques offer the possibility of an experimental realization of many important model Hamiltonians of condensed matter physics, and may also lead to the discovery of new physics. Recent study of this system has shown that strong interactions near Feshbach resonance will lead to the population of multiple lattice bands, and that collisions between atoms on neighboring sites cannot be neglected. These effects lead to a complicated Hamiltonian, but one which can be simplified to an effective single-band model equivalent to the generalized Hubbard model (GHM), which is an extension of the Hubbard model that includes correlated hopping terms. My main results concern the study of this model. The strong correlations between the particles make it difficult to definitively determine the many body physics of the GHM. As a first approach to understanding the GHM in optical lattices, I focus mainly on cases where the problem is greatly simplified by allowing interactions among only small groups of lattice sites. This restriction can be implemented in experiments using an optical superlattice potential. Our results include a proposed scheme (based on double-well superlattices) to empirically verify that the GHM describes this system and to directly measure the various parameters of this model. Other results include exact solutions on four-site square plaquettes, which demonstrate that d-wave excitations can occur in the low-energy states. By using a superlattice to give an array of weakly coupled plaquettes, one can thus produce a d-wave superfluid state. This is of relevance to the study of high-Tc superconductors, although I note certain key differences between the sort of d-wave superfluid described here and that of the superconductors.
Abstract Quantum gas systems provide a unique experimental platform to study the crossover between Bose–Einstein condensed molecular pairs and Bardeen–Cooper–Schrieffer superfluidity. The few studies in optical lattices have so far focused on the case when only the lowest Bloch band is populated, thus excluding orbital degrees of freedom. Here we demonstrate the preparation of ultracold Feshbach molecules of fermionic atoms in the second Bloch band of an optical square lattice. We cover a wide range of interaction strengths, including the regime of unitarity in the middle of the crossover. Binding energies and band relaxation dynamics are measured by means of a method resembling mass spectrometry. We find that the longest lifetimes arise for strongly interacting Feshbach molecules at the onset of unitarity. In the case of strong confinement in a deep lattice potential, we observe bound dimers also for negative values of the scattering length, extending previous findings for molecules in the lowest band.
This thesis presents quantum simulation of strongly-correlated systems beyond standard Hubbard models, using ultracold fermionic potassium atoms in both static and periodically-driven optical superlattices. For this study, we utilize a three-dimensional optical lattice setup, controlling particle interactions via magnetic Feshbach resonances and tunneling between lattice sites through optical lattice intensity. High-resolution absorption imaging combined with radio-frequency spectroscopy distinguishes between singly and doubly occupied sites. To enhance our systems capabilities beyond the standard Hubbard model, we extend the apparatus with an in-plane optical superlattice, creating a bi-chromatic structure by superposition of two optical lattices with commensurate lattice spacings. Using a phase locked loop with an environmental feed forward, we create an excellent phase stability of the superlattice exceeding 3 mrad. This precision allows us to explore both static and periodically-driven one-dimensional tight-binding models with strong interactions. We characterize the static superlattice through radio-frequency spectroscopy and Rabi oscillations, and validate the experimental data against theoretical calculations. In a tilted superlattice configuration, we successfully prepare and detect repulsively bound atom pairs, representing a highly excited eigenstate of the system. Furthermore, we demonstrate control over pair tunneling dynamics in a double-well potential using Floquet engineering, employing a low-noise periodic modulation of the optical superlattice tilt. Using an adiabatic band mapping technique, we directly observe the tunneling dynamics in the driven superlattice. We realize dynamic localization in quarter-filled wells and density-assisted tunneling up to the third harmonic order in half-filled wells. We observe a crossover from density-assited tunneling to dominant pair tunneling by tuning the effective interactions. Remarkably, the pair tunneling is not only enhanced relative to the suppressed single-particle tunneling but also exceeds the superexchange rate of a static double-well by more than a factor of two. This opens the possibility to study many-body systems with dominant pair tunneling, that extend beyond the standard Hubbard model.
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.
In the past fifteen years ultracold atoms confined to optical lattices, which are artificial crystals of light, have proven to be powerful tools in the study of strongly correlated many-body systems widely known from a condensed matter context. The detailed knowledge, high tunability and control of microscopic parameters has enabled the creation and control of highly non-trivial quantum systems for which a direct comparison of model calculations to experimental measurements is now possible. In order to gain precise information on the properties of ultracold gases in optical lattices, many powerful methods have been developed. In particular spectroscopic methods have enabled to probe different characteristic excitations. However, many fascinating properties of strongly interacting quantum many-body systems are not yet fully characterized. Therefore, this thesis explores further possibilities of lattice modulation spectroscopy which is a time-periodic modulation of the optical lattice amplitude. We theoretically investigate the response of different (mostly one-dimensional) cold atom systems to a lattice modulation by means of the time-dependent density matrix renormalization group method and different analytical approximations. In addition to the normal lattice modulation, we consider a superlattice modulation scheme where the lattice amplitude is modulated in a dimerized fashion, coupling to a certain class of excitations in the system. The lattice modulation spectroscopy is a versatile probe which we use to study different situations relevant for experimental applications. We show that a detection of signatures of the exotic bond order wave phase is feasible in a system of interacting fermions on a one-dimensional optical lattice with staggered energy offset. Moreover, we demonstrate that a temperature measurement of fermions confined to an optical lattice is possible as well as a determination of the interaction strength of bosonic atoms confined to a one-dimensional optical lattice. In addition, various excitations in all these systems are investigated in detail.