We propose a method to probe the local density of states (LDOS) of atomic systems that provides both spatial and energy resolution. The method combines atomic and tunneling techniques to supply a simple, yet quantitative and operational, definition of the LDOS for both interacting and non-interacting systems: It is the rate at which particles can be siphoned from the system of interest by a narrow energy band of non-interacting states contacted locally to the many-body system of interest. Ultracold atoms in optical lattices are a natural platform for implementing this broad concept to visualize the energy and spatial dependence of the atom density in interacting, inhomogeneous lattices. This includes models of strongly correlated condensed matter systems, as well as ones with non-trivial topologies.
We propose a method to probe the local density of states (LDOS) of atomic systems that provides both spatial and energy resolution. The method combines atomic and tunneling techniques to supply a simple, yet quantitative and operational, definition of the LDOS for both interacting and non-interacting systems: It is the rate at which particles can be siphoned from the system of interest by a narrow energy band of non-interacting states contacted locally to the many-body system of interest. Ultracold atoms in optical lattices are a natural platform for implementing this broad concept to visualize the energy and spatial dependence of the atom density in interacting, inhomogeneous lattices. This includes models of strongly correlated condensed matter systems, as well as ones with non-trivial topologies.
We propose a versatile experimental probe for cold atomic gases analogous to the scanning tunneling microscope (STM) in condensed matter. This probe uses the coherent coupling of a single particle to the system. Depending on the measurement sequence, our probe allows us to obtain either the local density and spatial density correlations, with a resolution on the nanometer scale, or the single particle correlation function in real time. We discuss applications of this scheme to the various possible phases for a two dimensional Hubbard system of fermions in an optical lattice.
We propose a scheme to measure the frequency-resolved local particle and hole spectra of any optical lattice-confined system of correlated ultracold atoms that offers single-site addressing and imaging, which is now an experimental reality. Combining perturbation theory and time-dependent density matrix renormalization group simulations, we quantitatively test and validate this approach of lattice-assisted spectroscopy on several one-dimensional example systems, such as the superfluid and Mott insulator, with and without a parabolic trap, and finally on edge states of the bosonic Su-Schrieffer-Heeger model. We highlight extensions of our basic scheme to obtain an even wider variety of interesting and important frequency resolved spectra.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
Ultracold quantum gases in optical lattices provide a rich experimental toolbox for simulating the physics of condensed matter systems. With atoms in the lattice playing the role of electrons or Cooper pairs in real materials, it is possible to experimentally realize condensed matter Hamiltonians in a controlled way. To realize the full potential of such quantum simulations, we leverage a quantum gas microscope which can spatially resolve the atoms in the optical lattice at the single site level and project arbitrary potential landscapes onto the atoms by combining the high resolution optics with static holographic masks or a spatial light modulator. The versatility of this system allows for a wide range of studies. In this thesis, we focus on three experiments that highlight the utility of a tunable platform and demonstrate the richness of physics that comes with interactions.\nIn the first, we observe on-site interparticle interactions introduce a non-linearity into the many-body energy spectrum of a harmonic oscillator. The excitation of a single atom into a higher band induces an energy shift in the excitation energy for the second atom, blockading the orbital excitation. We demonstrate a technique for deterministic number filtering based upon orbital excitation blockade. When applied to a high temperature Mott insulator, this number filtering realizes a form of algorithmic cooling, which can be used for initializing a large quantum register or creating low entropy initial states for many-body simulation.\nIn the second, we study the applicability of statistical physics in an isolated system governed by quantum mechanics. While the descriptive power of these two fields has been confirmed through repeated and varied empirical studies, their underlying axioms of entropy maximization and unitary evolution appear mutually exclusive. With our quantum gas microscope, we have the ability to probe local observables such as the on-site number statistics as well as measure the quantum mechanical purity through interference operations. With these capabilities, we are able to observe the local thermalization of a manifestly quantum mechanically pure many-body system.\nIn the last chapter, we report on the first cold atoms studies of an interacting system under an artificial gauge field. We consider the propagation of a pair of atoms in a 2timesN ladder governed by the Harper-Hofstadter model. The eigenstates of this system include both scattering states, which can exhibit chiral propagation, and bound states. A superexchange energy shift in our initial state leads to imbalanced population in the two chiral scattering sectors, leading to chiral propagation dynamics. This effect is the result of both the presence of interactions and the artificial gauge fields. These two components are essential ingredients for fractional quantum Hall physics. Moreover, the dynamic tunable gauge field we develop and the control afforded by a quantum gas microscope make this platform well-suited for future studies in this regime.
This thesis describes experiments which investigate ultracold atom \nensembles in an optical lattice. Such quantum gases are powerful models for solid state physics. Several novel methods are demonstrated that probe the special properties of strongly correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals spatial correlations in such states, which are hidden when using the usual methods of probing atomic gases. Another spectroscopic technique makes it possible to demonstrate the existence of a shell structure of regions with constant densities. Such coexisting phases separated by sharp boundaries had been theoretically predicted for the Mott insulating state.\nThe tunneling processes in the optical lattice in the strongly correlated regime are probed by preparing the ensemble in an optical superlattice potential. This allows the time-resolved observation of the tunneling dynamics, and makes it possible to directly identify correlated tunneling processes.\n
Abstract The energy spectrum of quantum systems contain a wealth of information about their underlying properties. Spectroscopic techniques, especially those with access to spatially resolved measurements, can be challenging to implement in real-space systems of cold atoms in optical lattices. Here we explore a technique for probing energy spectra in synthetic lattices that is analogous to scanning tunneling microscopy. Using one-dimensional synthetic lattices of coupled atomic momentum states, we explore this spectroscopic technique and observe qualitative agreement between the measured and simulated energy spectra for small two- and three-site lattices as well as a uniform many-site lattice. Finally, through simulations, we show that this technique should allow for the exploration of the topological bands and the fractal energy spectrum of the Hofstadter model as realized in synthetic lattices.