Recent developments in quantum gas microscopy open up the possibility of real-time observation of quantum many-body systems. To understand the dynamics of atoms under such circumstances, we formulate the dynamics under a real-time spatially resolved measurement and show that, in an appropriate limit of weak spatial resolution and strong atom-light coupling, the measurement indistinguishability of particles results in complete suppression of relative positional decoherence. As a consequence, quantum correlation in the multiparticle dynamics persists under a minimally destructive observation. We numerically demonstrate this for ultracold atoms in an optical lattice. Our theoretical framework can be applied to the feedback control of quantum many-body systems which may be realized in subwavelength-spacing lattice systems.
Recent developments in quantum gas microscopy open up the possibility of real-time observation of quantum many-body systems. To understand the dynamics of atoms under such circumstances, we formulate the dynamics under a real-time spatially resolved measurement and show that, in an appropriate limit of weak spatial resolution and strong atom-light coupling, the measurement indistinguishability of particles results in complete suppression of relative positional decoherence. As a consequence, quantum correlation in the multiparticle dynamics persists under a minimally destructive observation. We numerically demonstrate this for ultracold atoms in an optical lattice. Our theoretical framework can be applied to the feedback control of quantum many-body systems which may be realized in subwavelength-spacing lattice systems.
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].
We study the atom-light interaction in the fully quantum regime, with the focus on off-resonant light scattering into a cavity from ultracold atoms trapped in an optical lattice. Because of the global coupling between the atoms and the light modes, observing the photons leaking from the cavity allows the quantum nondemolition (QND) measurement of quantum correlations of the atomic ensemble, distinguishing between different quantum states. Moreover, the detection of the photons perturbs the quantum state of the atoms via the so-called measurement backaction. This effect constitutes an unusual additional dynamical source in a many-body strongly correlated system and it is able to efficiently compete with its intrinsic short-range dynamics. This competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period, without the need of single site addressing. We demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, breakup and protection of strongly interacting fermion pairs. We show that measurement backaction can be exploited for realizing quantum states with spatial modulations of the density and magnetization, thus overcoming usual requirement for a strong interatomic interactions. We propose detection schemes for implementing antiferromagnetic states and density waves and we demonstrate that such long-range correlations cannot be realized with local addressing. Finally, we describe how to stabilize these emerging phases with the aid of quantum feedback. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems and it is easily extendable to other systems promising for quantum technologies.
Atom-based quantum simulators offer a unique platform that enables the imaging of each particle in a many-body system. Until now, however, this capability has been limited to quantum systems in discretized space such as optical lattices and tweezers, where spatial degrees of freedom are quantized. Here, we introduce a novel method for imaging atomic quantum many-body systems in the continuum, allowing for in situ resolution of every particle. We demonstrate the capabilities of our approach on a two-dimensional atomic Fermi gas. We probe the density correlation functions, resolving their full spatial functional form, and reveal the shape of the Fermi hole arising from Pauli exclusion as a function of temperature. Our method opens the door to probing strongly correlated quantum gases in the continuum with unprecedented spatial resolution, providing in situ access to spatially resolved correlation functions of arbitrarily high order across the entire system.
Trapping ultracold atoms in optical lattices enabled numerous breakthroughs uniting several disciplines. Coupling these systems to quantized light leads to a plethora of new phenomena and has opened up a new field of study. Here we introduce an unusual additional source of competition in a many-body strongly correlated system: We prove that quantum backaction of global measurement is able to efficiently compete with intrinsic short-range dynamics of an atomic system. The competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period without the need of single site addressing. In coherence with a general physical concept, where new competitions typically lead to new phenomena, we demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, long-range entanglement, and correlated tunneling, as well as selective suppression and enhancement of dynamical processes beyond the projective limit of the quantum Zeno effect. We demonstrate both the breakup and protection of strongly interacting fermion pairs by measurement. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems.
Experiments with ultracold atoms in optical lattices provide outstanding opportunities to realize exotic quantum states due to a high degree of tunability and control. In this thesis, I present experiments that extend this control from global parameters to the level of individual particles. \n\nUsing a quantum gas microscope for 87Rb, we have developed a single-site addressing scheme based on digital amplitude holograms. The system self-corrects for aberrations in the imaging setup and creates arbitrary beam profiles. We are thus able to shape optical potentials on the scale of single lattice sites and control the dynamics of individual atoms. \n\nWe study the role of quantum statistics and interactions in the Bose-Hubbard model on the fundamental level of two particles. Bosonic quantum statistics are apparent in the Hong-Ou-Mandel interference of massive particles, which we observe in tailored double-well potentials. These underlying statistics, in combination with tunable repulsive interactions, dominate the dynamics in single- and two-particle quantum walks. We observe highly coherent position-space Bloch oscillations, bosonic bunching in Hanbury Brown-Twiss interference and the fermionization of strongly interacting bosons.\n\nMany-body states of indistinguishable quantum particles are characterized by large-scale spatial entanglement, which is difficult to detect in itinerant systems. Here, we extend the concept of Hong-Ou-Mandel interference from individual particles to many-body states to directly quantify entanglement entropy. We perform collective measurements on two copies of a quantum state and detect entanglement entropy through many-body interference. We measure the second order Rényi entropy in small Bose-Hubbard systems and detect the buildup of spatial entanglement across the superfluid-insulator transition.\n\nOur experiments open new opportunities for the single-particle-resolved preparation and characterization of many-body quantum states.
Light enables manipulating many-body states of matter, and atoms trapped in optical lattices is a prominent example. However, quantum properties of light are completely neglected in all quantum gas experiments. Extending methods of quantum optics to many-body physics will enable phenomena unobtainable in classical optical setups. We show how using the quantum optical feedback creates strong correlations in bosonic and fermionic systems. It balances two competing processes, originating from different fields: quantum backaction of weak optical measurement and many-body dynamics, resulting in stabilized density waves, antiferromagnetic and NOON states. Our approach is extendable to other systems promising for quantum technologies.