The subtle interplay between quantum statistics and interactions is at the origin of many intriguing quantum phenomena connected to superfluidity and quantum magnetism. The controlled setting of ultracold quantum gases is well suited to study such quantum correlated systems. Current efforts are directed towards the identification of their magnetic properties, as well as the creation and detection of exotic quantum phases. In this context, it has been proposed to map the spin-polarization of the atoms to the state of a single-mode light beam. Here we introduce a quantum-limited interferometer realizing such an atom-light interface with high spatial resolution. We measure the probability distribution of the local spin-polarization in a trapped Fermi gas showing a reduction of spin-fluctuations by up to 4.6(3) dB below shot-noise in weakly interacting Fermi gases and by 9.4(8) dB for strong interactions. We deduce the magnetic susceptibility as a function of temperature and discuss our measurements in terms of an entanglement witness.
The subtle interplay between quantum statistics and interactions is at the origin of many intriguing quantum phenomena connected to superfluidity and quantum magnetism. The controlled setting of ultracold quantum gases is well suited to study such quantum correlated systems. Current efforts are directed towards the identification of their magnetic properties, as well as the creation and detection of exotic quantum phases. In this context, it has been proposed to map the spin-polarization of the atoms to the state of a single-mode light beam. Here we introduce a quantum-limited interferometer realizing such an atom-light interface with high spatial resolution. We measure the probability distribution of the local spin-polarization in a trapped Fermi gas showing a reduction of spin-fluctuations by up to 4.6(3) dB below shot-noise in weakly interacting Fermi gases and by 9.4(8) dB for strong interactions. We deduce the magnetic susceptibility as a function of temperature and discuss our measurements in terms of an entanglement witness.
We show how spin–spin correlations, detected in a non-destructive way via spatially resolved quantum polarization spectroscopy, strongly characterize various phases realized in trapped ultracold fermionic atoms. Polarization degrees of freedom of the light couple to spatially resolved components of the atomic spin. In this way, quantum fluctuations of matter are faithfully mapped onto those of light. In particular, we demonstrate that quantum spin polarization spectroscopy provides a direct method to detect the Fulde–Ferrell–Larkin–Ovchinnikov phase realized in a one-dimensional imbalanced Fermi system.
Summary form only given. Ultra-cold atomic gases trapped in optical lattices offer an unprecedented playground for studying the quantum phases of many-body systems. In particular, quantum states of ultra-cold lattice gases with spin degrees of freedom may be used to simulate quantum magnetism and to investigate physics relevant for our understanding of high-Tcsuperconductivity. While enormous progress has been made towards engineering such systems, achieving the regime of high-Tcsuperconductivity remains experimentally extremely challenging because of the low temperatures required [1].Here, we describe a new technique for the preparation of quantum spin-correlations in a lattice gas of ultracold atoms using atom-light interaction of the kind routinely employed in quantum spin polarization spectroscopy (QPS) [2], a promising technique for detecting quantum phases in lattice gases via quantum non-demolition (QND) measurement. Motivated by recent experimental work demonstrating the generation of spin-squeezing and entanglement in atomic ensembles via QND measurement [3], and by the recent extension of these ideas to unpolarized ensembles [5], we propose an alternative approach to preparing quantum spin-correlations, demonstrating that a simple modification of the experimental scheme of Ref. [4] allows for the on-demand preparation of spatial spin-correlations in a quantum lattice gas. Our method is based on entropic cooling via QND measurement and feedback, and allows the creation and detection of quantum spin-correlations, as well as a certain degree of multipartite entanglement, which we verify by deriving a novel generalization of the entanglement witness decribed in Ref. [5]. The proposed technique works with an unpolarized ensemble of non-interacting spins such as may be obtained by loading ultracold atoms into a deep optical lattice. We illustrate the procedure with examples drawn from the bilinear-biquadratic Hamiltonian, which can be modeled by a 1D chain of spin-1 atoms, showing that it is possible to prepare exponentially- and algebraically-decaying correlations, as well as spatial correlation signatures of more exotic quantum phases such as quantum criticalities.
We describe a technique for the preparation of quantum spin correlations in a lattice gas of ultracold atoms using an atom-light interaction of the kind routinely employed in quantum spin polarization spectroscopy. Our method is based on entropic cooling via quantum nondemolition measurement and feedback, and allows the creation and detection of quantum spin correlations, as well as a certain degree of multipartite entanglement which we verify using a generalization of the entanglement witness described previously M. Cramer et al., Phys. Rev. Lett. 106, 020401 (2011). We illustrate the procedure with examples drawn from the bilinear-biquadratic Hamiltonian, which can be modeled by a one-dimensional chain of spin-1 atoms.
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].
At the beginning of the 20th century measurement precision was related exclusively to the capabilities of the experimenter and the apparatus. Any imprecision was attributed to imperfect devices for the measurement. Later on, when the quantumness of objects like photons, electrons, or atoms, was recognized, it became clear that the measurement and the object to be measured could no longer be separated. Both follow the laws of quantum physics which impose limits on the accuracy of any measurement. In the last three decades, a lot of research has been dedicated to find strategies to overcome these limitations. This new field of quantum metrology is where this work is placed.
This thesis describes the generation of interparticle entanglement in form of a squeezed spin state in a cloud of cold 87Rb atoms by performing nondestructive spin measurements. Towards this goal, we have implemented a shot-noise limited polarization probing and detection system, atom counting by means of absorption imaging, spin state preparation via optical pumping and nondestructive spin state detection. The quantum noise limited spin readout with polarized light is characterized in two complementary ways in terms of sensitivity and all possible quantum and classical noise sources are measured.
To address the rich opportunities provided in the multilevel structure of 87Rb with dispersive probing, we have developed and implemented a frequency offsetlock which allows a large tuning range of several GHz for the dispersive probing.
Working with a magnetically sensitive atomic system triggered the development of a magnetic field imaging technique. This applies the elongated atomic sample and internal atomic states as a way of measuring magnetic fields over several millimeters with micrometer resolution and sensitivities down to a few tens of pT/ Hz.
We developed a new method for tomographic measurements of the atomic density matrix. Based on our ability of shot noise limited detection of polarization rotations we can in principle, characterize the whole atomic spin state.
First, measurements are shown and possible improvements are discussed.
An in depth characterization of the light-atom interaction between polarized pulses of light and collective atomic states are the basis for measurements at the quantum level. On one side, we apply classical measurements of spin polarized atoms to measure the strength of the lightatom interaction. On the other side, we use quantum measurements of unpolarized atomic states to characterize all noise sources both technical and quantum.
One of the major results of this thesis is the realization of quantum nondemolition measurements in a largespin system. We realized limitations to the performance of the QND measurement implied by higher order light shifts in multilevel atoms, which are often neglected for these kind of systems. We develop a technique which suppresses the detrimental effects of higher order light shifts and recovers an ideal QND measurement.
The thesis culminates in the demonstration of spin squeezing in the magnetically sensitive ground state of 87Rb. We achieve a quantum noise reduction by 3 dB, where metrological sensitivity is improved by 2 dB beyond the standard quantum limit of a coherent spin state with the same spin polarization.
We address the question how spatial and temporal inhomogeneities both in light and atoms influence the preparation of nonclassical states. An existing covariance matrix approach is extended and we apply it to study effects of detector time resolution, spatial inhomogeneities and atomic motion.
We present a review of properties of ultracold atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. In the strong interacting limit and at very low temperatures, fermions form, together with bosons or bosonic holes, composite fermions. Composite fermions behave as a spinless interacting Fermi gas, and in the presence of local disorder they interact via random couplings and feel effective random local potential. This opens a wide variety of possibilities of realizing various kinds of ultracold quantum disordered systems. In this paper we review these possibilities, discuss the accessible quantum disordered phases, and methods for their detection. The discussed quantum phases include Fermi glasses, quantum spin glasses, ``dirty'' superfluids, disordered metallic phases, and phases involving quantum percolation.