edoc: No conditions. Results ordered -Date Deposited. 2024-09-07T12:23:42ZEPrintshttps://edoc.unibas.ch/images/uni-logo.jpghttps://edoc.unibas.ch/2019-04-04T17:02:16Z2020-10-28T08:15:58Zhttps://edoc.unibas.ch/id/eprint/68431This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/684312019-04-04T17:02:16ZQuantum metrology with nonclassical states of atomic ensemblesQuantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well-developed techniques for trapping, controlling, and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold, and ultracold gases of neutral atoms. Moreover, atoms can strongly couple to external forces and fields, which makes them ideal for ultraprecise sensing and time keeping. All these factors call for generating nonclassical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology. Luca PezzeAugusto SmerziMarkus K. OberthalerRoman SchmiedPhilipp Treutlein2017-12-28T10:21:47Z2017-12-28T10:21:47Zhttps://edoc.unibas.ch/id/eprint/58167This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/581672017-12-28T10:21:47ZOptimal entanglement witnesses in a split spin-squeezed Bose-Einstein condensateHow do we detect quantum correlations in bipartite scenarios using a split many-body system and collective measurements on each party? We address this question by deriving entanglement witnesses using either only first-order or both first-and second-order moments of local collective spin components. In both cases, we derive optimal witnesses for spatially split spin-squeezed states in the presence of local white noise. We then compare the two optimal witnesses with respect to their resistance to various noise sources operating either at the preparation or at the detection level. We finally evaluate the statistics required to estimate the value of these witnesses when measuring a split spin-squeezed Bose-Einstein condensate. Our results can be seen as a step toward Bell tests with many-body systems. Enky OudotJean-Daniel BancalRoman SchmiedPhilipp TreutleinNicolas Sangouard2017-12-28T10:18:44Z2017-12-28T10:18:44Zhttps://edoc.unibas.ch/id/eprint/58166This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/581662017-12-28T10:18:44ZBell Correlations in a Many-Body System with Finite StatisticsA recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this Letter, we address here the question of the statistics required to witness Bell correlated states, i.e., states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one-and two-body correlators only. Based on these inequalities, we then build up improved witnesses able to detect Bell correlated states in many-body systems using two collective measurements only. These witnesses can potentially detect Bell correlations in states with an arbitrarily low amount of spin squeezing. We then establish an upper bound on the statistics needed to convincingly conclude that a measured state is Bell correlated. Sebastian WagnerRoman SchmiedMatteo FadelPhilipp TreutleinNicolas SangouardJean-Daniel Bancal2017-02-20T15:31:51Z2017-02-20T15:31:51Zhttps://edoc.unibas.ch/id/eprint/53924This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/539242017-02-20T15:31:51ZTighter quantum uncertainty relations following from a general probabilistic boundUncertainty relations (URs) such as the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from estimation theory, a Cramér-Rao-like bound. The Heisenberg-Robertson UR is then obtained by using the Born rule and the Schrödinger equation. This allows a clear separation of the probabilistic nature of quantum mechanics from the Hilbert space structure and the dynamical law. It also simplifies the interpretation of the bound. In addition, the Heisenberg-Robertson UR is tightened for mixed states by replacing one variance by the quantum Fisher information. Thermal states of Hamiltonians with evenly gapped energy levels are shown to saturate the tighter bound for natural choices of the operators. This example is further extended to Gaussian states of a harmonic oscillator. For many-qubit systems, we illustrate the interplay between entanglement and the structure of the operators that saturate the UR with spin-squeezed states and Dicke states. Florian FröwisRoman SchmiedNicolas Gisin2017-02-20T13:37:49Z2017-02-20T13:37:49Zhttps://edoc.unibas.ch/id/eprint/53921This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/539212017-02-20T13:37:49ZArrays of individually controlled ions suitable for two-dimensional quantum simulationsA precisely controlled quantum system may reveal a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analogue quantum simulator that makes relevant observables, interactions and states of a quantum model accessible could permit insight into complex dynamics. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here, we operate two-dimensional arrays of three trapped ions in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 μm. In our approach, which is scalable to arbitrary two-dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as a tuning of couplings between ions within experimental sequences. Our work paves the way towards a quantum simulator of two-dimensional systems designed at will. Manuel MielenzHenning KalisMatthias WittemerFrederick HakelbergUlrich WarringRoman SchmiedMatthew BlainPeter MaunzDavid L. MoehringDietrich LeibfriedTobias Schaetz2017-02-15T13:50:58Z2017-02-15T13:50:58Zhttps://edoc.unibas.ch/id/eprint/52752This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/527522017-02-15T13:50:58ZQuantum state tomography of a single qubit: comparison of methodsThe tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical density matrix of a single qubit: (scaled) direct inversion, maximum likelihood estimation (MLE), minimum Fisher information distance and Bayesian mean estimation (BME). We discuss the different prior densities in the space of density matrices, on which both MLE and BME depend, as well as ways of including experimental errors and of estimating tomography errors. As a measure of the accuracy of these methods, we average the trace distance between a given density matrix and the tomographic density matrices it can give rise to through experimental measurements. We find that the BME provides the most accurate estimate of the density matrix, and suggest using either the pure-state prior, if the system is known to be in a rather pure state, or the Bures prior if any state is possible. The MLE is found to be slightly less accurate. We comment on the extrapolation of these results to larger systems. Roman Schmied2017-02-15T13:39:30Z2018-11-01T16:21:58Zhttps://edoc.unibas.ch/id/eprint/52751This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/527512017-02-15T13:39:30ZBell correlations in a Bose-Einstein condensateCharacterizing many-body systems through the quantum correlations between their constituent particles is a major goal of quantum physics. Although entanglement is routinely observed in many systems, we report here the detection of stronger correlations—Bell correlations—between the spins of about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation witness from a many-particle Bell inequality involving only one- and two-body correlation functions. Our measurement on a spin-squeezed state exceeds the threshold for Bell correlations by 3.8 standard deviations. Our work shows that the strongest possible nonclassical correlations are experimentally accessible in many-body systems and that they can be revealed by collective measurements. Roman SchmiedJean-Daniel BancalBaptiste AllardMatteo FadelValerio ScaraniPhilipp TreutleinNicolas Sangouard2017-02-15T13:32:05Z2017-02-15T13:32:05Zhttps://edoc.unibas.ch/id/eprint/52750This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/527502017-02-15T13:32:05ZSideband Rabi spectroscopy of finite-temperature trapped Bose gasesWe use Rabi spectroscopy to explore the low-energy excitation spectrum of a finite-temperature Bose gas of rubidium atoms across the phase transition to a Bose-Einstein condensate (BEC). To record this spectrum, we coherently drive the atomic population between two spin states. A small relative displacement of the spin-specific trapping potentials enables sideband transitions between different motional states. The intrinsic nonlinearity of the motional spectrum, mainly originating from two-body interactions, makes it possible to resolve and address individual excitation lines. Together with sensitive atom counting, this constitutes a feasible technique to count single excited atoms of a BEC and to determine the temperature of nearly pure condensates. As an example, we show that for a nearly pure BEC of N=800 atoms the first excited state has a population of less than five atoms, corresponding to an upper bound on the temperature of 30nK. Baptiste AllardMatteo FadelRoman SchmiedPhilipp Treutlein2014-01-31T09:51:06Z2018-04-05T12:20:03Zhttps://edoc.unibas.ch/id/eprint/30902This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/309022014-01-31T09:51:06ZQuantum Metrology with a Scanning Probe Atom InterferometerWe use a small atomic Bose-Einstein condensate as an interferometric scanning probe to map out a microwave field near a chip surface with a few micrometers resolution. Using entanglement between the atoms we overcome the standard quantum limit of interferometry by 4 dB and maintain enhanced performance for interrogation times up to 20 ms. This demonstrates the usefulness of quantum metrology with entangled states when the particle number is limited due to the small probe size. Extending atom interferometry to micrometer spatial resolution enables new applications in electromagnetic field sensing, surface science, and the search for fundamental short-range interactions. Caspar F. OckeloenRoman SchmiedMax F. RiedelPhilipp Treutlein2012-10-11T15:24:57Z2018-04-05T15:13:09Zhttps://edoc.unibas.ch/id/eprint/21775This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/217752012-10-11T15:24:57ZTomographic reconstruction of the Wigner function on the Bloch sphereWe present a filtered backprojection algorithm for reconstructing the Wigner function of a system of large angular momentum j from Stern-Gerlach-type measurements. Our method is advantageous over the full determination of the density matrix in that it is insensitive to experimental fluctuations in j, and allows for a natural elimination of high-frequency noise in the Wigner function by taking into account the experimental uncertainties in the determination of j, its projection m, and the quantization axis orientation. No data binning and no arbitrary smoothing parameters are necessary in this reconstruction. Using recently published data [Riedel et al., Nature 464:1170 (2010)] we reconstruct the Wigner function of a spin-squeezed state of a Bose-Einstein condensate of about 1250 atoms, demonstrating that measurements along quantization axes lying in a single plane are sufficient for performing this tomographic reconstruction. Our method does not guarantee positivity of the reconstructed density matrix in the presence of experimental noise, which is a general limitation of backprojection algorithms. Roman SchmiedPhilipp Treutlein