Prof. Dr. Markus Oberthaler

Phone: +49 6221 54 5170

markus.oberthaler@kip.uni-heidelberg.de

Yannick Deller

Phone: +49 6221 54 5178

yannick.deller@kip.uni-heidelberg.de

David Feiz Bakhsh Bazargani

Phone: +49 6221 54 5178

david.feiz@kip.uni-heidelberg.de

apl. Prof. Dr. Thomas Gasenzer

Phone: +49 6221 54 5173

thomas.gasenzer@kip.uni-heidelberg.de

Priv.-Doz. Dr. Martin Gärttner

Phone: +49 6221 54 9852

martin.gaerttner@kip.uni-heidelberg.de

Maurus Hans

Phone: +49 6221 54 5177

mhans@kip.uni-heidelberg.de

Luise Heiland

Phone: +49 6221 54 5178

luise.heiland@kip.uni-heidelberg.de

Joris Hoffmann

Phone: +49 6221 54 5188

joris.hoffmann@kip.uni-heidelberg.de

Elinor Kath

Phone: +49 6221 54 5177

elinor.kath@kip.uni-heidelberg.de

Stefan Lannig

Phone: +49 6221 54 5178

stefan.lannig@kip.uni-heidelberg.de

Nikolas Felix Laurenz Leonhardt

Phone: +49 6221 54 5177

nikolas_felix_laurenz.leonhardt@kip.uni-heidelberg.de

Nikolas Liebster

Phone: +49 6221 54 5177

nikolas.liebster@kip.uni-heidelberg.de

Timon Alexander Schmutz

Phone: +49 6221 54 5178

timon_alexander.schmutz@kip.uni-heidelberg.de

Marius Sparn

Phone: +49 6221 54 5177

marius.sparn@kip.uni-heidelberg.de

**You can find the lastest results of the project in:**

### Condensation and thermalization of an easy-plane ferromagnet in a spinor Bose gas

Paper, HD-KIP 22-54, 2022, Nature Physics PDF-FileBose–Einstein condensates are an ideal platform to explore dynamical phenomena emerging in the many-body limit, such as the build-up of long-range coherence, superfluidity or spontaneous symmetry breaking. Here we study the thermalization dynamics of an easy-plane ferromagnet employing a homogeneous one-dimensional spinor Bose gas. We demonstrate the dynamic emergence of effective long-range coherence for the spin field and verify spin-superfluidity by experimentally testing Landau’s criterion. We reveal the structure of one massive and two massless emerging modes—a consequence of explicit and spontaneous symmetry breaking, respectively. Our experiments allow us to observe the thermalization of an easy-plane ferromagnetic Bose gas. The relevant momentum-resolved observables are in agreement with a thermal prediction obtained from an underlying microscopic model within the Bogoliubov approximation. Our methods and results are a step towards a quantitative understanding of condensation dynamics in large magnetic spin systems and the study of the role of entanglement and topological excitations for their thermalization.

### Spiking neuromorphic chip learns entangled quantum states

Paper, HD-KIP 22-05, 2022, SciPost Phys. (12) PDF-FileThe approximation of quantum states with artificial neural networks has gained a lot of attention during the last years. Meanwhile, analog neuromorphic chips, inspired by structural and dynamical properties of the biological brain, show a high energy efficiency in running artificial neural-network architectures for the profit of generative applications. This encourages employing such hardware systems as platforms for simulations of quantum systems. Here we report on the realization of a prototype using the latest spike-based BrainScaleS hardware allowing us to represent few-qubit maximally entangled quantum states with high fidelities. Bell correlations of pure and mixed two-qubit states are well captured by the analog hardware, demonstrating an important building block for simulating quantum systems with spiking neuromorphic chips.

### Detecting Entanglement Structure in Continuous Many-Body Quantum Systems

Paper, HD-KIP 22-04, 2022, Phys. Rev. Lett. 128, 020402 (128) PDF-FileA prerequisite for the comprehensive understanding of many-body quantum systems is a characterization in terms of their entanglement structure. The experimental detection of entanglement in spatially extended many-body systems describable by quantum fields still presents a major challenge. We develop a general scheme for certifying entanglement and demonstrate it by revealing entanglement between distinct subsystems of a spinor Bose-Einstein condensate. Our scheme builds on the spatially resolved simultaneous detection of the quantum field in two conjugate observables which allows the experimental confirmation of quantum correlations between local as well as nonlocal partitions of the system. The detection of squeezing in Bogoliubov modes in a multimode setting illustrates its potential to boost the capabilities of quantum simulations to study entanglement in spatially extended many-body systems.

### Finding self-similar behavior in quantum many-body dynamics via persistent homology

Paper, HD-KIP 22-01, 2021, SciPost Phys. 11, 060 (2021) PDF-FileInspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a classical-statistical simulation of a two-dimensional Bose gas far from equilibrium. We discover a continuous spectrum of dynamical scaling exponents, which provides a refined classification of nonequilibrium self-similar phenomena. A possible explanation of the underlying processes is provided in terms of mixing strong wave turbulence and anomalous vortex kinetics components in point clouds. We find that the persistent homology scaling exponents are inherently linked to the geometry of the system, as the derivation of a packing relation reveals. The approach opens new ways of analyzing quantum many-body dynamics in terms of robust topological structures beyond standard field theoretic techniques.

### Analog cosmological reheating in an ultracold Bose gas

Paper, HD-KIP 21-56, 2021, Phys. Rev. A (104) PDF-FileCosmological reheating describes the transition of the postinflationary universe to a hot and thermal state. In order to shed light on the underlying dynamics of this process, we propose to quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. In our setup, the excitations on top of an atomic Bose-Einstein condensate play the role of the particles produced by the decaying inflaton field after inflation. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the nonrelativistic limit by a time dependence of the atomic interactions, which can be tuned experimentally via Feshbach resonances. As we illustrate by means of classical-statistical simulations for the case of two spatial dimensions, the dynamics of the atomic system exhibits the characteristic stages of far-from-equilibrium reheating, including the amplification of fluctuations via parametric instabilities and the subsequent turbulent transport of energy towards higher momenta. The transport is governed by a nonthermal fixed point showing universal self-similar time evolution as well as a transient regime of prescaling with time-dependent scaling exponents. While the classical-statistical simulations can capture only the earlier stages of the dynamics for weak couplings, the proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.

### Universell in der Zeit

Paper, HD-KIP 21-25, 2021, Physik Journal, Februar PDF-Filehttps://www.pro-physik.de/physik-journal/februar-2021

### High signal to noise absorption imaging of alkali atoms at moderate magnetic fields

Paper, HD-KIP 21-10, 2021, AIP Review of Scientific Instruments 92 PDF-FileWe present an improved scheme for absorption imaging of alkali atoms at moderate magnetic fields, where the excited state is well in the Paschen–Back regime, but the ground state hyperfine manifold is not. It utilizes four atomic levels to obtain an approximately closed optical cycle. With the resulting absorption of the corresponding two laser frequencies, we extract the atomic column density of a

^{39}K Bose–Einstein condensate. The scheme can be readily applied to all other alkali-like species.### Collisions of Three-Component Vector Solitons in Bose-Einstein Condensates

Paper, HD-KIP 20-89, 2020, Phys. Rev. Lett. (125) PDF-FileUltracold gases provide an unprecedented level of control for the investigation of soliton dynamics and collisions. We present a scheme for deterministically preparing pairs of three-component solitons in a Bose-Einstein condensate. Our method is based on local spin rotations which simultaneously imprint suitable phase and density distributions. This enables us to observe striking collisional properties of the vector degree of freedom which naturally arises for the coherent nature of the emerging multicomponent solitons. We find that the solitonic properties in the quasi-one-dimensional system are quantitatively described by the integrable repulsive three-component Manakov model.

### Spiking neuromorphic chip learns entangled quantum states

Paper, HD-KIP 20-59, 2020, arXiv PDF-FileNeuromorphic systems are designed to emulate certain structural and dynamical properties of biological neuronal networks, with the aim of inheriting the brain's functional performance and energy efficiency in artificial-intelligence applications [1,2]. Among the platforms existing today, the spike-based BrainScaleS system stands out by realizing fast analog dynamics which can boost computationally expensive tasks [3]. Here we use the latest BrainScaleS generation [4] for the algorithm-free simulation of quantum systems, thereby opening up an entirely new application space for these devices. This requires an appropriate spike-based representation of quantum states and an associated training method for imprinting a desired target state onto the network. We employ a representation of quantum states using probability distributions [5,6], enabling the use of a Bayesian sampling framework for spiking neurons [7]. For training, we developed a Hebbian learning scheme that explicitly exploits the inherent speed of the substrate, which enables us to realize a variety of network topologies. We encoded maximally entangled states of up to four qubits and observed fidelities that imply genuine N-partite entanglement. In particular, the encoding of entangled pure and mixed two-qubit states reaches a quality that allows the observation of Bell correlations, thus demonstrating that non-classical features of quantum systems can be captured by spiking neural dynamics. Our work establishes an intriguing connection between quantum systems and classical spiking networks, and demonstrates the feasibility of simulating quantum systems with neuromorphic hardware.

### Wie Quantensimulatoren neue Antworten geben können

Paper, HD-KIP 20-56, 2020, Physik Journal, Mai PDF-Filehttps://www.pro-physik.de/physik-journal/februar-2021

### Experimental extraction of the quantum effective action for a non-equilibrium many-body system

Paper, HD-KIP 20-53, 2020, Nat. Phys. PDF-File### A scalable realization of local U(1) gauge invariance in cold atomic mixtures

Paper, HD-KIP 20-02, 2020, Science, Vol. 367, Issue 6482 PDF-FileIn the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is quantum electrodynamics -- the theory of electrons interacting with the electromagnetic field -- based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. While quantum computers suggest a way forward, it is difficult to build large-scale digital quantum devices required for complex simulations. Here, we propose a fully scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. To engineer the local gauge symmetry, we employ inter-species spin-changing collisions in an atomic mixture. We demonstrate the experimental realization of the elementary building block as a key step towards a platform for large-scale quantum simulations of continuous gauge theories.

### Stability analysis of ground states in a one-dimensional trapped spin-1 Bose gas

Paper, HD-KIP 19-110, 2019, Communications in Nonlinear Science and Numerical Simulation, Volume 83, arXiv:1905.03069 (83) PDF-File### Simultaneous Readout of Noncommuting Collective Spin Observables beyond the Standard Quantum Limit

Paper, HD-KIP 19-86, 2019, Physical Review Letters, Volume 123, Issue 6, arXiv:1904.01471 PDF-File### Bidirectional universal dynamics in a spinor Bose gas close to a nonthermal fixed point

Paper, HD-KIP 18-171, 2018, Phys. Rev. A, Volume: 99, Issue: 3, arXiv:1812.08571 033611 PDF-FileWe numerically study the universal scaling dynamics of an isolated one-dimensional ferromagnetic spin-1 Bose gas. Preparing the system in a far-from-equilibrium initial state, simultaneous coarsening and refining is found to enable and characterize the approach to a nonthermal fixed point. A macroscopic length scale which scales in time according to LΛ(t)∼tβ, with β≃1/4, quantifies the coarsening of the size of spin textures. At the same time kinklike defects populating these textures undergo a refining process measured by a shrinking microscopic length scale Lλ∼tβ′, with β′≃−0.17. The combination of these scaling evolutions enables particle and energy conservation in the isolated system and constitutes a bidirectional transport in momentum space. The value of the coarsening exponent β suggests the dynamics to belong to the universality class of diffusive coarsening of the one-dimensional XY model. However, the universal momentum distribution function exhibiting nonlinear transport marks the distinction between diffusive coarsening and the approach of a nonthermal fixed point in the isolated system considered here. This underlines the importance of the universal scaling function in classifying nonthermal fixed points. Present-day experiments with quantum gases are expected to have access to the predicted bidirectional scaling.

### Observation of universal dynamics in a spinor Bose gas far from equilibrium

Paper, HD-KIP 18-143, 2018, Nature, Volume: 563, Issue: 7730 , arXiv:1805.11881 217-220 PDF-FileThe dynamics of quantum systems far from equilibrium represents one of the most challenging problems in theoretical many-body physics. While the evolution is in general intractable in all its details, relevant observables can become insensitive to microscopic system parameters and initial conditions. This is the basis of the phenomenon of universality. Far from equilibrium, universality is identified through the scaling of the spatio-temporal evolution of the system, captured by universal exponents and functions. Theoretically, this has been studied in examples as different as the reheating process in inflationary universe cosmology, the dynamics of nuclear collision experiments described by quantum chromodynamics, or the post-quench dynamics in dilute quantum gases in non-relativistic quantum field theory. However, an experimental demonstration of such scaling evolution in space and time in a quantum many-body system is lacking so far. Here we observe the emergence of universal dynamics by evaluating spatially resolved spin correlations in a quasi one-dimensional spinor Bose-Einstein condensate. For long evolution times we extract the scaling properties from the spatial correlations of the spin excitations. From this we find the dynamics to be governed by transport of an emergent conserved quantity towards low momentum scales. Our results establish an important class of non-stationary systems whose dynamics is encoded in time-independent scaling exponents and functions signaling the existence of non-thermal fixed points. We confirm that the non-thermal scaling phenomenon involves no fine-tuning, by preparing different initial conditions and observing the same scaling behaviour. Our analog quantum simulation approach provides the basis to reveal the underlying mechanisms and characteristics of non-thermal universality classes. One may use this universality to learn, from experiments with ultra-cold gases, about fundamental aspects of dynamics studied in cosmology and quantum chromodynamics.

### Spatially distributed multipartite entanglement enables EPR steering of atomic clouds

Paper, HD-KIP 18-84, 2018, Science, Volume: 360, Issue: 6387 413--416 PDF-FileA key resource for distributed quantum-enhanced protocols is entanglement between spatially separated modes. However, the robust generation and detection of entanglement between spatially separated regions of an ultracold atomic system remain a challenge. We used spin mixing in a tightly confined Bose-Einstein condensate to generate an entangled state of indistinguishable particles in a single spatial mode. We show experimentally that this entanglement can be spatially distributed by self-similar expansion of the atomic cloud. We used spatially resolved spin read-out to reveal a particularly strong form of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering between distinct parts of the expanded cloud. Based on the strength of EPR steering, we constructed a witness, which confirmed genuine 5-partite entanglement.

### Low-energy effective theory of non-thermal fixed points in a multicomponent Bose gas

Paper, HD-KIP 18-80, 2018, Physical Review A, arXiv:1807.10228 [cond-mat.quant-gas] PDF-FileNon-thermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of non-thermal fixed points in a bosonic quantum many-body system by integrating out long-wave-length density fluctuations. The system consists of N distinguishable spatially uniform Bose gases with O(N)×U(1)-symmetric interactions. The effective theory describes interacting Goldstone modes of the total and relative-phase excitations. It is similar in character to the non-linear Luttinger-liquid description of low-energy phonons in a single dilute Bose gas, with the markable difference of a universal non-local coupling function depending, in the large-N limit, only on momentum, single-particle mass, and density of the gas. Our theory provides a perturbative description of the non-thermal fixed point, technically easy to apply to experimentally relevant cases with a small number of fields N. Numerical results for N=3 allow us to characterize the analytical form of the scaling function and confirm the analytically predicted scaling exponents. The fixed point which is dominated by the relative phases is found to be Gaussian, while a non-Gaussian fixed point is anticipated to require scaling evolution with a distinctly lower power of time.

### Prescaling in a far-from-equilibrium Bose gas

Paper, HD-KIP 18-81, 2018, Phys. Rev. Lett., Volume: 122, Issue: 17, arXiv:1807.07514 170404 PDF-FileNon-equilibrium conditions give rise to a class of universally evolving low-energy configurations of fluctuating dilute Bose gases at a non-thermal fixed point. While the fixed point and thus full scaling in space and time is generically only reached at very long evolution times, we here propose that systems can show prescaling much earlier, on experimentally accessible time scales. During the prescaling evolution, some well-measurable short-distance properties of the spatial correlations already scale with the universal exponents of the fixed point while others still show scaling violations. Prescaling is characterized by the evolution obeying already, to a good approximation, the conservation laws which are associated with the asymptotically reached non-thermal fixed point, defining its belonging to a specific universality class. In our simulations, we consider N=3 spatially uniform three-dimensional Bose gases of particles labeled, e.g., by different hyperfine magnetic quantum numbers, with identical inter- and intra-species interactions. In this system, the approach of a non-thermal fixed point is marked by low-energy phase excitations self-similarly redistributing towards smaller wave numbers. During prescaling, the full U(N) symmetry of the model is broken while the conserved transport, reflecting the remaining U(1) symmetries, leads to the buildup of a rescaling quasicondensate distribution.

### Quenches near criticality of the quantum Ising chain-power and limitations of the discrete truncated Wigner approximation

Paper, HD-KIP 18-76, 2018, Quantum Sci. Technol., Volume: 4, Issue: 1, arXiv:1805.05221 014006 PDF-FileThe semi-classical discrete truncated Wigner approximation (dTWA) has recently been proposed as a simulation method for spin-1/2 systems. While it appears to provide a powerful approach which shows promising results in higher dimensions and for systems with long-range interactions, its performance is still not well understood in general. Here we perform a systematic benchmark on the one-dimensional transverse-field Ising model and point to limitations of the approximation arising after sudden quenches into the quantum critical regime. Our procedure allows to identify the limitations of the semi-classical simulations and with that to determine the regimes and questions where quantum simulators can provide information which is inaccessible to semi-classics.

### Active SU(1,1) atom interferometry

Paper, HD-KIP 17-74, 2017, Quantum Sci. Technol., Volume: 2, Issue: 4, arXiv:1711.04552 044009 PDF-FileActive interferometers use amplifying elements for beam splitting and recombination. We experimentally implement such a device by using spin exchange in a Bose–Einstein condensate. The two interferometry modes are initially empty spin states that get spontaneously populated in the process of parametric amplification. This nonlinear mechanism scatters atoms into both modes in a pairwise fashion and generates a non-classical state. Finally, a matched second period of spin exchange is performed that nonlinearly amplifies the output signal and maps the phase onto readily detectable first moments. Depending on the accumulated phase this nonlinear readout can reverse the initial dynamics and deamplify the entangled state back to empty spin states. This sequence is described in the framework of SU(1,1) mode transformations and compared to the SU(2) angular momentum description of passive interferometers.

### Universal equilibrium scaling functions at short times after a quench

Paper, HD-KIP 17-30, 2017, Phys. Rev. E, Volume: 96, Issue: 2, arXiv:1704.03517 022110 PDF-FileBy analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.

### Experimental observation of the Poincaré-Birkhoff scenario in a driven many-body quantum system

Paper, HD-KIP 17-12, 2017, Phys. Rev. A, Volume: 95, Issue: 1 011602 PDF-FileAccessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincaré-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.

### Implementing quantum electrodynamics with ultracold atomic systems

Paper, HD-KIP 17-10, 2017, New Journal of Physics, arXiv:1608.03480 (19) 023030 PDF-FileWe discuss the experimental engineering of model systems for the description of QED in one spatial dimension via a mixture of bosonic

^{23}Na and fermionic^{6}Li atoms. The local gauge symmetry is realized in an optical superlattice, using heteronuclear boson-fermion spin-changing interactions which preserve the total spin in every local collision. We consider a large number of bosons residing in the coherent state of a Bose-Einstein condensate on each link between the fermion lattice sites, such that the behavior of lattice QED in the continuum limit can be recovered. The discussion about the range of possible experimental parameters builds, in particular, upon experiences with related setups of fermions interacting with coherent samples of bosonic atoms. We determine the atomic system's parameters required for the description of fundamental QED processes, such as Schwinger pair production and string breaking. This is achieved by benchmark calculations of the atomic system and of QED itself using functional integral techniques. Our results demonstrate that the dynamics of one-dimensional QED may be realized with ultracold atoms using state-of-the-art experimental resources. The experimental setup proposed may provide a unique access to longstanding open questions for which classical computational methods are no longer applicable.### Observation of the Phononic Lamb Shift with a Synthetic Vacuum

Paper, HD-KIP 16-100, 2016, Physical Review X, arXiv:1605.01874 (6) 041041 PDF-FileIn contrast to classical empty space, the quantum vacuum fundamentally alters the properties of embedded particles. This paradigm shift allows one to explain the discovery of the celebrated Lamb shift in the spectrum of the hydrogen atom. Here, we engineer a synthetic vacuum, building on the unique properties of ultracold atomic gas mixtures, offering the ability to switch between empty space and quantum vacuum. Using high-precision spectroscopy, we observe the phononic Lamb shift, an intriguing many-body effect originally conjectured in the context of solid-state physics. We find good agreement with theoretical predictions based on the Fröhlich model. Our observations establish this experimental platform as a new tool for precision benchmarking of open theoretical challenges, especially in the regime of strong coupling between the particles and the quantum vacuum.

### Schwinger pair production with ultracold atoms

Paper, HD-KIP 16-72, 2016, Physics Letters B, arXiv:1506.01238 (760) 742-746 PDF-FileWe consider a system of ultracold atoms in an optical lattice as a quantum simulator for electron–positron pair production in quantum electrodynamics (QED). For a setup in one spatial dimension, we investigate the nonequilibrium phenomenon of pair production including the backreaction leading to plasma oscillations. Unlike previous investigations on quantum link models, we focus on the infinite-dimensional Hilbert space of QED and show that it may be well approximated by experiments employing Bose–Einstein condensates interacting with fermionic atoms. Numerical calculations based on functional integral techniques give a unique access to the physical parameters required to realize QED phenomena in a cold atom experiment. In particular, we use our approach to consider quantum link models in a yet unexplored parameter regime and give bounds for their ability to capture essential features of the physics. The results suggest a paradigmatic change towards realizations using coherent many-body states for quantum simulations of high-energy particle physics phenomena.

### Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics

Paper, HD-KIP 16-50, 2016, Physical Review Letters, Volume: 117, Issue: 1, arXiv:1602.07505 013001 PDF-FileWe experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

### Nonlinear dressed states at the miscibility-immiscibility threshold

Paper, HD-KIP 15-101, 2015, Physical Review A, Volume: 92, Issue: 5, arXiv:1407.8049 056314 PDF-FileThe dynamical evolution of spatial patterns in a complex system can reveal the underlying structure and stability of stationary states. As a model system we employ a two-component Bose-Einstein condensate at the transition from miscible to immiscible with the additional control of linear interconversion. Excellent agreement is found between the detailed experimental time evolution and the corresponding numerical mean-field computations. Analyzing the dynamics of the system, we find clear indications of stationary states that we term nonlinear dressed states. A steady-state bifurcation analysis reveals a smooth connection of these states with dark-bright soliton solutions of the integrable two-component Manakov model.

### Observation of Scaling in the Dynamics of a Strongly Quenched Quantum Gas

Paper, HD-KIP 15-92, 2015, PHYSICAL REVIEW LETTERS,Volume: 115, Issue: 24, arXiv:1509.02173 245301 PDF-FileWe report on the experimental observation of scaling in the time evolution following a sudden quench into the vicinity of a quantum critical point. The experimental system, a two-component Bose gas with coherent exchange between the constituents, allows for the necessary high level of control of parameters as well as the access to time-resolved spatial correlation functions. The theoretical analysis reveals that when quenching the system close to the critical point, the energy introduced by the quench leads to a short-time evolution exhibiting crossover reminiscent of the finite-temperature critical properties in the system’s universality class. Observing the time evolution after a quench represents a paradigm shift in accessing and probing experimentally universal properties close to a quantum critical point and allows in a new way benchmarking of quantum many-body theory with experiments.

### Twist-and-turn spin squeezing in Bose-Einstein condensates

Paper, HD-KIP 15-48, 2015, PHYSICAL REVIEW A, Volume: 92, Issue: 2, arXiv:1507.02930 023603 PDF-FileWe demonstrate experimentally an alternative method for the dynamic generation of atomic spin squeezing, building on the interplay between linear coupling and nonlinear phase evolution. Since the resulting quantum dynamics can be seen as rotation and shear on the generalized Bloch sphere, we call this scheme twist-and-turn. This is closely connected to an underlying instability in the classical limit of this system. The short-time evolution of the quantum state is governed by a fast initial spreading of the quantum uncertainty in one direction, accompanied by squeezing in the orthogonal axis. We find an optimal value of ξ

^{2}_{S}=−7.1(3) dB in a single Bose-Einstein condensate and scalability of the squeezing to more than 10^{4}particles with ξ^{2}_{S}=−2.8(4) dB.### Double-well atom trap for fluorescence detection at the Heisenberg limit

Paper, HD-KIP 15-07, 2015, PHYSICAL REVIEW A, Volume: 91, Issue: 1, arXiv:1411.5812 013412 PDF-FileWe experimentally demonstrate an atom number detector capable of simultaneous detection of two mesoscopic ensembles with single-atom resolution. Such a sensitivity is a prerequisite for quantum metrology at a precision approaching the Heisenberg limit. Our system is based on fluorescence detection of atoms in a hybrid trap in which a dipole barrier divides a magneto-optical trap into two separated wells. We introduce a noise model describing the various sources contributing to the measurement error and report a limit of up to 500 atoms for single-atom resolution in the atom number difference.

### Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates

Paper, HD-KIP 14-66, 2014, Physical Review Letters, Volume: 113, Issue: 10, arXiv:1405.6022 5 PDF-FileA major challenge in quantum metrology is the generation of entangled states with a macroscopic atom number. Here, we demonstrate experimentally that atomic squeezing generated via nonlinear dynamics in Bose-Einstein condensates, combined with suitable trap geometries, allows scaling to large ensemble sizes. We achieve a suppression of fluctuations by 5.3(5) dB for 12 300 particles, from which we infer that similar squeezing can be obtained for more than 10

^{7}atom. With this resource, we demonstrate quantum-enhanced magnetometry by swapping the squeezed state to magnetically sensitive hyperfine levels that have negligible nonlinearity. We find a quantum-enhanced single-shot sensitivity of 310(47) pT for static magnetic fields in a probe volume as small as 90 μm^{3}.### Fisher information and entanglement of non-Gaussian spin states

Paper, HD-KIP 14-57, 2014, SCIENCE, Volume: 345, Issue: 6195, arXiv:1507.03782 424-427 PDF-FileEntanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here, we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement, which we confirm by Bayesian phase estimation with sub–shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.

### Dissipative preparation of phase- and number-squeezed states with ultracold atoms

Paper, HD-KIP 14-07, 2014, PHYSICAL REVIEW A, arXiv:1309.6436 (89) 013620 PDF-FileWe develop a dissipative quantum state preparation scheme for the creation of phase- and number-squeezed states. It utilizes ultracold atoms in a double-well configuration immersed in a background Bose-Einstein condensate, with the latter consisting of an atom species different from the atoms in the double well and acting as a dissipative quantum reservoir. We derive a master equation for this system starting from microscopic physics and show that squeezing develops on a time scale proportional to 1/N, where N is the number of particles in the double well. This scaling, caused by bosonic enhancement, allows us to make the time scale for the creation of squeezed states very short. The lifetime of squeezed states is limited by dephasing arising from the intrinsic structure of the setup. However, the dephasing can be avoided by stroboscopically switching the driving off and on. We show that this approach leads to robust stationary squeezed states. Finally, we provide the necessary ingredients for a potential experimental implementation by specifying a parameter regime for rubidium atoms that leads to squeezed states.

### Accurate Atom Counting in Mesoscopic Ensembles

Paper, HD-KIP 13-97, 2013, PHYSICAL REVIEW LETTERS, Volume: 111, Issue: 25, arXiv:1307.7598 253001 PDF-FileMany cold atom experiments rely on precise atom number detection, especially in the context of quantum-enhanced metrology where effects at the single particle level are important. Here, we investigate the limits of atom number counting via resonant fluorescence detection for mesoscopic samples of trapped atoms. We characterize the precision of these fluorescence measurements beginning from the single-atom level up to more than one thousand. By investigating the primary noise sources, we obtain single-atom resolution for atom numbers as high as 1200. This capability is an essential prerequisite for future experiments with highly entangled states of mesoscopic atomic ensembles.

### Optimized absorption imaging of mesoscopic atomic clouds

Paper, HD-KIP 13-37, 2013, Applied Physics B-Laseres and Optics, Volume: 113, Issue: 1We report on the optimization of high-intensity absorption imaging for small Bose–Einstein condensates. The imaging calibration exploits the linear scaling of the quantum projection noise with the mean number of atoms for a coherent spin state. After optimization for atomic clouds containing up to 300 atoms, we find an atom number resolution of Δ det =3.7 Δ det = 3.7 atoms, mainly limited by photon shot noise and radiation pressure.

### Measuring and engineering entropy and spin squeezing in weakly linked Bose-Einstein condensates

Paper, HD-KIP 13-25, 2013, NEW JOURNAL OF PHYSICS, Volume 15, arXiv:1302.3040 8 PDF-FileWe propose a method to infer the single-particle entropy of bosonic atoms in an optical lattice and to study the local evolution of entropy, spin squeezing, and entropic inequalities for entangle- ment detection in such systems. This method is based on experimentally feasible measurements of non-nearest-neighbour coherences. We study a specific example of dynamically controlling atom tunneling between selected sites and show that this could potentially also improve the metrologically relevant spin squeezing.

### Dynamic generation of spin-squeezed states in bosonic Josephson junctions

Paper, HD-KIP 12-56, 2012, Phys. Rev. Lett. A, Volume: 86, Issue: 2, arXiv:1205.6756 023615 PDF-FileWe analyze the formation of squeezed states in a condensate of ultracold bosonic atoms confined by a double-well potential. The emphasis is set on the dynamical formation of such states from initially coherent many-body quantum states. Two cases are described: the squeezing formation in the evolution of the system around the stable point, and in the short-time evolution in the vicinity of an unstable point. The latter is shown to produce highly squeezed states on very short times. On the basis of a semiclassical approximation to the Bose-Hubbard Hamiltonian, we are able to predict the amount of squeezing, its scaling with N, and the speed of coherent spin formation with simple analytical formulas which successfully describe the numerical Bose-Hubbard results. This method of producing highly squeezed spin states in systems of ultracold atoms is compared to other standard methods in the literature.

### Atomic homodyne detection of continuous variable entangled twin-atom states

Paper, HD-KIP 11-85, 2011, NATURE, Volume: 480, Issue: 7376, arXiv:1112.4594 219-223 PDF-FileHistorically, the completeness of quantum theory has been questioned using the concept of bipartite continuous-variable entanglement. The non-classical correlations (entanglement) between the two subsystems imply that the observables of one subsystem are determined by the measurement choice on the other, regardless of the distance between the subsystems. Nowadays, continuous-variable entanglement is regarded as an essential resource, allowing for quantum enhanced measurement resolution, the realization of quantum teleportation and quantum memories or the demonstration of the Einstein–Podolsky–Rosen paradox. These applications rely on techniques to manipulate and detect coherences of quantum fields, the quadratures. Whereas in optics coherent homodyne detection of quadratures is a standard technique, for massive particles a corresponding method was missing. Here we report the realization of an atomic analogue to homodyne detection for the measurement of matter-wave quadratures. The application of this technique to a quantum state produced by spin-changing collisions in a Bose–Einstein condensate reveals continuous-variable entanglement, as well as the twin-atom character of the state. Our results provide a rare example of continuous-variable entanglement of massive particles. The direct detection of atomic quadratures has applications not only in experimental quantum atom optics, but also for the measurement of fields in many-body systems of massive particles.

### Rabi Flopping Induces Spatial Demixing Dynamics

Paper, HD-KIP 11-76, 2011, PHYSICAL REVIEW LETTERS, Volume: 107, Issue: 19, arXiv:1109.5601 193001 PDF-FileWe experimentally investigate the mixing and demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena.

### Local and spatially extended sub-Poisson atom-number fluctuations in optical lattices

Paper, HD-KIP 11-67, 2011, PHYSICAL REVIEW A, Volume: 84, Issue: 1, arXiv:1008.4603 011609 PDF-FileWe demonstrate that ultracold interacting bosonic atoms in an optical lattice with large on-site population show sub-Poisson on-site and intersite atom-number fluctuations. The experimental observations agree with numerical predictions of the truncated Wigner approximation. The correlations persist in the presence of multimode atom dynamics and even over large spatially extended samples involving several sites.

### Two-Well Bose-Einstein Condensates and Strategies for Einstein-Podolsky-Rosen Entanglement

Paper, HD-KIP 11-26, 2011, Phys. Rev. Lett., Volume: 106, Issue: 12, arXiv:1010.4121 4 PDF-FileCriteria suitable for measuring entanglement between two different potential wells in a Bose-Einstein condensation are evaluated. We show how to generate the required entanglement, utilizing either an adiabatic two-mode or a dynamic four-mode interaction strategy, with techniques that take advantage of s-wave scattering interactions to provide the nonlinear coupling. The dynamic entanglement method results in an entanglement signature with spatially separated detectors, as in the Einstein-Podolsky-Rosen paradox.

### Einstein-Podolsky-Rosen Correlations of Ultracold Atomic Gases

Paper, HD-KIP 11-22, 2011, Phys. Rev. Lett., Volume: 106, Issue: 12, arXiv:1009.2655 4 PDF-FileWe demonstrate that collective continuous variables of two species of trapped ultracold bosonic gases can be Einstein-Podolsky-Rosen-correlated (entangled) via inherent interactions between the species. We propose two different schemes for creating these correlations—a dynamical scheme and a static scheme analogous to two-mode squeezing in quantum optics. We quantify the correlations by using known measures of entanglement and study the effect of finite temperature on these quantum correlations.

### Classical Bifurcation at the Transition from Rabi to Josephson Dynamics

Paper, HD-KIP 10-62, 2010, Phys. Rev. Lett., Volume: 105, Issue: 20, arXiv:1008.3057 4 PDF-FileWe report on the experimental demonstration of the internal bosonic Josephson effect in a rubidium spinor Bose-Einstein condensate. The measurement of the full time dynamics in phase space allows the characterization of the theoretically predicted π-phase modes and quantitatively confirms analytical predictions, revealing a classical bifurcation. Our results suggest that this system is a model system which can be tuned from classical to the quantum regime and thus is an important step towards the experimental investigation of entanglement generation close to critical points.

### Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates

Paper, HD-KIP 10-16, 2010, Phys. Rev. A, Volume: 81, Issue: 6, arXiv:0909.2122 15 PDF-FileWe consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.

### Two-mode Bose gas: Beyond classical squeezing

Paper, HD-KIP 10-15, 2010, Phys. Rev. A, Volume: 81, Issue: 6, arXiv:1002.2504 14 PDF-FileThe dynamical evolution of squeezing correlations in an ultracold Bose-Einstein condensate distributed across two modes is investigated theoretically in the framework of the Bose-Hubbard model. It is shown that the eigenstates of the Hamiltonian do not exploit the full region allowed by Heisenberg’s uncertainty relation for number and phase fluctuations. The development of nonclassical correlations and relative number squeezing is studied in the transition from the Josephson to the Fock regime. Comparing the full quantum evolution with classical statistical simulations allows us to identify quantum aspects of the squeezing formation. In the quantum regime, the measurement of squeezing allows us to distinguish even and odd total particle numbers.

### Nonlinear atom interferometer surpasses classical precision limit

Paper, HD-KIP 10-10, 2010, Nature, Volume: 464, Issue: 7292, arXiv:1009.2374 PDF-FileInterference is fundamental to wave dynamics and quantum mechanics. The quantum wave properties of particles are exploited in metrology using atom interferometers, allowing for high-precision inertia measurements

^{1,2}. Furthermore, the state-of-the-art time standard is based on an interferometric technique known as Ramsey spectroscopy. However, the precision of an interferometer is limited by classical statistics owing to the finite number of atoms used to deduce the quantity of interest^{3}. Here we show experimentally that the classical precision limit can be surpassed using nonlinear atom interferometry with a Bose–Einstein condensate. Controlled interactions between the atoms lead to non-classical entangled states within the interferometer; this represents an alternative approach to the use of non-classical input states^{4, 5, 6, 7, 8}. Extending quantum interferometry^{9}to the regime of large atom number, we find that phase sensitivity is enhanced by 15 per cent relative to that in an ideal classical measurement. Our nonlinear atomic beam splitter follows the ‘one-axis-twisting’ scheme^{10}and implements interaction control using a narrow Feshbach resonance. We perform noise tomography of the quantum state within the interferometer and detect coherent spin squeezing with a squeezing factor of -8.2 dB (refs 11–15). The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms^{16}.### Ultrakalte Quantenpendel

Paper, HD-KIP 10-06, 2010, Physik Journal, Februar PDF-FileDas Phänomen des Tunnelns – das Durchdringen von Barrieren – ist ein Paradebeispiel dafür, dass sich Teilchen in der Quantenwelt anders verhalten als in der klassischen. Kürzlich gelang es erstmals, das Tunneln makroskopischer Atomgase im Experiment direkt zu beobachten. Unter gewissen Näherungen lässt sich das komplizierte Vielteilchensystem mit einem einzigen Freiheitsgrad beschreiben, dessen Bewegungsgleichung derjenigen des Fadenpendels entspricht.

### Dynamic control and probing of many-body decoherence in double-well Bose-Einstein condensates

Paper, HD-KIP 09-97, 2009, Phys. Rev. A, Volume: 80, Issue: 5 053613### Feynman path-integral treatment of the BEC-impurity polaron

Paper, HD-KIP 09-96, 2009, Phys. Rev. B,arXiv:0906.4455 (80) 184504 PDF-File### Squeezing and entanglement in a Bose-Einstein condensate

Paper, HD-KIP 08-28, 2008 PDF-FileEntanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound attainable by classical means. This results in the standard quantum limit, which is reached in today"s best available sensors of various quantities such as time and position. Many of these sensors are interferometers in which the standard quantum limit can be overcome by using quantum-entangled states (in particular spin squeezed states) at the two input ports. Bose–Einstein condensates of ultracold atoms are considered good candidates to provide such states involving a large number of particles. Here we demonstrate spin squeezed states suitable for atomic interferometry by splitting a condensate into a few parts using a lattice potential. Site-resolved detection of the atoms allows the measurement of the atom number difference and relative phase, which are conjugate variables. The observed fluctuations imply entanglement between the particles, a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.

Funding:

DFG: Systematische Verbesserung von Atom Trap Trace Anlaysis für 39Ar und deren Anwendung zur Erstellung einer tausendjährigen Paläotemperaturzeitreihe aus Grundwasser

DFG: ArTTA-10mL: Ein Instrument für die 39Ar-Datierung von kleinen Eis- und Wasserproben

ERC Advanced Grant-Horizon 2020: EntangleGen- Entanglement Generation in Universal Quantum Dynamics

DFG: Test des schwachen Äquivalenzprinzips mit Antimaterie