In quantum mechanics, two distant particles can be in an entangled state, meaning that they are "connected" in a way that cannot be described by classical correlations. It seems that measuring one of the particles can instantaneously affect the other one. This "spooky action at a distance", as Einstein called it, has puzzled physicists since the early days of quantum mechanics and is still an active research topic. Besides being of fundamental interest, entanglement is the fuel that quantum computers and quantum communication devices consume.

In the SynQS group we use perfectly controlled gases of ultracold atoms to explore both the fundamental aspects and applications of entanglement. For example, we observed the "spooky action" between two spatially separated parts of an atomic cloud and generated entanglement that can help improving the precision of atomic clocks and magnetometers.

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

Thomas Gasenzer

Phone: +49 6221 54 5173

thomas.gasenzer@kip.uni-heidelberg.de

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

Markus Oberthaler

Phone: +49 6221 54 5170

markus.oberthaler@kip.uni-heidelberg.de

Timon Alexander Schmutz

Phone: +49 6221 54 5178

timon_alexander.schmutz@kip.uni-heidelberg.de

Raphael Elias Schäfer

Phone: +49 6221 54 5178

raphael_elias.schaefer@kip.uni-heidelberg.de

Marius Sparn

Phone: +49 6221 54 5177

marius.sparn@kip.uni-heidelberg.de

Helmut Strobel

Phone: +49 6221 54 9276

helmut.strobel@kip.uni-heidelberg.de

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

HD-KIP 20-53, 2020, Nat. Phys. PDF-File### Observation of universal dynamics in a spinor Bose gas far from equilibrium

HD-KIP 18-143, 2018, Nature (563) 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

HD-KIP 18-84, 2018, Science (360) 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.

### Relating out-of-time-order correlations to entanglement via multiple-quantum coherences

HD-KIP 18-11, 2018, Phys. Rev. Lett., arXiv:1706.01616 (120) 040402 PDF-FileOut-of-time-order correlations (OTOCs) characterize the scrambling, or delocalization, of quantum information over all the degrees of freedom of a system and thus have been proposed as a proxy for chaos in quantum systems. Recent experimental progress in measuring OTOCs calls for a more thorough understanding of how these quantities characterize complex quantum systems, most importantly in terms of the buildup of entanglement. Although a connection between OTOCs and entanglement entropy has been derived, the latter only quantifies entanglement in pure systems and is hard to access experimentally. In this work, we formally demonstrate that the multiple-quantum coherence spectra, a specific family of OTOCs well known in NMR, can be used as an entanglement witness and as a direct probe of multiparticle entanglement. Our results open a path to experimentally testing the fascinating idea that entanglement is the underlying glue that links thermodynamics, statistical mechanics, and quantum gravity.

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

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.

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

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.### Fisher information and entanglement of non-Gaussian spin states

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.

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

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.