# Entanglement

Thomas Gasenzer

Phone: +49 6221 54 5173

thomas.gasenzer@kip.uni-heidelberg.de

Martin Gärttner

Phone: +49 6221 54 5185

martin.gaerttner@kip.uni-heidelberg.de

Maurus Hans

Phone: +49 6221 54 5177

mhans@kip.uni-heidelberg.de

Philipp Hauke

Phone: +49 6221 54 5185

philipp.hauke@kip.uni-heidelberg.de

Philipp Kunkel

Phone: +49 6221 54 5178

philipp.kunkel@kip.uni-heidelberg.de

Stefan Lannig

Phone: +49 6221 54 5178

stefan.lannig@kip.uni-heidelberg.de

Markus Oberthaler

Phone: +49 6221 54 5170

markus.oberthaler@kip.uni-heidelberg.de

Maximilian Prüfer

Phone: +49 6221 54 5178

maximilian.pruefer@kip.uni-heidelberg.de

Rodrigo Felipe Rosa-Medina Pimentel

Phone: +49 6221 54 5178

rodrigo.rosamedina@kip.uni-heidelberg.de

Christian-Marcel Schmied

Phone: +49 6221 54 5186

christian-marcel.schmied@kip.uni-heidelberg.de

Helmut Strobel

Phone: +49 6221 54 5177

helmut.strobel@kip.uni-heidelberg.de

Celia Viermann

Phone: +49 6221 54 5177

celia.viermann@kip.uni-heidelberg.de

## Recent publications

### 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. (120) 040402Out-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 (117) 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 (92) 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 (345) 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 (15) 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.

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