
L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, M. K. Joshi Observing the quantum Mpemba effect in quantum simulations,
PRL 133 10402 (20240701),
arXiv:2401.04270 arXiv:2401.04270 (ID: 721174)
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The nonequilibrium physics of manybody quantum systems harbors various unconventional phenomena. In this study, we experimentally investigate one of the most puzzling of these phenomena— the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trappedion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and postprocessed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.

H. Hainzer, D. Kiesenhofer, T. Ollikainen, M. Bock, F. Kranzl, M. K. Joshi, G. Yoeli, R. Blatt, T. Gefen, C. F. Roos Correlation Spectroscopy with MultiqubitEnhanced Phase Estimation,
Phys. Rev. X 14 24 (20240229),
URL (ID: 721249)
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Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the
oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution.
Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy
oscillator for a measurement of their transition frequency difference; this technique has enabled very
precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple
quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy
with N particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We
derive precision limits and optimal sensing techniques for this problem and compare the performance of
probe states and measurement with and without entanglement. Using one and twodimensional ion
Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ionion distances, transition frequency shifts, laserion detunings, and pathlength fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and
qubitresolved singleshot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays.

M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. Zache, R. Blatt, C. F. Roos, P. Zoller Exploring LargeScale Entanglement in Quantum Simulation,
Nature 624 539 (20231129),
http://dx.doi.org/10.1038/s41586023067680 doi:10.1038/s41586023067680 (ID: 721080)
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Entanglement is a distinguishing feature of quantum manybody systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we perform experimental investigations of entanglement based on the entanglement Hamiltonian, as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a 1D XXZ Heisenberg chain on a 51ion programmable quantum simulator and perform sampleefficient `learning' of the entanglement Hamiltonian for subsystems of up to 20 lattice sites. Our experiments provide compelling evidence for a local structure of the entanglement Hamiltonian. This observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatiallyvarying temperature profile as a signature of entanglement. Our results also show the transition from area to volumelaw scaling of Von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wideranging applicability to revealing and understanding entanglement in manybody problems with local interactions including higher spatial dimensions.

F. Kranzl, S. Birnkammer, M. K. Joshi, A. Bastianello, R. Blatt, M. Knap, C. F. Roos Observation of magnon bound states in the longrange, anisotropic Heisenberg model,
Phys. Rev. X 13 03101712 (20230811),
http://dx.doi.org/10.1103/PhysRevX.13.031017 doi:10.1103/PhysRevX.13.031017 (ID: 720909)
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Over the recent years coherent, timeperiodic modulation has been established as a versatile tool for realizing novel Hamiltonians. Using this approach, known as Floquet engineering, we experimentally realize a longranged, anisotropic Heisenberg model with tunable interactions in a trapped ion quantum simulator. We demonstrate that the spectrum of the model contains not only single magnon excitations but also composite magnon bound states. For the longrange interactions with the experimentally realized powerlaw exponent, the group velocity of magnons is unbounded. Nonetheless, for sufficiently strong interactions we observe bound states of these unconventional magnons which possess a nondiverging group velocity. By measuring the configurational mutual information between two disjoint intervals, we demonstrate the implications of the bound state formation on the entanglement dynamics of the system. Our observations provide key insights into the peculiar role of composite excitations in the nonequilibrium dynamics of quantum manybody systems.

F. Kranzl, A. Lasek, M. K. Joshi, A. Kalev, R. Blatt, C. F. Roos, N. Yunger Halpern Experimental observation of thermalization with noncommuting charges,
PRX Quantum 4 20318 (20230428),
http://dx.doi.org/10.1103/PRXQuantum.4.020318 doi:10.1103/PRXQuantum.4.020318 (ID: 720810)
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Quantum simulators have recently enabled experimental observations of the internal thermalization of quantum manybody systems. Often, the global energy and particle number are conserved and the system is prepared with a welldefined particle number—in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trappedion simulator. We prepare 6–21 spins in an approximate microcanonical subspace, a generalization of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have welldefined nontrivial values simultaneously. We simulate a Heisenberg evolution using laserinduced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted nonAbelian thermal state. This work bridges quantum manybody simulators to the quantum thermodynamics of noncommuting charges, the predictions of which can now be tested.

J. Franke, S. M. Muleady, C. R. Kaubrügger, F. Kranzl, R. Blatt, A. M. Rey, M. K. Joshi, C. F. Roos Quantumenhanced sensing on optical transitions through finiterange interactions,
Nature 621 740 (20230327),
http://dx.doi.org/10.1038/s4158602306472z doi:10.1038/s4158602306472z (ID: 721072)
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The control over quantum states in atomic systems has led to the most precise optical atomic clocks to date. Their sensitivity is currently bounded by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated particles, which can nevertheless be overcome when operated with entangled particles. Yet demonstrating a quantum advantage in real world sensors is extremely challenging and remains to be achieved aside from two remarkable examples, LIGO and more recently HAYSTAC. Here we illustrate a pathway for harnessing scalable entanglement in an optical transition using 1D chains of up to 51 ions with statedependent interactions that decay as a powerlaw function of the ion separation. We show our sensor can be made to behave as a oneaxistwisting (OAT) model, an iconic fully connected model known to generate scalable squeezing. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of finite momentum spinwave excitations, the generation of spin squeezing comparable to OAT (a Wineland parameter of −3.9±0.3 dB for only N = 12 ions) and the development of nonGaussian states in the form of atomic multiheaded cat states in the Qdistribution. The simplicity of our protocol enables scalability to large arrays with minimal overhead, opening the door to advances in timekeeping as well as new methods for preserving coherence in quantum simulation and computation. We demonstrate this in a Ramseytype interferometer, where we reduce the measurement uncertainty by −3.2±0.5 dB below the standard quantum limit for N = 51 ions.