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The oscillating magnetic field produced by unbalanced currents in radio-frequency ion traps induces transition frequency shifts and sideband transitions that can be harmful to precision spectroscopy experiments. Here, we describe a methodology, based on two-photon spectroscopy, for determining both the strength and direction of rf-induced magnetic fields without modifying any DC magnetic bias field or changing any trap RF power. The technique is readily applicable to any trapped-ion experiment featuring narrow linewidth transitions., Comment: 13 pages, 6 figures

The non-equilibrium physics of many-body 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 trapped-ion 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., Comment: 11 pages, 7 figures. Published version

Entanglement is a distinguishing feature of quantum many-body 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 51-ion programmable quantum simulator and perform sample-efficient `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 spatially-varying temperature profile as a signature of entanglement. Our results also show the transition from area to volume-law 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 wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions., Comment: 14 pages, 7 figures

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 state-dependent interactions that decay as a power-law function of the ion separation. We show our sensor can be made to behave as a one-axis-twisting (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 spin-wave excitations, the generation of spin squeezing comparable to OAT (a Wineland parameter of $-3.9 \pm 0.3$ dB for only N = 12 ions) and the development of non-Gaussian states in the form of atomic multi-headed cat states in the Q-distribution. 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 Ramsey-type interferometer, where we reduce the measurement uncertainty by $-3.2 \pm 0.5$ dB below the standard quantum limit for N = 51 ions., Comment: During the completion of our work, we became aware of three related experiments using dressed Rydberg interactions in tweezer and microtrap array platforms. See arXiv:2303.08053, arXiv:2303.08078 and arXiv:2303.08805. This manuscript contains 14 Pages and 5 figures

Over the recent years coherent, time-periodic modulation has been established as a versatile tool for realizing novel Hamiltonians. Using this approach, known as Floquet engineering, we experimentally realize a long-ranged, 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 long-range interactions with the experimentally realized power-law exponent, the group velocity of magnons is unbounded. Nonetheless, for sufficiently strong interactions we observe bound states of these unconventional magnons which possess a non-diverging 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 non-equilibrium dynamics of quantum many-body systems.

Quantum simulators have recently enabled experimental observations of quantum many-body systems' internal thermalization. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined 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 trapped-ion 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 well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced 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 non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, whose predictions can now be tested., Comment: 6.5 pages (3 figures) + appendices (10 pages); increased system size to 21 qubits; updated to match the version published in PRX Quantum

Scaling a trapped-ion based quantum simulator to a large number of ions creates a fully-controllable quantum system that becomes inaccessible to numerical methods. When highly anisotropic trapping potentials are used to confine the ions in the form of a long linear string, several challenges have to be overcome to achieve high-fidelity coherent control of a quantum system extending over hundreds of micrometers. In this paper, we describe a setup for carrying out many-ion quantum simulations including single-ion coherent control that we use for demonstrating entanglement in 50-ion strings. Furthermore, we present a set of experimental techniques probing ion-qubits by Ramsey and Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences that enable detection (and compensation) of power-line-synchronous magnetic-field variations, measurement of path length fluctuations, and of the wavefronts of elliptical laser beams coupling to the ion string.

We present a study of the coherence properties of a variety of motional states of a single ion confined in a Penning ion trap. We demonstrate that the motion of the ion has a coherence time of the order of one second, using Ramsey interferometry. We introduce a technique for preparing the ion in an incoherent superposition of highly-excited motional states using a simple modification of optical sideband cooling. Coherent manipulation of these states allow measurements of optical and motional coherence to be carried out. We show that these highly-excited motional state superpositions have long coherence times despite the incoherent preparation of the states. Such states can be useful for sensitive motional dephasing measurements., Comment: 18 pages, 8 figures

Identification of habitable planets beyond our solar system is a key goal of current and future space missions. Yet habitability depends not only on the stellar irradiance, but equally on constituent parts of the planetary atmosphere. Here we show, for the first time, that radiatively active mineral dust will have a significant impact on the habitability of Earth-like exoplanets. On tidally-locked planets, dust cools the day-side and warms the night-side, significantly widening the habitable zone. Independent of orbital configuration, we suggest that airborne dust can postpone planetary water loss at the inner edge of the habitable zone, through a feedback involving decreasing ocean coverage and increased dust loading. The inclusion of dust significantly obscures key biomarker gases (e.g. ozone, methane) in simulated transmission spectra, implying an important influence on the interpretation of observations. We demonstrate that future observational and theoretical studies of terrestrial exoplanets must consider the effect of dust., Comment: 15 pages, 4 figures, 3 tables

A key factor in determining the potential habitability of synchronously rotating planets is the strength of the atmospheric boundary layer inversion between the dark side surface and the free atmosphere. Here we analyse data obtained from polar night measurements at the South Pole and Alert Canada, which are the closest analogues on Earth to conditions on the dark sides of synchronously rotating exoplanets without and with a maritime influence, respectively. On Earth, such inversions rarely exceed 30 K in strength, because of the effect of turbulent mixing induced by phenomena such as so-called mesoscale slope winds, which have horizontal scales of 10s to 100s of km, suggesting a similar constraint to near-surface dark side inversions. We discuss the sensitivity of inversion strength to factors such as orography and the global-scale circulation, and compare them to a simulation of the planet Proxima Centauri b. Our results demonstrate the importance of comparisons with Earth data in exoplanet research, and highlight the need for further studies of the exoplanet atmospheric collapse problem using mesoscale and eddy-resolving models., Comment: Accepted by Astrophysical Journal Letters; 14 pages, 3 figures

In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a deep understanding of many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring R\'enyi entanglement entropies., Comment: 9 pages and 8 figures

The energy balance and climate of planets can be affected by the reflective properties of their land, ocean, and frozen surfaces. Here we investigate the effect of host star spectral energy distribution (SED) on the albedo of these surfaces using a one-dimensional (1-D) energy balance model (EBM). Incorporating spectra of M-, K-, G- and F-dwarf stars, we determined the effect of varying fractional and latitudinal distribution of land and ocean surfaces as a function of host star SED on the overall planetary albedo, climate, and ice-albedo feedback response. While noting that the spatial distribution of land masses on a given planet will have an effect on the overall planetary energy balance, we find that terrestrial planets with higher average land/ocean fractions are relatively cooler and have higher albedo regardless of star type. For Earth-like planets orbiting M-dwarf stars the increased absorption of water ice in the near-infrared (NIR), where M-dwarf stars emit much of their energy, resulted in warmer global mean surface temperatures, ice lines at higher latitudes, and increased climate stability as the ice-albedo feedback became negative at high land fractions. Conversely, planets covered largely by ocean, and especially those orbiting bright stars, had a considerably different energy balance due to the contrast between the reflective land and the absorptive ocean surface, which in turn resulted in warmer average surface temperatures than land-covered planets and a stronger potential ice-albedo feedback. While dependent on the properties of individual planetary systems, our results place so constraints on a range of climate states of terrestrial exoplanets based on albedo and incident flux., Comment: 12 pages, 4 figures

We describe a protocol for cross-platform verification of quantum simulators and quantum computers. We show how to measure directly the overlap $\textrm{Tr}\left[\rho_1 \rho_2\right]$ and the purities $\textrm{Tr}\left[\rho^2_{1,2}\right]$, and thus a fidelity of two possibly mixed quantum states $\rho_1$ and $\rho_2$ prepared in separate experimental platforms. We require only local measurements in randomized product bases, which are communicated classically. As a proof-of-principle, we present the measurement of experiment-theory fidelities for entangled $10$-qubit quantum states in a trapped ion quantum simulator., Comment: Published Version

Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments demonstrating self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics. Contrary to analog quantum simulation, this approach forgoes the requirement of realising the targeted Hamiltonian directly in the laboratory, thus allowing the study of a wide variety of previously intractable target models. Here, we focus on the Lattice Schwinger model, a gauge theory of 1D quantum electrodynamics. Our quantum co-processor is a programmable, trapped-ion analog quantum simulator with up to 20 qubits, capable of generating families of entangled trial states respecting symmetries of the target Hamiltonian. We determine ground states, energy gaps and, by measuring variances of the Schwinger Hamiltonian, we provide algorithmic error bars for energies, thus addressing the long-standing challenge of verifying quantum simulation., Comment: 6 + 12 pages, 10 figures

We investigate the atmospheric dynamics of terrestrial planets in synchronous rotation within the habitable zone of low-mass stars using the Community Atmosphere Model (CAM). The surface temperature contrast between day and night hemispheres decreases with an increase in incident stellar flux, which is opposite the trend seen on gas giants. We define three dynamical regimes in terms of the equatorial Rossby deformation radius and the Rhines length. The slow rotation regime has a mean zonal circulation that spans from day to night side, with both the Rossby deformation radius and the Rhines length exceeding planetary radius, which occurs for planets around stars with effective temperatures of 3300 K to 4500 K (rotation period > 20 days). Rapid rotators have a mean zonal circulation that partially spans a hemisphere and with banded cloud formation beneath the substellar point, with the Rossby deformation radius is less than planetary radius, which occurs for planets orbiting stars with effective temperatures of less than 3000 K (rotation period < 5 days). In between is the Rhines rotation regime, which retains a thermally-direct circulation from day to night side but also features midlatitude turbulence-driven zonal jets. Rhines rotators occur for planets around stars in the range of 3000 K to 3300 K (rotation period ~ 5 to 20 days), where the Rhines length is greater than planetary radius but the Rossby deformation radius is less than planetary radius. The dynamical state can be observationally inferred from comparing the morphology of the thermal emission phase curves of synchronously rotating planets., Comment: 33 pages, 11 figures. The update corrects the definition in Eq. (8) and of beta. The results are unaffected as these were transcription errors only and did not influence the calculations. Errata are published at doi:10.3847/1538-4357/ab9a4b and doi:10.3847/1538-4357/abb19a

This research paper focuses on how innovations support new market creation emerging from latent opportunities for low-income group. It also emphasizes on novel strategies that can be implemented for sustaining. The paper concludes with a discussion on the implications of the study and directions to stimulate future research on the subject., Comment: 13 pages

The main idea of this paper is to represent shopping items through vectors because these vectors act as the base for building em- beddings for customers and shopping carts. Also, these vectors are input to the mathematical models that act as either a recommendation engine or help in targeting potential customers. We have used exponential family embeddings as the tool to construct two basic vectors - product embeddings and context vectors. Using the basic vectors, we build combined embeddings, trip embeddings and customer embeddings. Combined embeddings mix linguistic properties of product names with their shopping patterns. The customer embeddings establish an understand- ing of the buying pattern of customers in a group and help in building customer profile. For example a customer profile can represent customers frequently buying pet-food. Identifying such profiles can help us bring out offers and discounts. Similarly, trip embeddings are used to build trip profiles. People happen to buy similar set of products in a trip and hence their trip embeddings can be used to predict the next product they would like to buy. This is a novel technique and the first of its kind to make recommendation using product, trip and customer embeddings., Comment: Cicling 2017

Distant planets in globally ice-covered, "snowball", states may depend on increases in their host stars' luminosity to become hospitable for surface life. Using a General Circulation Model (GCM), we simulated the equilibrium climate response of a planet to a range of instellations from an F-, G-, or M- dwarf star. The range of instellation that permits both complete ice cover and at least partially ice-free climate states is a measure of the climate hysteresis that a planet can exhibit. An ice-covered planet with high climate hysteresis would show a higher resistance to the initial loss of surface ice coverage with increases in instellation, and abrupt, extreme ice loss once deglaciation begins. Our simulations indicate that the climate hysteresis depends sensitively on the host star spectral energy distribution. Under fixed CO2 conditions, a planet orbiting an M-dwarf star exhibits a smaller climate hysteresis, requiring a smaller instellation to initiate deglaciation than planets orbiting hotter, brighter stars. This is due to the higher absorption of near-IR radiation by ice on the surfaces and greenhouse gases and clouds in the atmosphere of an M-dwarf planet. Increases in atmospheric CO2 further lower the climate hysteresis, as M-dwarf snowball planets exhibit a larger radiative response than G-dwarf snowball planets for the same increase in CO2. For a smaller hysteresis, planets near the outer edge of the habitable zone will thaw earlier in their evolutionary history, and will experience a less abrupt transition out of global ice cover., Comment: 19 pages, 4 figures, 1 table, accepted for publication in ApJ Letters

The effect of geometrical perturbations on ion oscillation frequencies in a 3-D quadrupole trap is analyzed by theoretical simulations and compared with the experimental results. Theoretically, the distorted potential within this non-ideal trap caused by the insertion of filament has been simulated. An analytical expression for the potential is then fitted and numerical solution of the equations of trapped ion motion is obtained. Motional frequencies are then calculated from the Fourier transformation of the simulated ion trajectories at any given trapping potential and compared with our experimental findings. The shift in the secular frequency with respect to the level of insertion of the filament within the trap is evaluated.

Planetary climate can be affected by the interaction of the host star spectral energy distribution with the wavelength-dependent reflectivity of ice and snow. Here we explore this effect using a one dimensional (1-D), line-by-line, radiative-transfer model to calculate broadband planetary albedos as input to a seasonally varying, 1-D energy-balance climate model. A three-dimensional general circulation model is also used to explore the atmosphere's response to changes in incoming stellar radiation, or instellation, and surface albedo. Using this hierarchy of models we simulate planets covered by ocean, land, and water ice of varying grain size, with incident radiation from stars of different spectral types. Terrestrial planets orbiting stars with higher near-UV radiation exhibit a stronger ice-albedo feedback. We find that ice-covered conditions occur on an F-dwarf planet with only a 2% reduction in instellation relative to the present instellation on Earth, assuming fixed CO2 (present atmospheric level on Earth). A similar planet orbiting the Sun at an equivalent flux distance requires an 8% reduction in instellation, while a planet orbiting an M-dwarf star requires an additional 19% reduction in instellation to become ice-covered, equivalent to 73% of the modern solar constant. The surface ice-albedo feedback effect becomes less important at the outer edge of the habitable zone, where atmospheric CO2 can be expected to be high in order to maintain clement conditions for surface liquid water. We show that 3-10 bars of CO2 will entirely mask the climatic effect of ice and snow, leaving the outer limits of the habitable zone unaffected by the spectral dependence of water ice and snow albedo. However, less CO2 is needed to maintain open water for a planet orbiting an M-dwarf star, than would be the case for hotter main-sequence stars., Comment: 63 pages, 2 tables, 20 figures; accepted for publication in Astrobiology

Stable, hydrogen-burning, M dwarf stars comprise about 75% of all stars in the Galaxy. They are extremely long-lived and because they are much smaller in mass than the Sun (between 0.5 and 0.08 MSun), their temperature and stellar luminosity are low and peaked in the red. We have re-examined what is known at present about the potential for a terrestrial planet forming within, or migrating into, the classic liquid-surface-water habitable zone close to an M dwarf star. Observations of protoplanetary disks suggest that planet-building materials are common around M dwarfs, but N-body simulations differ in their estimations of the likelihood of potentially-habitable, wet planets residing within their habitable zones, which are only ~ 1/5 to 1/50 of the width of that for a G star. Particularly in light of the claimed detection of the planets with masses as small as 5.5 and 7.5 MEarth orbiting M stars, there seems no reason to exclude the possibility of terrestrial planets. Tidally locked synchronous rotation within the narrow habitable zone doesn't necessarily lead to atmospheric collapse, and active stellar flaring may not be as much of an evolutionarily disadvantageous factor as has previously been supposed. We conclude that M dwarf stars may indeed be viable hosts for planets on which the origin and evolution of life can occur. A number of planetary processes such as cessation of geothermal activity, or thermal and non-thermal atmospheric loss processes may limit the duration of planetary habitability to periods far shorter than the extreme lifetime of the M dwarf star. Nevertheless, it makes sense to include M dwarf stars in programs that seek to find habitable worlds and evidence of life., Comment: To be published in Astrobiology. approx. 34 pages