In this work we provide a comprehensive review of theoretical and experimental studies of the properties of polarons formed by mobile impurities strongly interacting with quantum many-body systems. We present a unified perspective on the universal concepts and theoretical techniques used to characterize polarons in two distinct platforms, ultracold atomic gases and atomically-thin transition metal dichalcogenides, which are linked by many deep parallels. We review polarons in both fermionic and bosonic environments, highlighting their similarities and differences including the intricate interplay between few- and many-body physics. Various kinds of polarons with long-range interactions or in magnetic backgrounds are discussed, and the theoretical and experimental progress towards understanding interactions between polarons is described. We outline how polaron physics, regarded as the low density limit of quantum mixtures, provides fundamental insights regarding the phase diagram of complex condensed matter systems. Furthermore, we describe how polarons may serve as quantum sensors of many-body physics in complex environments. Our work highlights the open problems, identifies new research directions and provides a comprehensive framework for this rapidly evolving research field.

Bose-Einstein condensation represents a remarkable phase transition, characterized by the formation of a single quantum subsystem. As a result, the statistical properties of the condensate are highly unique. In the case of a Bose gas, while the mean number of condensed atoms is independent of the choice of statistical ensemble, the microcanonical, canonical, or grand canonical variances differ significantly among these ensembles. In this paper, we review the progress made over the past 30 years in studying the statistical fluctuations of Bose-Einstein condensates. Focusing primarily on the ideal Bose gas, we emphasize the inequivalence of the Gibbs statistical ensembles and examine various approaches to this problem. These approaches include explicit analytic results for primarily one-dimensional systems, methods based on recurrence relations, asymptotic results for large numbers of particles, techniques derived from laser theory, and methods involving the construction of statistical ensembles via stochastic processes, such as the Metropolis algorithm. We also discuss the less thoroughly resolved problem of the statistical behavior of weakly interacting Bose gases. In particular, we elaborate on our stochastic approach, known as the hybrid sampling method. The experimental aspect of this field has gained renewed interest, especially following groundbreaking recent measurements of condensate fluctuations. These advancements were enabled by unprecedented control over the total number of atoms in each experimental realization. Additionally, we discuss the fluctuations in photonic condensates as an illustrative example of grand canonical fluctuations. Finally, we briefly consider the future directions for research in the field of condensate statistics.

The physics of impurities in a bosonic quantum environment is a paradigmatic and challenging many-body problem that remains to be understood in its full complexity. Here, this problem is investigated for impurities with strong repulsive interactions based on Ramsey interferometry in a quantum degenerate gas of 39K atoms. We observe an oscillatory signal that is consistent with a quantum beat between two co-existing coherent quasiparticle states: the attractive and repulsive polarons. The interferometric signal allows us to extract the polaron energies for a wide range of interaction strengths, complimenting earlier spectroscopic measurements. We furthermore identify several dynamical regimes towards the formation of the Bose polaron in good agreement with theory. Our results improve the understanding of quantum impurities interacting strongly with a bosonic environment, and demonstrate how quasiparticles as well as short-lived non-equilibrium many-body states can be probed using Ramsey interferometry.

The accurate determination of atom numbers is an ubiquitous problem in the field of ultracold atoms. For modest atom numbers, absolute calibration techniques are available, however, for large numbers and high densities, the available techniques neglect many-body scattering processes. Here, a spatial calibration technique for time-of-flight absorption images of ultracold atomic clouds is presented. The calibration is obtained from radially averaged absorption images and we provide a practical guide to the calibration process. It is shown that the calibration coefficient scales linearly with optical density and depends on the absorbed photon number for the experimental conditions explored here. This allows for the direct inclusion of a spatially dependent calibration in the image analysis. For typical ultracold atom clouds the spatial calibration technique leads to corrections in the detected atom number up to ≈ 12 % and temperature up to ≈ 14 % in comparison to previous calibration techniques. The technique presented here addresses a major difficulty in absorption imaging of ultracold atomic clouds and prompts further theoretical work to understand the scattering processes in ultracold dense clouds of atoms for accurate atom number calibration.

The investigation of the fluctuations in interacting quantum systems at finite temperatures showcases the ongoing challenges in understanding complex quantum systems. Recently, atom number fluctuations in weakly interacting Bose-Einstein condensates were observed, motivating an investigation of the thermal component of partially condensed Bose gases. Here, we present a combined analysis of both components, revealing the presence of fluctuations in the thermal component. This analysis includes a comprehensive statistical evaluation of uncertainties in the preparation and parameter estimation of partially condensed Bose gases. Using Monte Carlo simulations of optical density profiles, we estimate the noise contributions to the atom number and temperature estimation of the condensed and thermal cloud, which is generally applicable in the field of ultracold atoms. Furthermore, we investigate the specific noise contributions in the analysis of atom number fluctuations and show that preparation noise in the total atom number leads to an important technical noise contribution. Subtracting all known noise contributions from the variance of the atom number in the BEC and thermal component allows us to improve the estimate of the fundamental peak fluctuations.

The fluctuations of the atom number between a Bose-Einstein condensate and the sur-rounding thermal gas have been the subject of a long standing theoretical debate. This discussion is centered around the appropriate thermodynamic ensemble to be used for theoretical predictions and the effect of interactions on the observed fluctuations. Here we introduce the so-called Fock state sampling method to solve this classic problem of current experimental interest for weakly interacting gases. A suppression of the pre-dicted peak fluctuations is observed when using a microcanonical with respect to a canonical ensemble. Moreover, interactions lead to a shift of the temperature of peak fluctuations for harmonically trapped gases. The absolute size of the fluctuations fur-thermore depends on the total number of atoms and the aspect ratio of the trapping potential. Due to the interplay of these effect, there is no universal suppression or en-hancement of fluctuations.

We study the statistical properties of a gas of interacting bosons trapped in a box potential in two and three dimensions. Our primary focus is the characteristic temperature $\tchar$, i.e. the temperature at which the fluctuations of the number of condensed atoms (or, in 2D, the number of motionless atoms) is maximal. Using the Fock State Sampling method, we show that $\tchar$ increases due to interaction. In 3D, this temperature converges to the critical temperature in the thermodynamic limit. In 2D we show the general applicability of the method by obtaining a generalized dependence of the characteristic temperature on the interaction strength. Finally, we discuss the experimental conditions necessary for the verification of our theoretical predictions.

Alkali-metal dimers, Ak2, residing on the surface of He nanodroplets, are doubly ionized due to multiphoton absorption from an intense 50-fs laser pulse leading to fragmentation into a pair of alkali-metal cations. Based on the measured kinetic energy distributions P(Ekin) of the Ak+ fragment ions, we retrieve the distribution of internuclear distances P(R) via the Ak22+ potential curve. Results are obtained for Na2, K2, Rb2, and Cs2 in both the 11Eg+ ground state and the lowest-lying triplet state 1 3Eu+ and for Li2 in the 1 3Eu+ state. For Li2, K2, and Rb2, the center of the measured P(R) is close to the center of the wave function kIi(R) of the vibrational ground state in the 1 1Eg+ and 13Eu+ states, whereas for Na2 and Cs2 small shifts are observed. For all the Ak2, the width of the measured P(R) is broader than |kIi(R)|2 by a factor of 2-4. We discuss that resonance effects in the multiphoton ionization and interaction of the Ak+ ion with the He droplet give rise to the observed deviations of P(R) from |kIi(R)|2. Despite these deviations, we deem that timed Coulomb explosion will allow imaging of vibrational wave packets in alkali-metal dimers on He droplets surfaces.

We summarise the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with the European Space Agency (ESA) and national space and research funding agencies.

We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behavior for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interaction, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.

Spectroscopic and interferometric measurements complement each other in extracting the fundamental properties of quantum many-body systems. While spectroscopy provides precise measurements of equilibrated energies, interferometry can elucidate the dynamical evolution of the system. For an impurity immersed in a bosonic medium, both are equally important for understanding the quasiparticle physics of the Bose polaron. Here, we compare the interferometric and spectroscopic timescales to the underlying dynamical regimes of the impurity dynamics and the polaron lifetime, highlighting the capability of the interferometric approach to clearly resolve polaron dynamics. In particular, interferometric measurements of the coherence amplitude at strong interactions reveal faster quantum dynamics at large repulsive interaction strengths than at unitarity. These observations are in excellent agreement with a short-time theoretical prediction including both the continuum and the attractive polaron branch. For longer times, qualitative agreement with a many-body theoretical prediction which includes both branches is obtained. Moreover, the polaron energy is extracted from interferometric measurements of the observed phase velocity in agreement with previous spectroscopic results from weak to strong attractive interactions. Finally, the phase evolution allows for the measurement of an energetic equilibration timescale, describing the initial approach of the phase velocity to the polaron energy. Theoretically, this is shown to lie within the regime of universal dynamics revealing a fast initial evolution towards the formation of polarons. Our results give a comprehensive picture of the many-body physics governing the Bose polaron and thus validates the quasiparticle framework for further studies.

Magnus G. Skou1, Kristian K. Nielsen1, Thomas G. Skov1, Andreas M. Morgen1, Nils B. Jørgensen1, Arturo Camacho-Guardian2, Thomas Pohl1, Georg M. Bruun1,3, and Jan J. Arlt1 1 Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark. 2 Departamento de Fı́sica Quı́mica, Instituto de Fı́sica, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Ciudad de México C.P. 01000, Mexico. and 3 Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China. (Dated: April 5, 2022)

Rubidium dimers residing on the surface of He nanodroplets are doubly ionized by an intense femtosecond laser pulse leading to fragmentation into a pair of Rb^{+} ions. We show that the kinetic energy of the Rb^{+} fragment ions can be used to identify dimers formed in either the X ^{1}Σ_{g}^{+} ground state or in the lowest-lying triplet state, a ^{3}Σ_{u}^{+}. From the experiment, we estimate the abundance ratio of dimers in the a and X states as a function of the mean droplet size and find values between 4∶1 and 5∶1. Our technique applies generally to dimers and trimers of alkali atoms, here also demonstrated for Li_{2}, Na_{2}, and K_{2}, and will enable femtosecond time-resolved measurements of their rotational and vibrational dynamics, possibly with atomic structural resolution.

Advancing our understanding of non-equilibrium phenomena in quantum many-body systems remains one of the greatest challenges in physics. Here we report on the experimental observation of a paradigmatic many-body problem, namely the non-equilibrium dynamics of a quantum impurity immersed in a bosonic environment(1,2). We use an interferometric technique to prepare coherent superposition states of atoms in a Bose-Einstein condensate with a small impurity-state component, and monitor the evolution of such quantum superpositions into polaronic quasiparticles. These results offer a systematic picture of polaron formation(3-7) from weak to strong impurity interactions. They reveal three distinct regimes of evolution with dynamical transitions that provide a link between few-body processes and many-body dynamics. Our measurements reveal universal dynamical behaviour in interacting many-body systems and demonstrate new pathways to study non-equilibrium quantum phenomena.

Remote control of experimental systems allows for improved collaboration between research groups as well as unique remote educational opportunities accessible by students and citizen scientists. Here, we describe an experiment for the production and investigation of ultracold quantum gases capable of asynchronous remote control by multiple remote users. This is enabled by a queuing system coupled to an interface that can be modified to suit the user, e.g. a gamified interface for use by the general public or a scripted interface for an expert. To demonstrate this, the laboratory was opened to remote experts and the general public. During the available time, remote users were given the task of optimising the production of a Bose-Einstein condensate (BEC). This work thus provides a stepping stone towards the exploration and realisation of more advanced physical models by remote experts, students and citizen scientists alike.

We observe monopole oscillations in a mixture of Bose-Einstein condensates, where the usually dominant mean-field interactions are canceled. In this case, the system is governed by the next-order Lee-Huang-Yang (LHY) correction to the ground state energy, which describes the effect of quantum fluctuations. Experimentally such a LHY fluid is realized by controlling the atom numbers and interaction strengths in a ^{39}K spin mixture confined in a spherical trap potential. We measure the monopole oscillation frequency as a function of the LHY interaction strength as proposed recently by Jrgensen et al. [Phys. Rev. Lett. 121, 173403 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.173403] and find excellent agreement with simulations of the complete experiment including the excitation procedure and inelastic losses. This confirms that the system and its collective behavior are initially dominated by LHY interactions. Moreover, the monopole oscillation frequency is found to be stable against variations of the involved scattering lengths in a broad region around the ideal values, confirming the stabilizing effect of the LHY interaction. These results pave the way for using the nonlinearity provided by the LHY term in quantum simulation experiments and for investigations beyond the LHY regime.

An impurity immersed in a medium constitutes a canonical scenario applicable in a wide range of fields in physics. Though our understanding has advanced significantly in the past decades, quantum impurities in a bosonic environment are still of considerable theoretical and experimental interest. Here, we discuss the initial dynamics of such impurities, which was recently observed in interferometric experiments. Experimental observations from weak to unitary interactions are presented and compared to a theoretical description. In particular, the transition between two initial dynamical regimes dominated by two-body interactions is analyzed, yielding transition times in clear agreement with the theoretical prediction. Additionally, the distinct time dependence of the coherence amplitude in these regimes is obtained by extracting its power-law exponents. This benchmarks our understanding and suggests new ways of probing dynamical properties of quantum impurities.

ABSTRACT Photoelectron images have been measured following the ionisation of aligned distributions of gas phase naphthalene and aniline molecules. Alignment in the adiabatic regime was achieved by interaction with a 100 ps infrared laser pulse, with ionisation achieved in a two-photon resonant scheme using a low intensity UV pulse of ∼6 ps duration. The resulting images are found to exhibit anisotropy that increases when the alignment pulse is present, with the aniline PADs peaking along the polarisation vector of the ionising light and the naphthalene PADs developing a characteristic four-lobed structure. Photoelectron angular distributions (PADs) that result from the ionisation of unaligned and fully aligned distributions of molecules are calculated using the ePolyScat ab initio suite and converted into two-dimensional photoelectron images. In the case of naphthalene excellent agreement is observed between experiment and the simulation for the fully aligned distribution, showing that the alignment step allows us to probe the molecular frame, but in the case of aniline it is clear that additional processes occur following the one-photon resonant step. GRAPHICAL ABSTRACT

The analysis of entangled atomic ensembles and their application for interferometry beyond the standard quantum limit requires an accurate determination of the number of atoms. We present an accurate fluorescence detection technique for atoms that is fully integrated into an experimental apparatus for the production of many-particle entangled quantum states. Number-resolved fluorescence measurements with single-atom accuracy for 1 up to 30 atoms are presented. According to our noise analysis, we extrapolate that the single-atom accuracy extends to a limiting atom number of 390(20) atoms. We utilize the accurate atom number detection for a number stabilization of the laser-cooled atomic ensemble. For a target ensemble size of 7 atoms prepared on demand, we achieve a 92(2)% preparation fidelity and reach number fluctuations 18(1) dB below the shot noise level using real-time feedback on the magneto-optical trap.