We study the ground state of a one-dimensional (1D) trapped Bose gas with two mobile impurity particles. To investigate this setup, we develop a variational procedure in which the coordinates of the impurity particles are slowlike variables. We validate our method using the exact results obtained for small systems. Then, we discuss energies and pair densities for systems that contain of the order of 100 atoms. We show that bosonic noninteracting impurities cluster. To explain this clustering, we calculate and discuss induced impurity-impurity potentials in a harmonic trap. Further, we compute the force between static impurities in a ring (in the manner of the Casimir force), and contrast the two effective potentials: the one obtained from the mean-field approximation, and the one due to the one-phonon exchange. Our formalism and findings are important for understanding (beyond the polaron model) the physics of modern 1D cold-atom systems with more than one impurity.

Strongly interacting one-dimensional quantum systems often behave in a manner that is distinctly different from their higher-dimensional counterparts. When a particle attempts to move in a one-dimensional environment it will unavoidably have to interact and ‘push’ other particles in order to execute a pattern of motion, irrespective of whether the particles are fermions or bosons. A present frontier in both theory and experiment are mixed systems of different species and/or particles with multiple internal degrees of freedom. Here we consider trapped two-component bosons with short-range inter-species interactions much larger than their intra-species interactions and show that they have novel energetic and magnetic properties. In the strongly interacting regime, these systems have energies that are fractions of the basic harmonic oscillator trap quantum and have spatially separated ground states with manifestly ferromagnetic wave functions. Furthermore, we predict excited states that have perfect antiferromagnetic ordering. This holds for both balanced and imbalanced systems, and we show that it is a generic feature as one crosses from few- to many-body systems.

We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.PACS numbers: 03.75. Mn,67.85.Pq An impurity interacting with a reservoir of quantum particles is an essential problem of fundamental physics. Famous examples include a single charge in a polarizable environment, the Landau-Pekar polaron [1, 2], a neutral particle in superfluid 4 He [3], a magnetic impurity in a metal resulting in the Kondo effect [4], and a single scattering potential inside an ideal Fermi gas [5,6]. The latter system is famous for the Anderson's orthogonality catastrophe [7]. In these settings the impurity behavior can provide key insights into the many-body physics and guide our understanding of more general setups.A complicating feature of many impurity problems is the presence of interactions at a level that often precludes the use of perturbative analysis and self-consistent mean-field approximations. This implies that analytical approaches are highly desirable and exact solutions are, when available, coveted tools for benchmarking other techniques. This is particularly true for one-dimensional (1D) homogeneous systems where solutions can often be found based on the Bethe ansatz [8][9][10][11][12][13]. These solutions are the essential ingredients for our analytical understanding of highly controllable experiments with cold atoms [14][15][16][17][18][19]. For instance, the exactly solvable problem of the single impurity in a 1D Fermi sea [10] -the Fermi polaron -can be used to study the atom-by-atom formation of a 1D Fermi sea [20].While Fermi polarons have been studied intensively in recent times using cold atomic setups both experimentally and theoretically [21][22][23][24][25], the physics of impurities in a bosonic environment is only now becoming a frontier in cold atom experiments [26][27][28][29]. This pursuit requires theoretical models for describing the Bose polaron [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], where, in contrast to the Fermi polaron, an exact solution is not known even for a homogeneous 1D system. Here we provide a new theoretical framework that captures the properties of an impurity in a bosonic bath confined in one spatial dimension. Our (semi)-analytical theory thus provides a state-of-the-art tool for exploring the properties of Bose polarons in 1D.The proposed framework works with a zero-range potential of any strength and handles any number of ma- FIG. 1: (color online) a)A sketch of the doubly-degenerate ground state for the system of one A and eight B particles trapped in a one-dimensional harmonic potential ...

The natural habitats of planktonic and swimming microorganisms, from algae in the oceans to bacteria living in soil or intestines, are characterized by highly heterogeneous fluid flows. The complex interplay of flow-field topology, self-propulsion, and porous microstructure is essential to a wide range of biophysical and ecological processes, including marine oxygen production, remineralization of organic matter, and biofilm formation. Although much progress has been made in the understanding of microbial hydrodynamics and surface interactions over the last decade, the dispersion of active suspensions in complex flow environments still poses unsolved fundamental questions that preclude predictive models for microbial transport and spreading under realistic conditions. Here, we combine experiments and simulations to identify the key physical mechanisms and scaling laws governing the dispersal of swimming bacteria in idealized porous media flows. By tracing the scattering dynamics of swimming bacteria in microfluidic crystal lattices, we show that hydrodynamic gradients hinder transverse bacterial dispersion, thereby enhancing stream-wise dispersion ∼100-fold beyond canonical Taylor–Aris dispersion of passive Brownian particles. Our analysis further reveals that hydrodynamic cell reorientation and Lagrangian flow structure induce filamentous density patterns that depend upon the incident angle of the flow and disorder of the medium, in striking analogy to classical light-scattering experiments.

Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the case of equal mass fermions or bosons with two or more internal degrees of freedom, one can map the problem onto the well-known Heisenberg spin models. However, many interesting physical systems contain mixtures of particles with different masses. Therefore, a generalization of the recent strong-coupling techniques would be highly desirable. This is particularly important since such problems are generally considered non-integrable and thus the hugely successful Bethe ansatz approach cannot be applied. Here we discuss some initial steps towards this goal by investigating small ensembles of one-dimensional harmonically trapped particles where pairwise interactions are either vanishing or infinitely strong with focus on the mass-imbalanced case. We discuss a (semi)-analytical approach to describe systems using hyperspherical coordinates where the interaction is effectively decoupled from the trapping potential. As an illustrative example we analyze mass-imbalanced four-particle two-species mixtures with strong interactions between the two species. For such systems we calculate the energies, densities and pair-correlation functions.