In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional (1D) systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that 1D fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro-and antiferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.

We discuss the ground state properties of a one-dimensional bosonic system doped with an impurity (the so-called Bose polaron problem). We introduce a formalism that allows us to calculate analytically the thermodynamic zero-temperature properties of this system with weak and moderate boson-boson interaction strengths for any boson-impurity interaction. Our approach is validated by comparing to exact quantum Monte Carlo calculations. In addition, we test the method in finite size systems using numerical results based upon the similarity renormalization group. We argue that the introduced approach provides a simple analytical tool for studies of strongly interacting impurity problems in one dimension.The weakly-interacting Bose gas is a beautiful model system [1], which is often used to study emergent manybody phenomena such as superfluidity, Bose-Einstein condensation, and topologically non-trivial many-body excitations like solitons and vortices. The basic properties of this model are well understood theoretically and tested experimentally (see, e.g., Refs. [2,3]). However, some important questions still remain open. One of them concerns the reaction of a Bose gas to a mobile impurity particle, which is usually referred to as the Bose polaron problem, in analogy to the polaron studied by Landau and Pekar [4]. Polaron problems are among the simplest problems exhibiting non-trivial many-body effects that shed light on the interplay of one-and many-body physics. However, the fate of the impurity in a gas is not of only formal interest. Properties of many systems in condensed matter physics can be understood by studying a single particle interacting with a reservoir. Prominent examples are given by a single 3 He atom in liquid 4 He [5] and an electron in an ionic crystal (often described as a particle interacting with a Bose field of ion vibrations), see [6] and references therein. The apparent simplicity of these problems is misleading, as to date they resist a full theoretical solution. Fortunately, experiments with cold atomic gases, realizing the idea of a quantum simulator [7], open up the possibility to create and study the Bose polaron [8][9][10][11][12][13][14][15] in a laboratory. This intriguing possibility motivated a flurry of recent theoretical works on this problem [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].One-dimensional (1D) systems are of special interest in this context, because strongly interacting bosons in 1D fermionize [36]. This phenomenon simplifies the analysis. For example, if all the masses in the system are identical, the Bose polaron problem is exactly solvable [37]. This is also true if the impurity is infinitely heavy [30]. Therefore, a solution of the problem for weak and moderate boson-boson interaction is enough to complete the picture for all interaction strengths. However, theoretical approaches face challenges in describing these parameter regimes if the boson-impurity interactions are strong [38]. In this case accurate results can be obtai...

We consider a one-dimensional gas of cold atoms with strong contact interactions and construct an effective spin-chain Hamiltonian for a two-component system. The resulting Heisenberg spin model can be engineered by manipulating the shape of the external confining potential of the atomic gas. We find that bosonic atoms offer more flexibility for tuning independently the parameters of the spin Hamiltonian through interatomic (intra-species) interaction which is absent for fermions due to the Pauli exclusion principle. Our formalism can have important implications for control and manipulation of the dynamics of few-and many-body quantum systems; as an illustrative example relevant to quantum computation and communication, we consider state transfer in the simplest non-trivial system of four particles representing exchange-coupled qubits.

The nature of strongly interacting Fermi gases and magnetism is one of the most important and studied topics in condensed-matter physics. Still, there are many open questions. A central issue is under what circumstances strong short-range repulsive interactions are enough to drive magnetic correlations. Recent progress in the field of cold atomic gases allows one to address this question in very clean systems where both particle numbers, interactions and dimensionality can be tuned. Here we study fermionic few-body systems in a one dimensional harmonic trap using a new rapidly converging effective-interaction technique, plus a novel analytical approach. This allows us to calculate the properties of a single spin-down atom interacting with a number of spin-up particles, a case of much recent experimental interest. Our findings indicate that, in the strongly interacting limit, spin-up and spin-down particles want to separate in the trap, which we interpret as a microscopic precursor of one-dimensional ferromagnetism in imbalanced systems. Our predictions are directly addressable in current experiments on ultracold atomic few-body systems.We are interested in obtaining numerically exact eigensolutions for the system of trapped atoms with arbitrary strong, zero-range interaction between different spin components. We use New J. Phys. 16 (2014) 063003 E J Lindgren et al New J. Phys. 16 (2014) 063003 E J Lindgren et al 3 New J. Phys. 16 (2014) 063003 E J Lindgren et al 5 New J. Phys. 16 (2014) 063003 E J Lindgren et al 7 4 We thank the group of Selim Jochim for a comparison of our results to their unpublished data for = − − g 1.3 1 .

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.