The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations. Finally, the experimental systems that can be described in terms of models of interacting bosons in one dimension are discussed

We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate T1(-1) at 250 mK and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and the Luttinger liquid model tested in detail over the whole fermion band.

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (C 5 H 12 N) 2 CuBr 4 (BPCB). We use a combination of numerical and analytical methods, in particular, the density-matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic-field dependence of the nuclear-magnetic-resonance relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore, we compute, using time-dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to describe directly the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high-energy part of the spectrum that are potentially testable in future experiments.

The ground state and structure of a one-dimensional Bose gas with dipolar repulsions is investigated at zero temperature by a combined Reptation Quantum Monte Carlo (RQMC) and bosonization approach. A non trivial Luttinger-liquid behavior emerges in a wide range of intermediate densities, evolving into a Tonks-Girardeau gas at low density and into a classical quasi-ordered state at high density. The density dependence of the Luttinger exponent is extracted from the numerical data, providing analytical predictions for observable quantities, such as the structure factor and the momentum distribution. We discuss the accessibility of such predictions in current experiments with ultracold atomic and molecular gases. More recent experiments have demonstrated that the range of the interactions can also be manipulated. Dipole interactions with long-range anisotropic character have been observed in 52 Cr atoms [7] after exploiting the large magnetic moments of this atomic species, that is µ d ≈ 6µ B with µ B being the Bohr magneton. A BEC containing up to 50000 52 Cr atoms has then been obtained below a transition temperature T c ≃ 700nK [8] and its dynamical behavior is being investigated [9]. Promising proposals to tune and shape the dipolar interaction strength in quantum gasees of heteronuclear polar molecules have more recently been suggested [10]. Significant theoretical predictions have accompanied such realizations [11]. The stability diagram of anisotropic confined dipolar gases has been predicted to be governed by the trapping geometry [12,13], as corroborated by Path-Integral QMC studies [14]. Different conclusions are reached by more recent Diffusion QMC simulations including the dependence of a on the dipole interaction [15]. PACSTuning of the interactions can be combined with the enhancement of quantum fluctuations after reducing their dimensionality by e.g. storing them in elongated traps [16,17], which could be relevant to applications such as precision measurements [18], quantum computing [19], atomtronic quantum devices, and theoretical investigations of novel quantum phase transitions [20].In the case of quasi one-dimensional (1D) condensates with short-range interactions, a rich phenomenology is known to emerge from the collective character of the single-particle degrees of freedom, despite the absence of broken symmetries [21]. Bosons are known to arrange in a Luttingerliquid state, with single particles being replaced by collective density excitations [22,23]. Strong repulsion may also lead to the fermionization of interacting bosons in the so-called Tonks-Girardeau (TG) regime [24,25,26]. Experiments in elongated traps have provided evidence for such 1D fluctuations [16].In the case of quasi-1D condensates with dipolar interactions, an interesting question arises whether the quantum fluctuations are sufficiently enhanced to drive the BEC in a strong-coupling regime. More recent Diffusion QMC simulations [27] for a homogeneous 1D dipolar Bose gas have revealed a crossover behavior with increasing li...

Field-controlled magnetic order in the quantum spin-ladder system (Hpip)2CuBr4