We show, using quasi-exact numerical simulations, that Anderson localization in a disordered one-dimensional potential survives in the presence of attractive interaction between particles. The localization length of the particles' center of mass-computed analytically for weak disorder-is in good agreement with the quasi-exact numerical observations using the time evolving block decimation algorithm. Our approach allows for simulation of the entire experiment including the final measurement of all atom positions. IOP Publishing Ltd and Deutsche Physikalische Gesellschaft to a recent revival of interest in localization properties in general, and in AL in particular. AL is characterized by the inhibition of transport in a quantum system, whose classical counterpart behaves diffusively. It is accompanied by an exponential localization of eigenstates in the configuration space, |ψ(r )| 2 ∝ exp(−|r |/L), where L is the localization length. AL is due to the interference between various multiple scattering paths which favors the return of the particle to its initial position and thus decreases the probability of it traveling a long distance. As the geometry of these paths depends on the system dimension, so AL features depend on the dimension too. For one-dimensional (1D) systems, AL is a generic single-particle behavior even for very small disorder when the particle 'flies' above the potential fluctuations.A fundamental question is to understand how interaction between particles affects AL. Presently, there is no consensus on the possible existence and properties of many-body localization. Some results suggest that AL survives for few-body systems, although with a modified localization length [3]; studies of cold bosonic systems in the mean-field regime show that AL is destroyed and replaced by a sub-diffusive behavior [4,5], but the validity of the meanfield approximation at long times is questionable. There are even predictions that AL survives at finite temperature in the thermodynamic limit, in the presence of interactions [6]. In this paper, we show, using a specific example, that 1D AL survives in the presence of attractive interactions and is even a rather robust phenomenon. The novelty of our approach is that it uses a quasi-exact numerical scheme to solve the full many-body problem in the presence of disorder. Here, quasiexact means that all numerical errors can be controlled and reduced below an arbitrary value, just at the cost of increased computational resources. The big advantage of this approach is not to rely on neglecting a priori any physical process.Atomic matter waves have several advantages that made possible an unambiguous demonstration of single-particle AL in 1D [7,8]: atom-atom interaction can be reduced by either diluting the atomic gas or using Feshbach resonances, ensuring a very long coherence time of the atomic matter wave; the spatial and temporal orders of magnitude are very convenient, allowing a direct spatio-temporal visualization of the dynamics; all microscopic ingredients are well c...

Potential realization of a quantum thermometer operating in the nanokelvin regime, formed by a few-fermionic mixture confined in a one-dimensional harmonic trap, is proposed. Thermal states of the system are studied theoretically from the point of view of fundamental sensitivity to temperature changes. It is pointed out that the ability to control the interaction strength in such systems allows obtaining high-temperature sensitivity in the regime where the temperature is much lower than the characteristic temperature scale determined by a harmonic confinement. This sensitivity is very close to the fundamental bound that involves optimal engineering of level separations. The performance of practical measurement schemes and the possible experimental coupling of the thermometer to the probe are discussed.

We study the influence of Rydberg dressed interactions in a one-dimensional (1D) Bose-Einstein Condensate (BEC). We show that a 1D geometry offers several advantages over 3D for observing BEC Rydberg dressing. The effects of dressing are studied by investigating collective BEC dynamics after a rapid switch-off of the Rydberg dressing interaction. The results can be interpreted as an effective modification of the s-wave scattering length. We include this modification in an analytical model for the 1D BEC, and compare it to numerical calculations of Rydberg dressing under realistic experimental conditions.

The accumulation of atoms in the lowest energy level of a trap and the subsequent out-coupling of these atoms is a realization of a matter-wave analog of a conventional optical laser. Optical random lasers require materials that provide optical gain but, contrary to conventional lasers, the modes are determined by multiple scattering and not a cavity. We show that a Bose-Einstein condensate can be loaded in a spatially correlated disorder potential prepared in such a way that the Anderson localization phenomenon operates as a band-pass filter. A multiple scattering process selects atoms with certain momenta and determines laser modes which represents a matter-wave analog of an optical random laser.Comment: 4 pages, 3 figures version accepted for publication in Phys. Rev. A; minor changes, the present title substituted for "Atom Random Laser

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