Abstract. This article reviews the recent theoretical and experimental advances in the study of ultracold gases made of bosonic particles interacting via the longrange, anisotropic dipole-dipole interaction, in addition to the short-range and isotropic contact interaction usually at work in ultracold gases. The specific properties emerging from the dipolar interaction are emphasized, from the meanfield regime valid for dilute Bose-Einstein condensates, to the strongly correlated regimes reached for dipolar bosons in optical lattices.

We find that pancake dipolar condensates can exhibit a roton-maxon character of the excitation spectrum, so far only observed in superfluid helium. We also obtain a condition for the dynamical stability of these condensates. The spectrum and the border of instability are tunable by varying the particle density and/or the confining potential. This opens wide possibilities for manipulating the superfluid properties of dipolar condensates.Recent progress in cooling and trapping of polar molecules [1, 2] opens fascinating prospects for achieving quantum degeneracy in trapped gases of dipolar particles. Being electrically or magnetically polarized, polar molecules interact with each other via long-range anisotropic dipole-dipole forces. This makes the properties of such dipolar gases drastically different from the properties of commonly studied atomic cold gases, where the interparticle interaction is short-range. Other candidates to form a dipolar gas are atoms with large magnetic moments [3,4], and atoms with dc-field-[5] or lightinduced electric dipole moments [6,7,8].The dipole-dipole interaction is responsible for a variety of novel phenomena in ultracold dipolar systems. The energy independence of the dipole-dipole scattering amplitude for any orbital angular momenta provides realistic possibilities for achieving a superfluid BCS transition in single-component dipolar Fermi gases (see [9] and refs. therein). Dipolar bosons in optical lattices have been shown to provide a highly controllable environment for engineering various quantum phases [10]. In addition to superfluid and Mott-Insulator ones, recently observed in Munich experiments [11] with bosonic atoms, the long-range dipole-dipole potential provides supersolid and checker-board phases. Dipole-dipole interactions are also responsible for spontaneous polarization and spin waves in spinor condensates in optical lattices [12], and may lead to self-bound structures in the field of a traveling wave [13]. Recently, dipolar particles have been considered as promising candidates for the implementation of fast and robust quantum-computing schemes [8,14].The long-range and anisotropic (partially attractive) character of dipole-dipole forces ensures a strong dependence of the stability of trapped dipolar Bose-Einstein condensates on the trapping geometry [7]. For cylindrical traps with the aspect ratio l z /l ρ > l * = 0.43, a purely dipolar condensate is dynamically unstable if the number of particles N exceeds a critical value. A detailed study of the excitation modes for this geometry is contained in Ref. [15]. It has also been argued in Ref. [7] that in pancake traps with l z /l ρ < l * the ground state solution is expected for any N .In this Letter we analyze the nature of excitations and instability of pancake-shaped dipolar condensates. For this purpose, we consider the physically transparent case of an infinite pancake trap, with the dipoles perpendicular to the trap plane. For the maximum condensate density n 0 → ∞, the dynamical stability requires the pre...

We discuss Bose-Einstein condensation in a trapped gas of bosonic particles interacting dominantly via dipole-dipole forces. We find that in this case the mean-field interparticle interaction and, hence, the stability diagram are governed by the trapping geometry. Possible physical realisations include ultracold heteronuclear molecules, or atoms with laser induced electric dipole moments.Bose-Einstein condensation (BEC) of trapped atomic gases [1,2] offers unique possibilities to highlight a general physical problem of how the nature and stability of a Bose-condensed state is influenced by the character of interparticle interaction. In this respect, especially interesting are ultra-cold gases with attractive interaction between particles (scattering length a < 0). As known [3], spatially homogeneous condensates with a < 0 are absolutely unstable with regard to local collapses. The presence of the trapping field changes the situation drastically. This has been revealed in the successful experiments at Rice [2] on BEC of magnetically trapped atomic 7 Li (a = −14Å). As found in theoretical studies [3], if the number of Bose-condensed particles is sufficiently small (of order 10 3 in the conditions of the Rice experiments) and the spacing between the trap levels exceeds the mean-field interparticle interaction n 0 |g| (n 0 is the condensate density, g = 4πh 2 a/M , where M is the atom mass), there will be a metastable Bose-condensed state. In other words, the condensate is stabilized if the negative pressure caused by the interparticle attraction is compensated by the quantum pressure imposed by the trapping potential. In some sense, this is similar to the gas-liquid phase transition in a classical system with interparticle attraction: The gas phase is stable as long as the thermal pressure exceeds the (negative) interactioninduced pressure (see [4]).The recent success in creating ultra-cold molecular clouds [5][6][7] opens fascinating prospects to achieve quantum degeneracy in trapped gases of heteronuclear molecules. In a sufficiently high electric field "freezing" their rotational motion, these molecules interact via the dipole-dipole forces. This interaction is long-range and anisotropic (partially attractive), and there is a nontrivial question of achieving BEC and manipulating condensates in trapped gases of dipolar particles.Thus far, only the interaction between (small) atomic dipoles has been included in the discussion of the condensate properties. Góral et al. [8] considered the effect of magnetic dipole interaction in a trapped spinpolarized atomic condensate. Magnetic dipoles are small (of the order the Bohr magneton µ B ), and even for atoms like Chromium (6µ B ) the magnetic interactions are dominated by the Van der Waals forces. Nevertheless, for a relatively small scattering length a the condensate wave function may develop novel structures reflecting the interplay between the two types of forces. These effects can be amplified by modyfing a, which hopefully will soon become a standard technique [9]...

The ground state of dipolar bosons placed in an optical lattice is analyzed. We show that the modification of experimentally accessible parameters can lead to the realization and control of different quantum phases, including superfluid, supersolid, Mott insulator, checkerboard, and collapse phases.

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.

In a joint experimental and theoretical effort, we report on the formation of a macro-droplet state in an ultracold bosonic gas of erbium atoms with strong dipolar interactions. By precise tuning of the s-wave scattering length below the so-called dipolar length, we observe a smooth crossover of the ground state from a dilute Bose-Einstein condensate (BEC) to a dense macro-droplet state of more than 10 4 atoms. Based on the study of collective excitations and loss features, we quantitative prove that quantum fluctuations stabilize the ultracold gas far beyond the instability threshold imposed by mean-field interactions. Finally, we perform expansion measurements, showing the evolution of the normal BEC towards a three-dimensional self-bound state and show that the interplay between quantum stabilization and three-body losses gives rise to a minimal expansion velocity at a finite scattering length.

Interferometers with atomic ensembles are an integral part of modern precision metrology. However, these interferometers are fundamentally restricted by the shot noise limit, which can only be overcome by creating quantum entanglement among the atoms. We used spin dynamics in Bose-Einstein condensates to create large ensembles of up to 10(4) pair-correlated atoms with an interferometric sensitivity -1.61(-1.1)(+0.98) decibels beyond the shot noise limit. Our proof-of-principle results point the way toward a new generation of atom interferometers.

An ultracold atomic Bose gas in an optical lattice is shown to provide an ideal system for the controlled analysis of disordered Bose lattice gases. This goal may be easily achieved under the current experimental conditions by introducing a pseudorandom potential created by a second additional lattice or, alternatively, by placing a speckle pattern on the main lattice. We show that, for a noncommensurable filling factor, in the strong-interaction limit, a controlled growing of the disorder drives a dynamical transition from superfluid to Bose-glass phase. Similarly, in the weak interaction limit, a dynamical transition from superfluid to Anderson-glass phase may be observed. In both regimes, we show that even very low-intensity disorder-inducing lasers cause large modifications of the superfluid fraction of the system.