We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the selfconsistent theory of localization to show that the long-time behavior of the condensate density is controlled by a single parameter equal to the ratio of the mobility edge and the chemical potential of the condensate. We find that the two critical exponents of the localization transition determine the evolution of the condensate density in time and space. Recently there has been much interest in the possibility of observing Anderson localization of Bose-Einstein condensates obtained by trapping and cooling bosonic atoms [5,6,7,8]. A Bose-Einstein condensate is characterized by a macroscopic occupation of a single quantum state [9] and hence exhibits quantum, wave-like behavior despite its macroscopic size. Atomic Bose-Einstein condensates subjected to random external (optical) potentials are potentially good candidates for observing Anderson localization of matter waves. Up to now, the experiments have focused on 1D configurations [5], where all single-particle eigenstates are localized. In a typical experiment, the condensate is created in an optical or magneto-optical trap. The trap is then turned off and the condensate is allowed to expand.In this Letter we study the expansion of the BoseEinstein condensate in a 3D random potential. Unlike in 1D, a critical energy (the mobility edge ǫ c ) exists in 3D which separates extended and localized states. An eigenstate is extended (localized) if the corresponding energy is larger (smaller) than ǫ c . When the condensate is released from the trap, the atoms achieve kinetic energies up to the chemical potential µ of the trapped condensate. For weak disorder ǫ c < µ, and a fraction of atoms diffuses away, whereas the remainder is localized, as was pointed out in [7]. We show here that, surprisingly, even for strong disorder ǫ c > µ only a fraction of the condensate will be localized. We study the full dynamics of the condensate expansion by accounting for weak localization at energies ǫ > ǫ c , strong localization at ǫ < ǫ c , and critical behavior around the mobility edge. Our main result is that the effect of disorder on the expansion of the condensate is controlled by a single parameter ǫ c /µ, and that Anderson localization plays an important role even when the chemical potential of the condensate µ is much larger than the mobility edge ǫ c . We show that the behavior of the average condensate densityn(r, t) at large distances r and long times t is governed by the critical exponents ν and s of the localization transition. This could provide a direct way to measure these exponents. The density of the localized part of the condensaten(r, ∞) does not decay exponentially with r, as one could have expected, but follows a power law.Consider a Bose-Einstein condensate of N ≫ 1 atoms of mass m trapped in a 3D spherically-symmetric harmonic potential V ω (r), characterized by the trap freque...

We study how macroscopic superpositions of coherent states produced by the nondissipative dynamics of binary mixtures of ultracold atoms are affected by atom losses. We identify different decoherence scenarios for symmetric or asymmetric loss rates and interaction energies in the two modes. In the symmetric case the quantum coherence in the superposition is lost after a single loss event. By tuning appropriately the energies we show that the superposition can be protected, leading to quantum correlations useful for atom interferometry even after many loss events.

We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle-number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength, and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Because of the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states.