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The response of a particle in a periodic potential to an applied force is commonly described by an effective mass which accounts for the detailed interaction between the particle and the surrounding potential. Using a Bose-Einstein condensate of 87 Rb atoms initially in the ground band of an optical lattice, we experimentally show that the initial response of a particle to an applied force is in fact characterized by the bare mass. Subsequently, the particle response undergoes rapid oscillations and only over timescales long compared to that of the interband dynamics is the effective mass observed to be an appropriate description.PACS numbers: 37.10.Jk, The concept of the effective mass is ubiquitous in solid state physics, allowing for a simple semiclassical treatment of the response of a particle in a solid to an external force. The complex interaction between the particle and the surrounding potential dresses the particle with an effective mass, distinctly different from its bare mass, and allows for a description of the particles dynamics based on Newton's second law[1]:where a is the expectation value of the acceleration of the particle under an applied force F , and m * N (k) is the effective mass for a particle with crystal momentum k and band index N . The effective mass is inversely related to the curvature of the dispersion relation, and in 1D is given bywhere E N (k) is the energy of the state, andh is Planck's constant. The modern description of electronic conduction in solids is intimately tied to the concept of the effective mass. However, a direct application of Ehrenfest's theorem [2] shows that, for a particle originally in one band, the initial acceleration due to an applied force is F/m 0 , where m 0 is the bare mass, and not F/m * . This is because the external force unavoidably leads to interaction energies associated with both intraband and interband dynamics, and while the intraband portion of the interaction alone would lead to a response described by the effective mass, the additional interband contribution ensures an initial response given by the bare mass [3,4]. Over time, the interband coupling results in rapid oscillations in the complex amplitudes of the initial and neighbouring bands, and an acceleration which itself oscillates around F/m * (see Fig. 1). In the presence of interband dephasing these oscillations die out. The steady state however contains small contributions from neighbouring bands, as imposed by the force, such that the total acceleration tends to F/m * after the decay of the transients [5]. We use the term dynamical mass to refer to the mass associated with this transient response of the particle, and effective mass dynamics to refer to its variation in time. See Supplementary Information for further details on the theoretical description.In typical solid state systems, the fast timescales of the transient oscillations and dephasing effects have thus far prohibited observation of the effective mass dynamics. Duque-Gomez and Sipe [4] have recently revisited this id...

We experimentally study tunneling of Bose-condensed ^{87}Rb atoms prepared in a quasibound state and observe a nonexponential decay caused by interatomic interactions. A combination of a magnetic quadrupole trap and a thin 1.3  μm barrier created using a blue-detuned sheet of light is used to tailor traps with controllable depth and tunneling rate. The escape dynamics strongly depend on the mean-field energy, which gives rise to three distinct regimes-classical spilling over the barrier, quantum tunneling, and decay dominated by background losses. We show that the tunneling rate depends exponentially on the chemical potential. Our results show good agreement with numerical solutions of the 3D Gross-Pitaevskii equation.

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Recent experiments on macroscopic quantum tunneling reveal a non-exponential decay of the number of atoms trapped in a quasibound state behind a potential barrier. Through both experiment and theory, we demonstrate this non-exponential decay results from interactions between atoms. Quantum tunneling of tens of thousands of 87 Rb atoms in a Bose-Einstein condensate is modeled by a modified Jeffreys-Wentzel-Kramers-Brillouin model, taking into account the effective time-dependent barrier induced by the mean-field. Three-dimensional Gross-Pitaevskii simulations corroborate a mean-field result when compared with experiments. However, with one-dimensional modeling using time-evolving block decimation, we present an effective renormalized mean-field theory that suggests many-body dynamics for which a bare mean-field theory may not apply.