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 study the behaviour of the expectation value of the acceleration of a particle in a onedimensional periodic potential when an external homogeneous force is suddenly applied. The theory is formulated in terms of modified Bloch states that include the interband mixing induced by the force. This approach allows us to understand the behaviour of the wavepacket, which responds with a mass that is initially the bare mass, and subsequently oscillates around the value predicted by the effective mass. If Zener tunneling can be neglected, the expression obtained for the acceleration of the particle is valid over timescales of the order of a Bloch oscillation, which are of interest for experiments with cold atoms in optical lattices. We discuss how these oscillations can be tuned in an optical lattice for experimental detection.

We study the linear optical absorption of bulk semiconductors in the presence of a homogeneous constant (dc) electric field with an approach suitable for including excitonic effects while working with many-band models. The absorption coefficient is calculated from the time evolution of the interband polarization excited by an optical pulse. We apply the formalism to a numerical calculation for GaAs using a 14-band k · p model, which allows us to properly include interband coupling, and the exchange self-energy to account for the excitonic effects due to the electron-hole interaction. The Coulomb interaction enhances the features of the absorption coefficient captured by the k · p model. We consider the dependence of the enhancement on the strength of the dc field and the polarization of the optical field.

The semiclassical description of the dynamics of wave packets in periodic potentials and subject to an applied force relies on the concepts of effective mass and anomalous transport. This picture is valid if the force changes slowly in time and space, so that the particle described by the wave packet has time to respond according to the properties of the lattice. We analyze the dynamical corrections to this picture when a uniform force is suddenly applied, identifying separate corrections to the usual group and anomalous velocities. We find approximate semianalytical expressions for generalized "dynamical" group and anomalous velocities and the associated accelerations. We use a two-dimensional optical lattice with finite Berry curvature to illustrate the semianalytical approximation in a regime where the dynamical corrections are significant, suggesting the possibility of experiments to detect them; we compare the results with a full numerical solution, showing excellent agreement for weak forces.

The concept of the effective mass is ubiquitous in the study of electronic conduction in solid state physics, allowing for a semi-classical treatment of a particle's response to an external force. However, in 1954 Pfirsch and Spenke [1] predicted that this description breaks down on very short timescales, and that the initial response to a force is in fact described by the bare mass. This is because the external force F 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 m * , the interband contribution ensures an initial response given by the bare mass m o . Over time, the interband coupling results in rapid oscillations in the complex amplitudes of the initial and neighbouring bands, and an acceleration a which itself oscillates around F/m * . For typical solid state systems, the fast timescales of these dynamics have thus far prohibited observation of this phenomenon. Duque-Gomez and Sipe [2] have recently revisited this idea specifically in the context of ultracold atoms in optical lattices, where the narrow momentum widths and inherent length and time scales involved make observation of long-range quantum coherent phenomena experimentally accessible.