4 nomenon is well known in the context of interacting BECs and is attributed to the appearance of dynamical instabilities [25]. In contrast, with modulation, the quasi-momentum dis- tribution remains narrow and BOs can still be well resolved after 750 Bloch cycles. Evidently, the effects of dynamical instabilities are strongly suppressed. In summary, we have studied the coherent evolution of mat- ter waves in tilted periodic potentials under forced driving and have observed giant sBOs, which result from a beat of BOs with the drive when a small detuning$_{D}$$_{n}$ from the Bloch frequency is introduced. Localization as a result of BOs is broken, allowing us to engineer matter wave transport over macroscopic distances in lattice potentials with high relevance to atom interferometry [26]. We are now in a position to inves- tigate the effect of interactions on driven transport, for which subdiffusive and chaotic dynamics have been proposed [27]. During the final preparation of the manuscript we became aware of related work on non-dissipative transport in a quan- tum ratchet [28]. We thank A. R. Kolovsky, A. Zenesini, and A. Wacker for discussions and R. Grimm for generous support. We gratefully acknowledge funding by the Austrian Ministry of Science and Research and the Austrian Science Fund and by the European Union within the framework of the EuroQUASAR collective research project QuDeGPM. R.H. is supported by a Marie Curie International Incoming Fellow- ship within FP7. FIG. 5. (color online) Inducing transport and suppressing inter- action-induced dephasing. (a) Linear motion for resonant modula- tion. D f = 0 ◦ diamonds, 65 ◦ circles, 120 ◦ triangles, 190 ◦ squares. D f = 0 ◦ and$_{D}$$_{f}$ = 190 ◦ were chosen to maximize the speed in op- posite directions. The solid lines are linear fits to the data points excluding the first data point. (b) Directed motion for off-resonant modulation. D n was switched from − 1 Hz to 1 Hz after 400 ms. For comparison, (c) shows the oscillatory motion without switch- ing (time steps of 80 ms). The parameters are F$_{0}$ = 0 . 096 ( 1 ) mg , $_{D}$F = 0 . 090 ( 4 ) mg . (d)-(f) BOs in quasi-momentum space after 10 BO cycles with no drive (d), after 17 BO cycles with drive (e), after 750 BO cycles with drive (f). The parameters are F$_{0}$ = 0 . 096 ( 1 ) mg , $_{D}$F = 0 . 045 ( 3 ) mg ,$_{D}$$_{n}$ = − 1 Hz. The time steps are 1 ms. (c) 60  µ m 30  µ m (a) 0 10 20 30 40 50 60 70 80 90 -60 -40 -20 0 20 40 60 time (T$_{B}$) position (d) switch detuning (b) time 60  µ m 30  µ m (d) (e) (f) 2 ћ k initial conditions. In the work of Ref.[22], the breathing can be understood in terms of an incoherent sum over localized Wannier-Stark states that individually show a breathing mo- tion with period T [17]. The results above provide two mechanisms to circumvent the localization inherent in BOs and to induce coherent trans- port in an otherwise insulating context. As shown in Fig. 5(a), resonant modulation ($_{D}$$_{n}$ = 0) causes directed motion of the wave packet’s center-of-mass. For longer times, we find that the motion is approximately linear. The mean velocity de- pends on the relative phase f of the Bloch oscillator and the drive. In the experiment, we varied$_{f}$ via$_{f}$ =$_{f}$$_{0}$ +$_{D}$$_{f}$ , where f$_{0}$ is a constant phase offset, which depends on the details how BOs are initiated. For off-resonant modulation, transport can be induced by switching the sign of D n before a half- cycle of a sBO is completed. The wave packet then continues to move in the original direction. This motion is shown in Fig. 5(b), where we switch the sign after 400 ms. For compar- ison, Fig. 5(c) shows a sBO with T = 1 s without switching. 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