Single-Particle Tunneling in Strongly Driven Double-Well Potentials

We report on the first direct observation of coherent control of single-particle tunneling in a strongly driven double-well potential. In our setup atoms propagate in a periodic arrangement of double wells allowing the full control of the driving parameters such as frequency, amplitude, and even the space-time symmetry. Our experimental findings are in quantitative agreement with the predictions of the corresponding Floquet theory and are also compared to the predictions of a simple two mode model. Our experiments reveal directly the critical dependence of coherent destruction of tunneling on the generalized parity symmetry.

Figure 1

Coherent control of single-particle tunneling. (a) A single atom is realized on the right side of the double-well potential and the subsequent tunneling dynamics can be directly observed in momentum space. Since a periodic arrangement of double-well potentials is used the momentum distribution is given by a diffraction pattern as shown in the insets. The gray shaded areas are evaluated to obtain the shown diffraction efficiencies. (b) Adding symmetric driving leads to the predicted slowing of the dynamics. (c) Breaking the generalized parity symmetry by applying a sawtooth driving force destroys this effect. Here the gray shaded area indicates the preparation phase. The solid lines are sinusoidal fits to the data.

Figure 2

Schematics of the experimental setup. The well collimated atomic beam impinges on periodic light shift potentials, which adiabatically increase along the propagation direction. The interaction time is adjusted by changing the extension of the light field in $y$ direction. The momentum distribution is detected in the far field by a multichannel plate. The used optical setup with an acousto-optical deflector is depicted on the right-hand side. In the inset the change of symmetry due to residual phase shifts at the mirror surface is shown.

Figure 3

The Floquet state quasienergies for the experimentally realized parameters. The initial preparation of a particle localized on one side leads to the population of mainly two Floquet states and the corresponding eigenenergies are indicated as dark-gray and black dots. The tunneling dynamics is given by the quasienergy difference. (a) In the case of symmetric driving the Floquet states cross for at ${\omega }_{\mathrm{CDT}}$ leading to coherent destruction of tunneling. (b) Breaking the temporal symmetry as indicated in the inset introduces an anticrossing. Clearly for high driving frequencies independent on the driving symmetry the tunneling splitting increases and thus faster tunneling is expected.

Figure 4

Systematic study of the tunneling dynamics with symmetric driving. (a) The graph shows the driving frequency dependence of the tunneling rate. If the driving frequency is close to the resonance to the third excited state the driving leads to an acceleration of the tunneling. The experimental results (solid dots) are explained by the full Floquet analysis without free parameter over the whole range. The solid line represents the prediction within the two mode approximation. (b) In this graph we compare our experimental data obtained for fixed driving frequency but changing the driving amplitude with the theoretical predictions. For these specific experimental parameters also the two mode approximation explains quantitatively the observations.

Figure 5

Tunneling dynamics for different driving symmetries. (a) The open circles represent the tunneling dynamics in a stationary potential while the solid dots reveal the slowing down of the dynamics due to symmetric driving. (b) Applying a sawtooth temporal driving to a spatially symmetric double well leads to significant tunneling during the interaction time. (c) Breaking the spatial symmetry, i.e., asymmetric double well, but employing symmetric sinusoidal temporal driving also leads to the expected increase of the tunneling rate. Parameters: $S=2.05\frac{E_r}{\mu \mathrm{m}}$, $\omega =5.5\mathrm{kHz}$, $V_1=5.65E_r$, $V_2=3.22E_r$.