Negative Differential Conductivity in an Interacting Quantum Gas

We report on the observation of negative differential conductivity (NDC) in a quantum transport device for neutral atoms employing a multimode tunneling junction. The system is realized with a Bose-Einstein condensate loaded in a one-dimensional optical lattice with high site occupancy. We induce an initial difference in chemical potential at one site by local atom removal. The ensuing transport dynamics are governed by the interplay between the tunneling coupling, the interaction energy, and intrinsic collisions, which turn the coherent coupling into a hopping process. The resulting current-voltage characteristics exhibit NDC, for which we identify atom number-dependent tunneling as a new microscopic mechanism. Our study opens new ways for the future implementation and control of complex neutral atom quantum circuits.

Figure 1

System under investigation. Two reservoirs can exchange particles with coupling strength $J$ through a tunneling barrier. The particles in both sides can occupy many spatial modes and have different chemical potentials.

Figure 2

(a) Experimental setup: Two blue detuned laser beams $({\overrightarrow{k}}_{\mathrm{L}})$ create a one-dimensional optical lattice in which we load a Bose-Einstein condensate. Removing atoms from the central site of this system leads to an out-of-equilibrium state as an implementation of Fig. 1 (see text). (b) Sketch of the energy level structure (not to scale). Particles of a full site with chemical potential ${\mu }_1$ are resonant with higher radial states of the empty site (indicated as dotted lines) in which they tunnel with a reduced effective tunneling rate $J_{\mathrm{eff}}$. Subsequently, the atoms thermalize by collisional decoherence in the initially empty well.

Figure 3

Experimental results. (a) Refilling dynamics for three different tunneling couplings. The solid lines are the prediction of our effective model [see Eq. (3) below]. (b) Negative differential conductivity. The experimental points are extracted from the data set with $J/\hslash =100{\mathrm{s}}^{-1}$. After a linear initial rise (red line), the current drops for an increasing imbalance in chemical potential. The dashed line indicates the critical current at which NDC sets in. (c) Critical current for NDC versus coupling strength. Evaluating the critical current for different tunneling couplings $J$, we find a power law $J^{\alpha }$, with $\alpha =1.8(2)$.

Figure 4

Normalized radial density distribution in the central lattice site for the refilling dynamics at $J/\hslash =230{\mathrm{s}}^{-1}$. After 6 ms (blue dots, 220 atoms), the distribution is governed by thermal energy, and we find a temperature of $T=36(2)\mathrm{nK}$. The equilibrium state (red triangles, 600 atoms), which is reached after 400 ms, is dominated by interaction energy and its width gets smaller. Solid lines are Gaussian fits with horizontal bars indicating their $2\sigma$ width.

Figure 5

Behavior of the time scale for different settings. (a) Refilling time versus tunneling coupling for a constant decoherence rate. We fit a power law with an exponent of $\alpha =1.9(1)$. (b) Refilling time versus decoherence rate: manifestation of the quantum Zeno effect. ${\tau }_{\mathrm{eff}}$ scales linearly with ${\mathrm{\Gamma }}_{\mathrm{dec}}$ (red line).