Datta-Das transistor for atomtronic circuits using artificial gauge fields

Spin-dependent electrical injection has found useful applications in storage devices, but fully operational spin-dependent semiconductor electronics remain a challenging task because of weak spin-orbit couplings and/or strong spin relaxations. These limitations are lifted considering atoms instead of electrons or holes as spin carriers. In this emerging field of atomtronics, we demonstrate the equivalent of a Datta-Das transistor using a degenerate Fermi gas of strontium atoms as spin carriers in interaction with a tripod laser-beams scheme. We explore the dependence of spin rotation, and we identify two key control parameters which we interpret as equivalent to the gate-source and drain-source voltages of a field effect transistor. Our finding broadens the spectrum of atomtronics devices for implementation of operational spin-sensitive circuits.

Figure 1

Principle of the atomtronics DDT. (a) The tripod scheme used in the experiment. A magnetic field of $67\mathrm{G}$ is applied to isolate the Zeeman substate $|F_e=9/2,m_F=7/2\rangle$ of the triplet ${}^3{P}_1$ excited level. (b) Schematic showing the operating principle of an atomtronic DDT device with the arrangement of tripod beams as seen from a moving atom at velocity $\mathit{v}=v_z{\widehat{\mathit{e}}}_z$. Spin-polarized atoms emanating from an atomtronic source (left black box) enter the spin-orbit coupled gate region and their spin is rotated. Depending on their final spin they arrive at a different location in the drain (right black box). The polarization of each the beam is indicated in the figure where we use the following notation convention $1\equiv {\sigma }_{+}$, $2\equiv \pi$, and $3\equiv {\sigma }_{-}$. (c) Rabi frequencies of the tripod lasers as a function of time in the atom's proper frame with ${\sigma }_t=8\mu \mathrm{s}$ and $\eta =1.8$. The normalized laser beam intensity of ${\sigma }_{+}$ (standard deviation of ${\sigma }_t$) is shown as a blue-dotted curve.

Figure 2

Atomtronics DTT output populations. (a) Ground-state populations at the output of the interacting region as a function of the gate parameter $\xi ={\mathrm{\Omega }}_{03}/{\mathrm{\Omega }}_{01}$ for laser pulse sequence shown in Fig. 1. Here ${\mathrm{\Omega }}_{01}={\mathrm{\Omega }}_{02}\approx 2\pi \times 270\mathrm{kHz}$. The plain curves correspond to the model prediction using the unitary operator of Eq. (4). (b) Fluorescence images of the cloud after the laser pulses and a time of flight of $9\mathrm{ms}$. The images are associated with the shaded data points on panel (a). (c) Fluorescence images of the cloud when the order of pulse sequence is reversed, i.e., in the order 2, 3, and 1.

Figure 3

Sensitivity of the pseudospin rotation. The polar angle $\theta$ as function of $\xi$ for three different values of the pulse separation $\eta$ for ${\sigma }_t=8\mu \text{s}$. The other experimental parameters are the same as Fig. 2. Inset: ${\mathrm{\Sigma }=\mathrm{\Delta }\theta /\mathrm{\Delta }\xi |}_{\theta =\pi /2}$ indicates the sensitivity of the pseudospin rotation as function of $\eta$. The solid curves are the theory prediction using the unitary operator of Eq. (4).

Figure 4

Compressing or inflating the gate region. (a) RMS deviation of the experimental data from the theoretical prediction using the unitary operator of Eq. (4) is plotted as a function of ${\sigma }_t$ for two values of $\eta$ are plotted. Large RMSD values indicate that the model approximations are not sufficient to capture the experimental behavior. Inset shows such an example for $\eta =2.2$ and ${\sigma }_t=16\mu \text{s}$. The dashed curve correspond to the prediction. (b) $\rho =$ output population/input population as a function of ${\sigma }_t$ for the two values of $\eta$ indicated in panel (a).