We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate atomic transport across a variety of lattice configurations. We demonstrate how the behavior of an electronic diod
e, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate AND logic gate behavior in an optical lattice.
We illustrate that open quantum systems composed of neutral, ultracold atoms in one-dimensional optical lattices can exhibit behavior analogous to semiconductor electronic circuits. A correspondence is demonstrated for bosonic atoms, and the experime
ntal requirements to realize these devices are established. The analysis follows from a derivation of a quantum master equation for this general class of open quantum systems.
