An atom Michelson interferometer is implemented on an "atom chip." The chip uses lithographically patterned conductors and external magnetic fields to produce and guide a Bose-Einstein condensate. Splitting, reflecting, and recombining of condensate atoms are achieved by a standing-wave light field having a wave vector aligned along the atom waveguide. A differential phase shift between the two arms of the interferometer is introduced by either a magnetic-field gradient or with an initial condensate velocity. Interference contrast is still observable at 20% with an atom propagation time of 10 ms.

Atomtronics focuses on atom analogs of electronic materials, devices and circuits. A strongly interacting ultracold Bose gas in a lattice potential is analogous to electrons in solid-state crystalline media. As a consequence of the band structure, cold atoms in a lattice can exhibit insulator or conductor properties. P-type and N-type material analogs can be created by introducing impurity sites into the lattice. Current through an atomtronic wire is generated by connecting the wire to an atomtronic battery which maintains the two contacts at different chemical potentials. The design of an atomtronic diode with a strongly asymmetric current-voltage curve exploits the existence of superfluid and insulating regimes in the phase diagram. The atomtronic analog of a bipolar junction transistor exhibits large negative gain. Our results provide the building blocks for more advanced atomtronic devices and circuits such as amplifiers, oscillators and fundamental logic gates.

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 experimental 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. [4,5,6] behavior in atomic systems. We calculate the device characteristics of these semiconductor-like systems by construction of complete atomtronic circuits. Such circuits contain the analog of electronic power supplies or batteries, and the necessary device connections. This opens up the possibility for more complex circuits in which atomtronic device components can be cascaded. The approach we introduce develops a general theoretical method for solving the dynamics of strongly-interacting, many-body, open quantum systems.A diode is in essence a device which exhibits an asymmetric response; applying a potential gradient one way leads to a large current and the opposite way leads to virtually no current. The atomtronic diode we present is novel compared to some previously proposed devices [2,3] in that it does this without relying on an intrinsic irreversibility of the device itself (e.g. the spontaneous emission of a photon or phonon). The atomtronic transistor presented here contrasts with other proposals [4,5], in that it operates in steady-state, rather than only in an initial (transient) regime. It also reproduces the essential transistor behavior, including the control of a larger atomtronic current with a smaller one, the ability to perform digital logic, and exhibits linear amplification. One motivation for designing atomtronic diode and transistor components that are intrinsically reversible is that they can then be combined in quantum computing applications where coherent logic is required.This topic is relevant for the emerging field of stronglycorrelated dynamical and nonequilibrium phenomena in ultracold atomic gases [7,8,9,10]. Atomtronic devices require site-by-site control of the temporal or spatial properties of optical lattices [11,12,13,14], a common goal for numerous experiments aiming to utilize optical lattices for quantum control, quantum transport, quantum computing, and quantum simulation [15,16,17]. What is novel here is that the atomtronic systems we consider are open quantum systems, meaning that they are composed of optical lattices coupled to two or three reservoirs, with the reservoirs acting as sources or sinks for particles.The Hamiltonian takes the separable formwhereĤ sys andĤ res denote system and reservoir Hamiltonians, respectively, andĤ V their interaction. Although atomtronic devices can utilize either fermionic or bosonic atoms, we focus our discussion on the bosonic case, providing contrast with electronics where the carriers are fermionic. In the lowest band approximation,Ĥ sys is the Bose-Hubbard Hamiltonian that describes ultracold bosons in a on...