Open quantum systems approach to atomtronics

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Atomtronics has the goal of developing a one-to-one analogy of electronic systems, components and devices with ultracold atoms trapped in optical lattices. It is being researched at the University of Colorado. The Atomtronic Anderson Group of Optical Physics

Their atom-optical analogy to electronic circuits begins with the definition of the `atomtronic battery’, which is composed of two reservoirs of ultracold atoms having different chemical potentials (corresponding to different electric potentials at the terminals of a conventional battery). The `wires’ and atomtronic components are composed of optical lattices, and current refers to the number of atoms that pass a specific point in a given amount of time. The atomtronic diode is a device that allows an atomic flux to flow across it in essentially only one direction. The desired function of an atomtronic transistor is to enable a weak atomtronic current to be amplified or to switch,either on or off, a much larger one.

the Colorado atomtronic researchers have published an Open quantum systems approach to atomtronics in Arxiv

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 diode, 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.

The motivation to construct and study atomtronic analogs of electronic systems comes from several directions.

1. The experimental atomtronic realizations promise to be extremely clean. Imperfections such as lattice defects or phonons can be completely eliminated. This allows one to study an idealized system from which all inessential complications have been stripped. Consequently, one may obtain an improved understanding of the essential requirements that make certain electronic devices work. It is possible that a deeper understanding may feed back to the design of conventional electronic systems and could lead to future improvements. This lies parallel to the recent interest in single electron transistors in mesoscopic systems and molecules, where many themes common with atomtronics emerge. A consequence of the near-ideal experimental conditions for optical lattice systems is that theoretical descriptions for atomtronic systems can be developed from first principles. This allows theorists to develop detailed models that can reliably predict the properties of devices.

2. Atomtronics systems are richer than their electronic counterparts because atoms possess more internal degrees of freedom than electrons. Atoms can be either bosons or fermions, and the interactions between atoms can be widely varied from short to long range and from strong to weak. This can lead to behavior that is qualitatively different to that of electronics. Consequently, one can study repulsive, attractive, or even non-interacting atoms in the same experimental setup. Additionally, current experimental techniques allow the detection of atoms with fast, state-resolved, near unit quantum efficiency. Thus it is possible, in principle, to follow the dynamics of an atomtronic system in real time.

3. Neutral atoms in optical lattices can be well isolated from the environment, reducing decoherence. They combine a powerful means of state readout and preparation with methods for entangling atoms. Such systems have all the necessary ingredients to be the building blocks of quantum signal processors. The close analogies with electronic devices can serve as a guide in the search for new quantum information architectures, including novel types of quantum logic gates that are closely tied with the conventional architecture in electronic computers.

4. Recent experiments studying transport properties of ultracold atoms in optical lattices can be discussed in the context of the atomtronics framework. In particular, one can model the short-time transport properties of an optical lattice with the open quantum system formalism discussed here.

The quantum system formalism was used to show how neutral atoms in custom optical lattices can exhibit electronic diode, FET, BJT, and AND gate behavior. Looking forward, we aim to develop more complicated atomtronic devices such as additional logic elements, flip-flops, and constant current sources by cascading our current atomtronic components in a manner analogous to the development more sophisticated electronic devices. The simulation of the AND gate is promising since it demonstrates the possibility of cascading atomtronic components to make more sophisticated devices.

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