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arXiv:1005.3069 · Physical Review A

Open quantum systems approach to atomtronics

Ronald Pepino, J. Cooper, D. Meiser, Dana Z. Anderson, Murray Holland

Published Jul 28, 2010• 52 citations
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Abstract

We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate the atomic transport of bosons 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.

DOI
10.1103/physreva.82.013640

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Open Quantum System Studies of Optical Lattices and Nonlinear Optical Cavities: A Comprehensive Development of Atomtronics

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A generalized open quantum theory that models the transport properties of bosonic systems is derived from first principles. This theory is shown to correctly describe the long-time behavior of a specific class of non-Markovian system-reservoir interactions. Starting with strongly-interacting bosons in optical lattices, we use this theory to construct a novel, one-to-one analogy with electronic systems, components, and devices. Beginning with the concept of a wire, we demonstrate theoretically the ultracold boson analog of a semiconductor diode, a field-effect transistor, and a bipolar junction transistor. In a manner directly analogous to electronics, we show that it is possible to construct combinatorial logic structures from the fundamental electronic-emulating devices just described. In this sense, our proposal for atomtronic devices is a useful starting point for arrangements with more complex functionality. In addition we show that the behavior of the proposed diode should also be possible utilizing a weakly-interacting, coherent bosonic drive. After demonstrating the formal equivalence between systems comprised of bosons in optical lattices and photons in nonlinear cavity networks, we use the formalism to extend the ideas and concepts developed earlier in ultracold boson systems to nonlinear optical systems. We adapt the open quantum system theory to this new physical environment, and demonstrate theoretically how a few-photon optical diode can be realized in a coupled nonlinear cavity system. An analysis of different practical cavity quantum electrodynamics systems is presented and experimentally-viable candidates are evaluated.

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Abstract : Theoretical work established a quantum framework in which to address atom analogs of electronic devices and circuits. Initial focus was on isolated elements, particularly atom diodes and atom transistors. Two theoretical approaches addressed different device strategies, one based on double and triple potential wells, the other based on periodic structures that are analogous to semiconductor materials. The first approach is suited to implementations using ultracold atom chip technology, whereas the second is amenable to optical lattice experiments. Both approaches established the presence of atom flux gain in a simple transistor configuration. Further theoretical work developed an open quantum systems approach to simple yet complete circuits. This work provides the analytical tools for treating more complex atomtronic circuits. Corresponding experimental work focused on building an atom chip based Bose-Einstein Condensation (BEC) system for carrying out atom transistor experiments. Chip development demonstrated technology for fabricating structures having nanowires suspended across a substrate groove to avoid the deleterious impact of Van der Waals forces. This work established the foundation of atomtronics and the possibility of experimentally demonstrating such circuits in the near future.

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Atomtronics: Ultracold-atom analogs of electronic devices

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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 gapped many-body energy spectrum, cold atoms in a lattice exhibit insulatorlike or conductorlike properties. $P$-type and $N$-type material analogs are 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 atom 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.

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Atomtronics: An ultracold analogue of semiconductor devices

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A collection of ultracold atoms subject to a spatially periodic potential energy can exhibit behavior analogous to electrons in a crystal lattice. This fact was profoundly established by the demonstration of the superfluid to Mott-insulator transition of atoms in an optical lattice. An optical lattice consists of atoms subject to a periodic potential produced by interfering laser beams. The analogy between ultracold atoms in optical lattices and electrons in crystal lattices is manifestly a rich one. Recently, we have made a a proposal to extend the analogy to doped semiconductor materials. Lattice ”defects” achieve behaviors similar to P-type and N-type semiconductor materials. Naturally the interest is to adjoin P-type and N-type atoms lattices to produce an atom diode, and then an NPN or PNP lattice ”sandwich” to achieve bipolar transistor-like behavior for ultracold atoms. Such heterogeneous structures can indeed be made to mimic their electronic counterparts.

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Atomtronics: Coherent Control of Atomic Flow via Adiabatic Passage

Albert Benseny, Joan Bagudà, Xavier Oriols +2 more

This chapter discusses an efficient and robust technique to coherently transport a single neutral atom, a single hole, or even a Bose–Albert Einstein condensate between the two extreme traps of a triple-well optical potential. It describes the main features of the optical microtrap array system used to isolate and manipulate individual neutral atoms. The chapter also discusses the main ideas behind the coherent control of matter wave tunneling based on adiabatic passage. It explains both a coherent single-hole diode and a coherent single-hole transistor in a triple-well potential. The chapter presents a single-hole diode by using the collisional interaction between two bosons as a control parameter to allow the whole transport from left to right, and inhibit the transport from right to left. Atomtronics is one of the foremost bottom-top approaches to quantum information science, where neutral atoms in optical, magnetic, and electric potentials form the building blocks of coherent diode and transistor-like devices.

•May 24, 2019•2 citations
We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate the atomic transport of bosons 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.
A generalized open quantum theory that models the transport properties of bosonic systems is derived from first principles. This theory is shown to correctly describe the long-time behavior of a specific class of non-Markovian system-reservoir interactions. Starting with strongly-interacting bosons in optical lattices, we use this theory to construct a novel, one-to-one analogy with electronic systems, components, and devices. Beginning with the concept of a wire, we demonstrate theoretically the ultracold boson analog of a semiconductor diode, a field-effect transistor, and a bipolar junction transistor. In a manner directly analogous to electronics, we show that it is possible to construct combinatorial logic structures from the fundamental electronic-emulating devices just described. In this sense, our proposal for atomtronic devices is a useful starting point for arrangements with more complex functionality. In addition we show that the behavior of the proposed diode should also be possible utilizing a weakly-interacting, coherent bosonic drive. After demonstrating the formal equivalence between systems comprised of bosons in optical lattices and photons in nonlinear cavity networks, we use the formalism to extend the ideas and concepts developed earlier in ultracold boson systems to nonlinear optical systems. We adapt the open quantum system theory to this new physical environment, and demonstrate theoretically how a few-photon optical diode can be realized in a coupled nonlinear cavity system. An analysis of different practical cavity quantum electrodynamics systems is presented and experimentally-viable candidates are evaluated.
Abstract : Theoretical work established a quantum framework in which to address atom analogs of electronic devices and circuits. Initial focus was on isolated elements, particularly atom diodes and atom transistors. Two theoretical approaches addressed different device strategies, one based on double and triple potential wells, the other based on periodic structures that are analogous to semiconductor materials. The first approach is suited to implementations using ultracold atom chip technology, whereas the second is amenable to optical lattice experiments. Both approaches established the presence of atom flux gain in a simple transistor configuration. Further theoretical work developed an open quantum systems approach to simple yet complete circuits. This work provides the analytical tools for treating more complex atomtronic circuits. Corresponding experimental work focused on building an atom chip based Bose-Einstein Condensation (BEC) system for carrying out atom transistor experiments. Chip development demonstrated technology for fabricating structures having nanowires suspended across a substrate groove to avoid the deleterious impact of Van der Waals forces. This work established the foundation of atomtronics and the possibility of experimentally demonstrating such circuits in the near future.
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 gapped many-body energy spectrum, cold atoms in a lattice exhibit insulatorlike or conductorlike properties. PPP-type and NNN-type material analogs are 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 atom 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.
A collection of ultracold atoms subject to a spatially periodic potential energy can exhibit behavior analogous to electrons in a crystal lattice. This fact was profoundly established by the demonstration of the superfluid to Mott-insulator transition of atoms in an optical lattice. An optical lattice consists of atoms subject to a periodic potential produced by interfering laser beams. The analogy between ultracold atoms in optical lattices and electrons in crystal lattices is manifestly a rich one. Recently, we have made a a proposal to extend the analogy to doped semiconductor materials. Lattice ”defects” achieve behaviors similar to P-type and N-type semiconductor materials. Naturally the interest is to adjoin P-type and N-type atoms lattices to produce an atom diode, and then an NPN or PNP lattice ”sandwich” to achieve bipolar transistor-like behavior for ultracold atoms. Such heterogeneous structures can indeed be made to mimic their electronic counterparts.
This chapter discusses an efficient and robust technique to coherently transport a single neutral atom, a single hole, or even a Bose–Albert Einstein condensate between the two extreme traps of a triple-well optical potential. It describes the main features of the optical microtrap array system used to isolate and manipulate individual neutral atoms. The chapter also discusses the main ideas behind the coherent control of matter wave tunneling based on adiabatic passage. It explains both a coherent single-hole diode and a coherent single-hole transistor in a triple-well potential. The chapter presents a single-hole diode by using the collisional interaction between two bosons as a control parameter to allow the whole transport from left to right, and inhibit the transport from right to left. Atomtronics is one of the foremost bottom-top approaches to quantum information science, where neutral atoms in optical, magnetic, and electric potentials form the building blocks of coherent diode and transistor-like devices.