Aharonov-Bohm interferometer

Phase Measurements in Closed Aharonov-Bohm Interferometers... 

However, the experimental measurement of olqd has only become accessible since 1995 [6, 7], using the Aharonov-Bohm interferometer (ABI) [8]. 

K. Kobayashi, H. Aikawa, S. Katsumoto, Y. Iye, Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer, Phys. Rev. Lett. 88 (2002) 256806/1. 

Electron transport through a triple-terminal Aharonov-Bohm interferometer is theotetically studied. By applying a local Rashba interaction to a quantum dot, we find that spin polarization and spin separation can be simultaneously realized with the adjustment of quantum dot levels, i.e., an incident electron from one terminal can select a specific terminal to depart from the quantum dots according to its spin state. 

Figure 1. Schematic of a triple-QD Aharonov-Bohm interferometer with a local Rashba interaction applied on QD-1.

For example, the description of the Aharonov-Bohm effect and other types of interferometry become closely similar. The Young interferometer, for example, is described by... 

It is the present writer s opinion that the existence of the obstruction changes the situation entirely. Without the existence of the solenoid in the interferometer, the loop of the two paths can be reduced to a single point and the region occupied by the interferometer is then simply connected. But with the existence of the solenoid, the loop of the two paths cannot be reduced to a single point and the region occupied by this special interferometer is multiply connected. The Aharonov-Bohm effect only exists in the multiply connected scenario. But we should note that the Aharonov-Bohm effect is a physical effect and simple and multiple connectedness are mathematical descriptions of physical situations. 

We referred to the physical situation of the Aharonov-Bohm effect as an interferometer around an obstruction and it is two-dimensional. It is important to note that the situation is not provided by a toroid, although a toroid is also a physical situation with an obstruction and the fields existing on a toroid are also of SU(2) symmetry. However, the toroid provides a two-to-one mapping of fields in not only the x and y dimensions but also in the z dimension, and without the need of an electromagnetic field pointing in two directions + and —. The physical situation of the Aharonov-Bohm effect is defined only in the x and y dimensions (there is no z dimension) and in order to be of SU(2)/Z2 symmetry requires a field to be oriented differentially on the separate paths. If the differential field is removed from the Aharonov-Bohm situation, then that situation reverts to a simple interferometric raceway which can be reduced to a single point and with no interesting physics. 

Spin-orbit(SO) coupling is an important mechanism that influences the electron spin state [1], In low-dimensional structures Rashba SO interaction comes into play by introducing a potential to destroy the symmetry of space inversion in an arbitrary spatial direction [2-6], Then, based on the properties of Rashba effect, one can realize the controlling and manipulation of the spin in mesoscopic systems by external fields. Recently, Rashba interaction has been applied to some QD systems [6-8]. With the application of Rashba SO coupling to multi-QD structures, some interesting spin-dependent electron transport phenomena arise [7]. In this work, we study the electron transport properties in a three-terminal Aharonov-Bohm (AB) interferometer where the Rashba interaction is taken into account locally to a QD. It is found that Rashba interaction changes the quantum interference in a substantial way. 

Figure 20. The scheme of one-dimensional Aharonov-Bohm loop, surrounding the direction of propagation of a longitudinal mode and weakly coupled at points A and B with the external leads L and Li [(a) and (b)]. (d) The model of an ac normal-metal interferometer. R and R2 are the thermal reservoirs held at voltages V/2, respectively.

Cao J, Wang Q, Rolandi M and Dai H J (2004) Aharonov-bohm interference and beating in single-walled carbon-nanotube interferometers, Phys Rev Lett 93 216803. 

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