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วารสารวิทยาศาสตร์ มศว (Srinakharinwirot Science Journal)

แบบจำลองเชงพลศาสตรของการกระโดดของอเลกตรอนในวงแหวนควอนตมค Dynamical Simulation of Electron Hoping in Double Quantum Rings

ชลเทพ กิจสินธพชัย, สุธี บุญช่วย

Published Sep 11, 2013• 0 citations
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Abstract

แบบจำลองของอิเล็กตรอนที่เคลื่อนที่ผ่านวงแหวนควอนตัมภายใต้สนามแม่เหล็กคงตัวสามารถจำลองได้โดยการสร้างตัวแปลงเพื่อแก้ชุดสมการเชิงอนุพันธ์ให้ไปอยู่ในรูปคาโนนิคอลซึ่งแรงลอเรนซ์ที่เกิดขึ้นทำให้อิเล็กตรอนที่เคลื่อนผ่านวงแหวนมีการเอนเอียงไปด้านหนึ่ง และขณะเดียวกันผลจากปรากฏการณ์ของAharonov-Bohmซึ่งเป็นการเลื่อนเฟสได้ทำให้อิเล็กตรอนที่ปลายวงแหวนเกิดการแทรกสอดทำให้ความสามารถในการส่งผ่านลดลงผลลัพธ์จากการคำนวณแสดงให้เห็นว่าสาหรับกรณีที่ไม่มีสนามแม่เหล็กหรือสนามแม่เหล็กที่เกิดขึ้นบนวงแหวนทั้งสองมีค่าใกล้เคียงกันอิเล็กตรอนจะสามารถเคลื่อนที่ผ่านไปได้แต่สำหรับกรณีที่สนามแม่เหล็กมีค่าแตกต่างกันมากอิเล็กตรอนจะไม่สามารถเคลื่อนที่ผ่านวงแหวนวงแรกได้The wave packet of electron hoping through quantumrings under the static magnetic field is solved by transformation to thecanonical form of certain system of differential equations. The Lorentz forceleads to electron asymmetry which enhances the electron passing through aquantum ring while the Aharanov-Bohm effect (AB effect) reduces the probabilityof transmission by phase shifted interference. For zero or similar magneticfield of both rings, the wave packet can pass both quantum rings to the exitquantum wire while different magnetic field of both rings prevent the secondring’s injection of electron.

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แบบจำลองของอิเล็กตรอนที่เคลื่อนที่ผ่านวงแหวนควอนตัมภายใต้สนามแม่เหล็กคงตัวสามารถจำลองได้โดยการสร้างตัวแปลงเพื่อแก้ชุดสมการเชิงอนุพันธ์ให้ไปอยู่ในรูปคาโนนิคอลซึ่งแรงลอเรนซ์ที่เกิดขึ้นทำให้อิเล็กตรอนที่เคลื่อนผ่านวงแหวนมีการเอนเอียงไปด้านหนึ่ง และขณะเดียวกันผลจากปรากฏการณ์ของAharonov-Bohmซึ่งเป็นการเลื่อนเฟสได้ทำให้อิเล็กตรอนที่ปลายวงแหวนเกิดการแทรกสอดทำให้ความสามารถในการส่งผ่านลดลงผลลัพธ์จากการคำนวณแสดงให้เห็นว่าสาหรับกรณีที่ไม่มีสนามแม่เหล็กหรือสนามแม่เหล็กที่เกิดขึ้นบนวงแหวนทั้งสองมีค่าใกล้เคียงกันอิเล็กตรอนจะสามารถเคลื่อนที่ผ่านไปได้แต่สำหรับกรณีที่สนามแม่เหล็กมีค่าแตกต่างกันมากอิเล็กตรอนจะไม่สามารถเคลื่อนที่ผ่านวงแหวนวงแรกได้The wave packet of electron hoping through quantumrings under the static magnetic field is solved by transformation to thecanonical form of certain system of differential equations. The Lorentz forceleads to electron asymmetry which enhances the electron passing through aquantum ring while the Aharanov-Bohm effect (AB effect) reduces the probabilityof transmission by phase shifted interference. For zero or similar magneticfield of both rings, the wave packet can pass both quantum rings to the exitquantum wire while different magnetic field of both rings prevent the secondring’s injection of electron.
The wave packet of electron hoping through quantum rings under the static magnetic field is solved by transformation to the canonical form of certain system of differential equations. The Lorentz force leads to electron asymmetry which enhances the electron passing through a quantum ring while the Aharanov›Bohm effect (AB effect) reduces the probability of transmis- sion by phase shifted interference. For zero or similar magnetic field of both rings, the wave packet can pass both quantum rings to the exit quantum wire while different magnetic field of both rings prevent the second ringus injection of electron.
This article describes the Aharonov-Bohm (AB) effect of electron waves travelling in free space and its application to the observation of gauge fields (vector potentials). The AB effect is inconceivable in classical physics since an observable effect is produced on electrons passing through field-free spaces. Electrons can be affected only by Lorentz forces due to electromagnetic fields. The situation is different in quantum mechanics, where electrons show wave properties: the concept of force is no longer relevant, so electric field E and magnetic field B, defined as forces acting on a unit charge, take on secondary meanings. “Phase shifts” come into play, and the primary physical entities become neither E nor B but electrostatic potential V and vector potential A. These potentials interact with electron waves and shift their phases.
Confined in a lossless conductive ring, fractional revival of electron wave packet can form a set of coherently coupled qubits. It is demonstrated that if several magnetic solenoids are mounted at specific locations around the outer rim of the ring, the local phase of electron wave can be dynamically adjusted to a desired value. This will change the wave packet revival evolution thereafter. In some senses, this phenomenon is similar to the Aharonov–Bohm effect. However, here no net magnetic flux passes through the ring which is the path loop of electron wave. By computer simulation, it is shown that some important qubit operations can be realized by this approach.
The Aharonov-Bohm effect is measured in a four-terminal open ring geometry. Two quantum dots are embedded in the structure, one in each of the two interfering paths. The number of electrons in the two dots can be controlled independently. The transmission phase is measured as electrons are added to or taken away from the individual quantum dots. Although the measured phase shifts are in qualitative agreement with theoretical predictions, the phase evolution exhibits unexpected dependence on the magnetic field. Phase lapses are found only in certain ranges of the magnetic field.
We consider the phase-coherent transport of electrons passing through an Aharonov–Bohm ring while interacting with a tunnel charge in a double quantum dot (representing a charge qubit) which couples symmetrically to both arms of the ring. For Aharonov–Bohm flux Φ AB = h /2 e we find that electrons can only be transmitted when they flip the charge qubit's pseudospin parity an odd number of times. The perfect correlations of the dynamics of the pseudospin and individual electronic transmission and reflection events can be used to entangle the charge qubit with an individual passing electron.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux  through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc     , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.