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Journal of Applied Physics

Local phase control of electron wave revival in a ring and related qubit operations

Wei Li

Published Aug 15, 2009• 3 citations
Publisher

Abstract

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.

DOI
10.1063/1.3204657

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Physical review. B, Condensed matter•Oct 15, 1995•8 citations
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.
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.
We calculate the oscillations of the dc conductance across a mesoscopic ring, simultaneously tuned by applied magnetic and electric fields orthogonal to the ring. The oscillations depend on the Aharonov-Bohm flux and of the spin-orbit coupling. They result from mixing of the dynamical phase, including the Zeeman spin splitting, and of geometric phases. By changing the applied fields, the geometric phase contribution to the conductance oscillations can be tuned from the adiabatic (Berry) to the nonadiabatic (Ahronov-Anandan) regime. To model a realistic device, we also include nonzero backscattering at the connection between ring and contacts, and a random phase for electron wave function, accounting for dephasing effects.
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 Aharonov-Bohm effect is a fundamental topological phenomenon with a wide range of applications. It consists of a charge encircling a region with a magnetic flux in a superposition of wave packets having their relative phase affected by the flux. In this work we analyze this effect using an entropic measure known as realism, originally introduced as a quantifier of a system's degree of reality and mathematically related to notions of global and local quantum coherence. More precisely, we look for observables that lead to gauge-invariant realism associated with the charge before it completes its loop. We find that the realism of these operators has a sudden change when the line connecting the center of both wave packets crosses the solenoid. Moreover, we consider the case of a quantized magnetic-field source, pointing out similarities and differences between the two cases. Finally, we discuss some consequences of these results.
The Aharonov-Bohm oscillations in the transmission probability of a one-dimensional mesoscopic ring between two electrodes are considered numerically where a time-periodical flux \ensuremath{\gamma}(t)=\ensuremath{\gamma}+\ensuremath{\lambda} cos\ensuremath{\omega}t is applied. Such a flux simulates a phase-coherent inelastic scattering due to the absorption/emission processes of modulation quanta. An increase of alternating flux amplitude \ensuremath{\lambda} drastically changes the Aharonov-Bohm oscillations of the transmission though the exact period remains ${\mathrm{\ensuremath{\varphi}}}_{0}$=hc/e. A frequency dependence of the transmission has abrupt steps at \ensuremath{\omega}=(E-EF{\mathit{E}}_{\mathit{F}}EF​)/n, caused by the locking of the transmission in the nth channel where EF{\mathit{E}}_{\mathit{F}}EF​ is the Fermi level. Moreover, for transmission of a narrow wave packet the time-periodical flux gives rise to two effects. The first is a fractioning of the input wave packet by the ring in such a way that the output wave function consists of a few separate wave packets. Their number, distance apart, and height essentially depend on the static flux \ensuremath{\gamma}. The second effect is a strong space squeezing of the output wave packet.