Recent work on the role of decoherence in quantum physics has suggested that the quantum to classical decay is governed by a discrete set of pointer states, which are quite stable and uncoupled from other states in the system. We have studied extensively the conductance oscillations exhibited by open quantum dots in varying gate voltages and magnetic fields. These oscillations are governed by a discrete set of stable quantum states which have the properties of the pointer states, and which are closely related to trapped classical orbits in the open dot. These states are essentially classical in nature, as evidenced by their energy level spacing, and their decay is apparently in the environment as opposed to within the dots.
More recently, we have investigated the dynamics of an array of coupled electron quantum dots, by using a magnetic field to dramatically modify the underlying mixed phase space. At specific values of the magnetic field the sea of chaos is "drained". At these fields there exist reflected or transmitted orbits associated with maxima and minima in the experimentally observed magneto-resistance. These effects are studied by comparing the classical and quantum-mechanical phase space dynamics leading to a basic understanding of the role of chaos in the transport in an array of billiards.
The measured magneto-resistance for a seven-dot array (T= 10 mK) is shown in the figure below. The arrows indicate the positions of the resonant maxima and minima expressed by the values of w(+) and w(-). The inset shows a micrograph of the seven dot array.
The next image shows a comparison of classical trajectories and quantum trajectories. Upper row: classically calculated trajectories for certain initial conditions in the entrance constriction. Lower row: quantum-mechanical density probabilities (yellow: highest, black: lowest probability). According to the geometrical shape of the measured sample the parameters of the potential are chosen as:w(x,d) = 1.06 x 10^12 /s, w(y) = 0.848 x 10^12 /s, w(x,c) = 2.16 x 10^12 /s; extension in x-direction: 0.32 micron (dot), 0.076 micron (constriction). These omegas are the "harmonic oscillator" frequencies describing the potential in the dots and in the constrictions.
The next figures show an overlay of the Husimi representations (HR) for different ratios of w(+/-): white dots represent the classical phase space, colour plots the HR (red: high, blue: low quantum-mechanical phase-space probability). (a) w(+)/w(-)= 1.6269. The classical mixed phase shows two types of KAM-islands symbolized by (1) and (2) and a "sticky layer" (light grey) around them. The type-2 KAM islands in each dot have highest phase-space probability. (b) w(+)/w(-)= 2.0000. The large white dots, in the regions where the chaotic sea has been drained, correspond to different periodic orbits. The red triangle (first dot, highest probability) represents a back-scattered orbit (same initial condition as in the above figure at w(+)/w(-) = 2.0000).
Recent Publications:
(with A. Cummings, Graduate student)
In recent years, a great deal of speculation has concerned the impending termination of Moore's Law as it relates to CMOS technology. As a result, a significant amount of research has been focused on alternate methods of computation. Two of the more popular areas of research are those of spintronics and quantum computation. Generally, the field of spintronics deals with any application that attempts to manipulate the spin of an electron. The field of quantum computation similarly has attracted attention because of its potential to offer an exponential speedup over classical computation for certain problems. A quantum-computational algorithm usually requires that all quantum bits (qubits) be initialized. Then, the bits are placed into a superposition state e.g. with the Hadamard transform. Among a variety of other possibilities, electron spin has been proposed as the qubit in a mobile quantum computational system.
We have studied a device for generating spin-polarized currents via Rashba spin-orbit coupling, without the use of spin-dependent interference, similar to those presented by others. In those papers, spin polarization due to the Rashba effect was demonstrated in branching structures, and its robustness to changes in energy was studied. We extended this work by examining the effect of a variable Rashba interaction strength, and by considering various structure sizes. Our simulations of this device make use of the Rashba spin-orbit Hamiltonian in two dimensions with a perpendicular electric field. We assume that the spin-orbit coupling is uniform and present throughout the system under investigation. Our structure is shown in the figure below.
The spin polarization of the left and right output wires as a function of the Rashba spin-orbit coupling strength, for the structure shown above. Dark shades are spin up and light shades are spin down.
