The mathematical design of a realistic three-position quantum switch controlled by the classical electric field is suggested in form of a circular quantum well — a unit disc on a plane with four straight channels attached to it. This device implements a triple splitting of an input waveguide. The magnitude of the constant electric field directed parallel to the disc may be defined such that rotation of this field in the plane of the device permits manipulation of the electron current through the triple splitting. The problem of calculating of the current through the switch is reduced to the construction of scattered waves for the Schrödinger operator on the corresponding composite domain with the homogeneous Dirichlet conditions on the boundary. The Dirichlet boundary conditions are found to correspond most closely to real experimental conditions on the boundary of a deep quantum well. Explicit expression for transmission coefficient from one channel to another is obtained. Technically the analysis of the corresponding infinitely-dimensional spectral problem is reduced to the analysis of a relevant finite-dimensional analytic matrix function. We estimate the errors that arise from replacement of infinite-dimensional operator by the finite matrix. Our main result is the calculation of the working point of the switch in the multi-dimensional space of the numerical parameters of the switch which permits the resonance manipulation of the current. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The mathematical design of a realistic three-position quantum switch controlled by the classical electric field is suggested in form of a circular quantum well — a unit disc on a plane with four straight channels attached to it. This device implements a triple splitting of an input waveguide. The magnitude of the constant electric field directed parallel to the disc may be defined such that rotation of this field in the plane of the device permits manipulation of the electron current through the triple splitting. The problem of calculating of the current through the switch is reduced to the construction of scattered waves for the Schrödinger operator on the corresponding composite domain with the homogeneous Dirichlet conditions on the boundary. The Dirichlet boundary conditions are found to correspond most closely to real experimental conditions on the boundary of a deep quantum well. Explicit expression for transmission coefficient from one channel to another is obtained. Technically the analysis of the corresponding infinitely-dimensional spectral problem is reduced to the analysis of a relevant finite-dimensional analytic matrix function. We estimate the errors that arise from replacement of infinite-dimensional operator by the finite matrix. Our main result is the calculation of the working point of the switch in the multi-dimensional space of the numerical parameters of the switch which permits the resonance manipulation of the current. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum Switch is one of most important elements of quantum networks, see, for instance [53, 54, 55]. In the present paper mathematical modeling of the Resonance Quantum Switch is reduced to the solution of the corresponding Scattering Problem on a network consisting of a quantum well and few quantum wires attached to it. In a simplest practical problem the roles of quantum wires are played by straight rectangular channels and the role of the quantum well is played by a circular domain, with the boundary having no flat pieces to match the rectangular channels. We suggest a procedure of matching the rectangular channels and a general convex domain with piecewise smooth boundary. The matching problem is reduced to some finite-dimensional equation with matrix-functions. Important spectral characteristics of the above scattering problem such as positions and life-times of resonances may be found numerically from the corresponding determinant condition or via asymptotic analysis — for sufficiently narrow channels.
In quantum computing based on semiconductor quantum dots, adding dots (or just electrons) allows a wider search for an optimal qubit-encoding scheme that is both controllable and coherent. This work reports experiments to realize a hybrid charge-spin qubit in a linear triple quantum dot with asymmetric tunnel couplings, in a multielectron charge configuration. This qubit's energy splitting can be tuned conveniently over a wide range, and the authors attain qualitative understanding of the observations in terms of a three-electron system. This should stimulate further exploration of quantum coherent dynamics in the few-electron regime for semiconductor quantum processors.
Abstract. The reaction matrix of a cavity with attached waveguides connects scattering properties to properties of a corresponding closed billiard for which the waveguides are cut off by straight walls. On the one hand this matrix is directly related to the S-matrix, on the other hand it can be expressed by a spectral sum over all eigenfunctions of the closed system. However, in the physically relevant situation where these eigenfunctions vanish on the impenetrable boundaries of the closed billiard, the spectral sum for the reaction matrix, as it was used before, fails to converge and does not reliably reproduce the scattering properties. We derive here a convergent representation of the reaction matrix in terms of eigenmodes satisfying Dirichlet boundary conditions and demonstrate its validity in the rectangular and the Sinai billiards. Recently, there has been some interest in the application of the reaction-matrix theory of Wigner and Eisenbud [1] and the projection-operator formalism of Feshbach [2], originally developed for the description of nuclear collisions, to chaotic cavities with attached scattering channels [3, 4, 5, 6, 7]. Such models are frequently used as paradigms
In this chapter we generalize the results of Chapter 2 to infinite-dimensional Hilbert spaces. So let H be a Hilbert space and let B ( H ) be the set of all bounded operators on H . Here a notable point is that linear operators on finite - dimensional Hilbert spaces are automatically bounded, whereas in general they are not. Thus we impose boundedness as an extra requirement, beyond linearity. This is very convenient, because as in the finite-dimensional case, B ( H ) is a C*-algebra, cf. §C.1. At the same time, assuming boundedness involves no loss of generality whatsoever, since we can alway replace closed unbounded operators by bounded ones through the bounded transform , as explained in §B.21. Nonetheless, even the relatively easy setting of bounded operators leads to some technical complications we have to deal with. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We present a theoretical proposal of a tunable charge qubit, hosted in triple quantum dots. The manipulation is solely performed by changing the heights of the two potential barriers between the three dots, while the energies of all three dots are fixed. We have found that when the relative heights of the two barriers are changed, the direction of the axis of rotation in performing single-qubit gates can be varied. On the other hand, the corresponding rotation speed can be tuned by raising or lowering the two barriers at the same time. Our proposal therefore allows for tunability of both the rotation axis and rotating speed for a charge qubit via all-electrical control, which may facilitate realization of quantum algorithms in these devices.
Passing from finite phase spaces X to infinite ones yields many fascinating new phenomena, some of which even seem genuinely “emergent” in not having any finite dimensional shadow, approximate or otherwise. Nonetheless, practically all results in the previous chapter remain valid, typically after the inclusion of some technical condition(s) that restrict the almost unlimited freedom allowed by infinite sets. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.