We study the effect of spin-orbit interaction and in-plane effective magnetic field on the conductance of a quasi-one-dimensional ballistic electron system. The effective magnetic field includes the externally applied field, as well as the field due to polarized nuclear spins. The interplay of the spin-orbit interaction with effective magnetic field significantly modifies the band structure, producing additional sub-band extrema and energy gaps, introducing the dependence of the sub-band energies on the field direction. We generalize the Landauer formula at finite temperatures to incorporate these special features of the dispersion relation. The obtained formula describes the conductance of a ballistic conductor with an arbitrary dispersion relation.Recently, there have been numerous studies, both theoretical and experimental, of the properties of quasi-one-dimensional systems [1][2][3][4][5][6][7][8]. The motivation behind this interest has been the observation of conductance quantization. Most quasi-one-dimensional systems, or Quantum Wires (QW), are created by a split gate technique in a two-dimensional electron gas (2DEG) [6,7]. When a negative potential is applied to the gates, the electrons are depleted underneath. Thus, a one-dimensional channel or constriction is created between two reservoirs, in this case the 2DEG. For ballistic transport to occur [1], this constriction should be less than the electron mean free path, and have a width of the order of de Broglie wavelength [6][7][8]. When these conditions are satisfied, the electrons will move ballistically in the lateral direction and are confined transversely. The transverse confinement creates a discrete set of modes in the channel.The explanation for conductance quantization is found by using a non-interacting electron model.With a small bias applied across the channel, the electrons move from one reservoir to the other. Due to the transverse confinement in channel, the electrons are distributed, according to the Fermi-Dirac distribution, among various sub-bands in the channel. The calculation of the conductance has been summarized in the Landauer-Büttiker formalism [6][7][8]. Each one of the sub-bands contributes to the conductance.

Coulomb interaction turns anyonic quasiparticles of a primary quantum Hall liquid with filling factor ν = 1/(2m + 1) into hard-core anyons. We have developed a model of coherent transport of such quasiparticles in systems of multiple antidots by extending the Wigner-Jordan description of 1D abelian anyons to tunneling problems. We show that the anyonic exchange statistics manifests itself in tunneling conductance even in the absence of quasiparticle exchanges. In particular, it can be seen as a non-vanishing resonant peak associated with quasiparticle tunneling through a line of three antidots. [5,6]. The situation with fractional statistics is so far less certain even in the case of the abelian statistics, which is the subject of this work. Although the recent experiments [7] demonstrating unusual flux periodicity of conductance of a quasiparticle interferometer can be interpreted as a manifestation of the fractional statistics [8,9], this interpretation is not universally accepted [10,11]. There is a number of theoretical proposals (see, e.g., [12,13]) suggesting tunnel structures where the statistics manifests itself through noise properties. Partly due to complexity of noise measurements, such experiments have not been performed successfully up to now. In this work, we show that coherent quasiparticle dynamics in multiantidot structures should provide clear signatures of the exchange statistics in dc transport. Most notably, in tunneling through a line of three antidots, fractional statistics leads to a non-vanishing peak of the tunnel conductance which would vanish for integer statistics.These effects rely on the ability of quantum antidots to localize individual quasiparticles of the QH liq- uids [4,14,15]. The resulting transport phenomena in antidots are very similar to those associated with the Coulomb blockade [16] in tunneling of individual electrons in dots. For instance, similarly to a quantum dot [19], the linear conductance of one antidot shows periodic oscillations with each period corresponding to the addition of one quasiparticle [4,14,15,17,18]. Recently, we have developed a theory of such Coulomb-blockade-type tunneling for a double-antidot system [20], where quasiparticle exchange statistics does not affect the transport. The goal of this work is to extend this theory to antidot structures where the statistics does affect the conductance. The two simplest structures with this property consist of three antidots and have quasi-1D geometries with either periodic or open boundary conditions (Fig. 1). A technical issue that needed to be resolved to calculate the tunnel conductance is that the anyonic field operators defined through the Wigner-Jordan transformation [21,22,23,24], are not fully sufficient in the situations of tunneling. As we show below, to obtain correct matrix elements for anyon tunneling, one needs to keep track of the appropriate boundary conditions of the wavefunctions which are not accounted for in the field operators.Specifically, we consider the antidots coupled by tunneli...

We have studied the decoherence properties of adiabatic quantum computation (AQC) in the presence of in general non-Markovian, e.g., low-frequency, noise. The developed description of the incoherent Landau-Zener transitions shows that the global AQC maintains its properties even for decoherence larger than the minimum gap at the anticrossing of the two lowest energy levels. The more efficient local AQC, however, does not improve scaling of the computation time with the number of qubits n as in the decoherence-free case. The scaling improvement requires phase coherence throughout the computation, limiting the computation time and the problem size n.The adiabatic ground-state scheme of quantum computation [1,2] represents an important alternative to the gate-model approach. In adiabatic quantum computation (AQC) the Hamiltonian H S of the qubit register and its wave function |ψ undergo adiabatic evolution in such a way that, while the transformations of |ψ represent some meaningful computation, this state also remains close to the instantaneous ground state |ψ G of H S throughout the process. This is achieved by starting the evolution from a sufficiently simple initial Hamiltonian H i , the ground state of which can be reached directly (e.g., by energy relaxation), and evolving into a final Hamiltonian H f , whose ground state provides the solution to some complex computation problem:where s(t) changes from 0 to 1 between some initial (t i =0) and final (t f ) times.The advantage of performing a computation this way, besides its insensitivity to gate errors, is that the energy gap between the ground and excited states of the Hamiltonian H S ensures some measure of protection against decoherence. This protection, as partly demonstrated in this work, is not absolute. Nevertheless, it allows for the ground state to maintain its coherence properties in time far beyond what would be the single-qubit decoherence time in the absence of the ground-state protection. This feature of the AQC remains intact [3] even if the decoherence strength and/or temperature is much larger than the minimum gap.In general, the performance of an adiabatic algorithm depends on the structure of the energy spectrum of its Hamiltonian H S . Here we consider a situation, which is typical for complex search and optimization problems [3], when the performance is limited by the anticrossing of the two lowest energy states. The minimum gap g m between those states shrinks with an increasing number n of qubits in the algorithm, although the exact scaling relation is not known in general. In an isolated system with no decoherence, the limitation is due to the usual Landau-Zener tunneling at the anticrossing, which drives the system out of the ground state with the probability given by the "adiabatic theorem". Different formulations of the theorem all give the computation time as some power of the minimum gap: t f ∝ g that there exists a well-defined energy gap between the two lowest energy states of the system. In a more realistic case with decoherenc...

We devise an approach to measure the polarization of nuclear spins via conductance measurements. Specifically, we study the combined effect of external magnetic field, nuclear spin polarization, and Rashba spin-orbit interaction on the conductance of a quantum wire. Nonequilibrium nuclear spin polarization affects the electron energy spectrum making it time-dependent. Changes in the extremal points of the spectrum result in time-dependence of the conductance. The conductance oscillation pattern can be used to obtain information about the amplitude of the nuclear spin polarization and extract the characteristic time scales of the nuclear spin subsystem.PACS numbers: 72.25. Dc, The promise of spintronics and quantum computing has motivated recent theoretical and experimental investigations of spin-related effects in semiconductor heterostructures [1,2,3,4,5,6,7,8,9,10]. Nuclear and electron spins have been considered as candidates for qubit implementations in solid state systems [1,2,3,4,5,6]. The final stage of a quantum computation process involves readout of quantum information. In the case of a spin qubit one would have to measure the state of a single spin. Yet, in spite of recent efforts in this field, a single nuclear spin measurement is still a great challenge.There are several proposals for single-and few-spin measurement. For example, a change of the oscillation frequency of a micro-mechanical resonator (cantilever) [11] is used. Another possibility to obtain information about a qubit state lies in the measurement [12] of current or its noise spectrum in a mesoscopic system (e.g., quantum wire, quantum dot, or single electron transistor) coupled to a qubit [13,14,15]. Significant progress in spin measurements has been made using magnetic resonance force microscopy [16], which presently allows one to probe the state of 100 fully polarized electron spins. Recently, an experimental architecture to manipulate the magnetization of nuclear spin domains was proposed [5,6].The present work demonstrates that a relatively small ensemble of nuclear spins can significantly influence transport through a quantum wire (QW). This offers a new detector design, with the operation based on a new effect arising as a consequence of the combined influence of the spin-orbit interaction and nuclear spin polarization on the electron subsystem. Recent progress in investigations of QWs [17,18,19,20,21,22,23,24,25,26,27,28] makes them a promising nanoscale device component.We consider transport through a QW in the presence of an external in-plane magnetic field, Rashba spin-orbit coupling [29] and a nonequilibrium nuclear spin polarization. We assume that the external magnetic field is directed along a wire. If the nuclear spin polarization has a non-zero component perpendicular to the external field at the initial moment of time (i.e. the two vectors are not aligned), then we will demonstrate that the conductance of the wire exhibits damped oscillations. These oscillations are a direct consequence of the interplay between the evol...