11 research outputs found
Spin decoherence and manipulation in quantum dots : the role of the spin-orbit interaction
Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques,
the spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes.
We reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins.
Chapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies.
Chapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble
Cluster States From Heisenberg Interaction
We show that a special type of entangled states, cluster states, can be
created with Heisenberg interactions and local rotations in 2d steps where d is
the dimension of the lattice. We find that, by tuning the coupling strengths,
anisotropic exchange interactions can also be employed to create cluster
states. Finally, we propose electron spins in quantum dots as a possible
realization of a one-way quantum computer based on cluster states
Spin Decay in a Quantum Dot Coupled to a Quantum Point Contact
We consider a mechanism of spin decay for an electron spin in a quantum dot
due to coupling to a nearby quantum point contact (QPC) with and without an
applied bias voltage. The coupling of spin to charge is induced by the
spin-orbit interaction in the presence of a magnetic field. We perform a
microscopic calculation of the effective Hamiltonian coupling constants to
obtain the QPC-induced spin relaxation and decoherence rates in a realistic
system. This rate is shown to be proportional to the shot noise of the QPC in
the regime of large bias voltage and scales as where is the
distance between the quantum dot and the QPC. We find that, for some specific
orientations of the setup with respect to the crystallographic axes, the
QPC-induced spin relaxation and decoherence rates vanish, while the charge
sensitivity of the QPC is not changed. This result can be used in experiments
to minimize QPC-induced spin decay in read-out schemes.Comment: 10 pages, 2 figures, 2 table
Two-spin relaxation of P-dimers in Silicon
We study two-electron singlet-triplet relaxation of donor-bound electrons in
Silicon. Hyperfine interaction of the electrons with the phosphorus (P) nuclei,
in combination with the electron-phonon interaction, lead to relaxation of the
triplet states. Within the Heitler-London and effective mass approximations, we
calculate the triplet relaxation rates in the presence of an applied magnetic
field. This relaxation mechanism affects the resonance peaks in current
Electron Spin Resonance (ESR) experiments on P-dimers. Moreover, the estimated
time scales for the spin decay put an upper bound on the gate pulses needed to
perform fault-tolerant two-qubit operations in donor-spin-based quantum
computers (QCs).Comment: 3 figures, 1 tabl
Spin Manipulation and Relaxation in Spin-Orbit Qubits
We derive a generalized form of the Electric Dipole Spin Resonance (EDSR)
Hamiltonian in the presence of the spin-orbit interaction for single spins in
an elliptic quantum dot (QD) subject to an arbitrary (in both direction and
magnitude) applied magnetic field. We predict a nonlinear behavior of the Rabi
frequency as a function of the magnetic field for sufficiently large Zeeman
energies, and present a microscopic expression for the anisotropic electron
g-tensor. Similarly, an EDSR Hamiltonian is devised for two spins confined in a
double quantum dot (DQD), where coherent Rabi oscillations between the singlet
and triplet states are induced by jittering the inter-dot distance at the
resonance frequency. Finally, we calculate two-electron-spin relaxation rates
due to phonon emission, for both in-plane and perpendicular magnetic fields.
Our results have immediate applications to current EDSR experiments on nanowire
QDs, g-factor optimization of confined carriers, and spin decay measurements in
DQD spin-orbit qubits.Comment: 4 figures, 1 Tabl
Electric-dipole-induced spin resonance in quantum dots
An alternating electric field, applied to a quantum dot, couples to the electron spin via the spin-orbit interaction. We analyze different types of spin-orbit coupling known in the literature and find two efficient mechanisms of spin control in quantum dots. The linear in momentum Dresselhaus and Rashba spin-orbit couplings give rise to a fully transverse effective magnetic field in the presence of a Zeeman splitting at lowest order in the spin-orbit interaction. The cubic in momentum Dresselhaus terms are efficient in a quantum dot with anharmonic confining potential and give rise to a spin-electric coupling proportional to the orbital magnetic field. We derive an effective spin Hamiltonian, which can be used to implement spin manipulation on a time scale of 10 ns with the current experimental setups
Holonomic quantum computation with electron spins in quantum dots
With the help of the spin-orbit interaction, we propose a scheme to perform
holonomic single qubit gates on the electron spin confined to a quantum dot.
The manipulation is done in the absence (or presence) of an applied magnetic
field. By adiabatic changing the position of the confinement potential, one can
rotate the spin state of the electron around the Bloch sphere in semiconductor
heterostructures. The dynamics of the system is equivalent to employing an
effective non-Abelian gauge potential whose structure depends on the type of
the spin-orbit interaction. As an example, we find an analytic expression for
the electron spin dynamics when the dot is moved around a circular path (with
radius R) on the two dimensional electron gas (2DEG), and show that all single
qubit gates can be realized by tuning the radius and orientation of the
circular paths. Moreover, using the Heisenberg exchange interaction, we
demonstrate how one can generate two-qubit gates by bringing two quantum dots
near each other, yielding a scalable scheme to perform quantum computing on
arbitrary N qubits.
This proposal shows a way of realizing holonomic quantum computers in
solid-state systems
Spin decay in a quantum dot coupled to a quantum point contact
We consider a mechanism of spin decay for an electron spin in a quantum dot due to coupling to a nearby quantum point contact (QPC) with and without an applied bias voltage. The coupling of spin to charge is induced by the spin-orbit interaction in the presence of a magnetic field. We perform a microscopic calculation of the effective Hamiltonian coupling constants to obtain the QPC-induced spin relaxation and decoherence rates in a realistic system. This rate is shown to be proportional to the shot noise of the QPC in the regime of large bias voltage and scales as a(-6) where a is the distance between the quantum dot and the QPC. We find that, for some specific orientations of the setup with respect to the crystallographic axes, the QPC-induced spin relaxation and decoherence rates vanish, while the charge sensitivity of the QPC is not changed. This result can be used in experiments to minimize QPC-induced spin decay in read-out schemes.(1
Theory of spin qubits in nanostructures
We review recent advances on the theory of spin qubits in nanostructures. We focus on four selected topics. First, we show how to form spin qubits in the new and promising material graphene. Afterwards, we discuss spin relaxation and decoherence in quantum dots. In particular, we demonstrate how charge fluctations in the surrounding environment cause spin decay via spin-orbit coupling. We then turn to a brief overview of how one can use electric dipole spin resonance (EDSR) to perform single spin rotations in quantum dots using an oscillating electric field. The final topic we cover is the spin-spin coupling via spin-orbit interaction which is an alternative to the usual spin-spin coupling via the Heisenberg exchange interaction