Daniel Loss

Quantum computation with quantum dots

We propose an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a recently derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments that would provide an initial demonstration of the desired nonequilibrium spin dynamics are proposed.

Quantum computing in molecular magnets

Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shors algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grovers algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grovers algorithm that uses molecular magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105, with access times as short as 10-10 seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.

Semiconductor spintronics and quantum computation

1 Ferromagnetic III-V Semiconductors and Their Heterostructures.- 2 Spin Injection and Transport in Micro- and Nanoscale Devices.- 3 Electrical Spin Injection: Spin-Polarized Transport from Magnetic into Non-Magnetic Semiconductors.- 4 Spin Dynamics in Semiconductors.- 5 Optical Manipulation, Transport and Storage of Spin Coherence in Semiconductors.- 6 Spin Condensates in Semiconductor Microcavities.- 7 Spins for Quantum Information Processing.- 8 Electron Spins in Quantum Dots as Qubits for Quantum Information Processing.- 9 Regulated Single Photons and Entangled Photons From a Quantum Dot Microcavity.

Coupled quantum dots as quantum gates

We consider a quantum-gate mechanism based on electron spins in coupled semiconductor quantum dots. Such gates provide a general source of spin entanglement and can be used for quantum computers. We determine the exchange coupling J in the effective Heisenberg model as a function of magnetic (B) and electric fields, and of the interdot distance a within the Heitler-London approximation of molecular physics. This result is refined by using sp hybridization, and by the Hund-Mulliken molecular-orbit approach, which leads to an extended Hubbard description for the two-dot system that shows a remarkable dependence on B and a due to the long-range Coulomb interaction. We find that the exchange J changes sign at a finite field (leading to a pronounced jump in the magnetization) and then decays exponentially. The magnetization and the spin susceptibilities of the coupled dots are calculated. We show that the dephasing due to nuclear spins in GaAs can be strongly suppressed by dynamical nuclear-spin polarization and/or by magnetic fields.

Spin qubits in graphene quantum dots

The main characteristics of good qubits are long coherence times in combination with fast operating times. It is well known that carbon-based materials could increase the coherence times of spin qubits, which are among the most developed solid-state qubits. Here, we propose how to form spin qubits in graphene quantum dots. A crucial requirement to achieve this goal is to find quantum-dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with armchair boundaries. The most remarkable new feature of the proposed spin qubits is that, in an array of many qubits, it is possible to couple any two of them via Heisenberg exchange with the others being decoupled by detuning. This unique feature is a direct consequence of the quasi-relativistic spectrum of graphene.

Nonballistic spin-field-effect transistor

We propose a spin-field-effect transistor based on spin-orbit coupling of both the Rashba and the Dresselhaus types. Different from earlier proposals, spin transport through our device is tolerant against spin-independent scattering processes. Hence the requirement of strictly ballistic transport can be relaxed. This follows from a unique interplay between the Dresselhaus and the Rashba coupling; these can be tuned to have equal strengths, leading to k-independent eigenspinors even in two dimensions. We discuss two-dimensional devices as well as quantum wires. In the latter, our setup presents strictly parabolic dispersions which avoids complications from anticrossings of different bands.

Electron spin decoherence in quantum dots due to interaction with nuclei

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei. The decay is caused by the spatial variation of the electron wave function within the dot, leading to a nonuniform hyperfine coupling A. We evaluate the spin correlation function and find that the decay is not exponential but rather power (inverse logarithm) lawlike. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by (planck)N/A, where N is the number of nuclei inside the dot, and the amplitude of precession decays to a finite value. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.

Spin qubits with electrically gated polyoxometalate molecules

Spin qubits offer one of the most promising routes to the implementation of quantum computers. Very recent results in semiconductor quantum dots show that electrically-controlled gating schemes are particularly well-suited for the realization of a universal set of quantum logical gates. Scalability to a larger number of qubits, however, remains an issue for such semiconductor quantum dots. In contrast, a chemical bottom-up approach allows one to produce identical units in which localized spins represent the qubits. Molecular magnetism has produced a wide range of systems with properties that can be tailored, but so far, there have been no molecules in which the spin state can be controlled by an electrical gate. Here we propose to use the polyoxometalate [PMo12O40(VO)2]q-, where two localized spins with S = 1/2 can be coupled through the electrons of the central core. Through electrical manipulation of the molecular redox potential, the charge of the core can be changed. With this setup, two-qubit gates and qubit readout can be implemented.

Quantum dot as spin filter and spin memory

We consider a quantum dot in the Coulomb blockade regime weakly coupled to current leads and show that in the presence of a magnetic field it acts as an efficient spin filter (at the single-spin level), producing a spin-polarized current. Conversely, if the leads are fully spin polarized the up or the down state of the spin on the dot results in a large sequential or a small cotunneling current, and, thus, together with ESR techniques, the setup can be operated as a single-spin memory.

Phonon-induced decay of the electron spin in quantum dots

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit (SO) interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time T-2 is as large as the spin relaxation time T-1, under realistic conditions. For the Dresselhaus and Rashba SO couplings, we find that, in leading order, the effective B field can have only fluctuations transverse to the applied B field. As a result, T-2=2T(1) for arbitrarily large Zeeman splittings, in contrast to the naively expected case T-2