5 research outputs found
On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
We investigate the quantum Jaynes-Cummings model - a particular case of the
Gaudin model with one of the spins being infinite. Starting from the Bethe
equations we derive Baxter's equation and from it a closed set of equations for
the eigenvalues of the commuting Hamiltonians. A scalar product in the
separated variables representation is found for which the commuting
Hamiltonians are Hermitian. In the semi classical limit the Bethe roots
accumulate on very specific curves in the complex plane. We give the equation
of these curves. They build up a system of cuts modeling the spectral curve as
a two sheeted cover of the complex plane. Finally, we extend some of these
results to the XXX Heisenberg spin chain.Comment: 16 page
Nonequilibrium Cooper pairing in the nonadiabatic regime
We obtain a complete solution for the mean-field dynamics of the BCS paired
state with a large, but finite number of Cooper pairs in the non-adiabatic
regime. We show that the problem reduces to a classical integrable Hamiltonian
system and derive a complete set of its integrals of motion. The condensate
exhibits irregular multi-frequency oscillations ergodically exploring the part
of the phase-space allowed by the conservation laws. In the thermodynamic limit
however the system can asymptotically reach a steady state.Comment: 4 pages, no figure
Recipes for spin-based quantum computing
Technological growth in the electronics industry has historically been
measured by the number of transistors that can be crammed onto a single
microchip. Unfortunately, all good things must come to an end; spectacular
growth in the number of transistors on a chip requires spectacular reduction of
the transistor size. For electrons in semiconductors, the laws of quantum
mechanics take over at the nanometre scale, and the conventional wisdom for
progress (transistor cramming) must be abandoned. This realization has
stimulated extensive research on ways to exploit the spin (in addition to the
orbital) degree of freedom of the electron, giving birth to the field of
spintronics. Perhaps the most ambitious goal of spintronics is to realize
complete control over the quantum mechanical nature of the relevant spins. This
prospect has motivated a race to design and build a spintronic device capable
of complete control over its quantum mechanical state, and ultimately,
performing computations: a quantum computer.
In this tutorial we summarize past and very recent developments which point
the way to spin-based quantum computing in the solid-state. After introducing a
set of basic requirements for any quantum computer proposal, we offer a brief
summary of some of the many theoretical proposals for solid-state quantum
computers. We then focus on the Loss-DiVincenzo proposal for quantum computing
with the spins of electrons confined to quantum dots. There are many obstacles
to building such a quantum device. We address these, and survey recent
theoretical, and then experimental progress in the field. To conclude the
tutorial, we list some as-yet unrealized experiments, which would be crucial
for the development of a quantum-dot quantum computer.Comment: 45 pages, 12 figures (low-res in preprint, high-res in journal)
tutorial review for Nanotechnology; v2: references added and updated, final
version to appear in journa