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Register a new userEvolution of a quantum spin system to its ground state: Role of entanglement and interaction symmetry
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We study the decoherence of two ferro- and antiferromagnetically coupled spins that interact with a frustrated spin-bath environment in its ground state. The conditions under which the two-spin system relaxes from the initial spin-up - spin-down state towards its ground state are determined. It is shown that the two-spin system relaxes to its ground state for narrow ranges of the model parameters only. It is demonstrated that the symmetry of the coupling between the two-spin system and the environment has an important effect on the relaxation process. In particular, we show that if this coupling conserves the magnetization, the two-spin system readily relaxes to its ground state whereas a non-conserving coupling prevents the two-spin system from coming close to its ground state.
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We consider the evolution of a quantum state of a Hamiltonian which is parametrically perturbed via a term proportional to the adiabatic parameter lambda (t). Starting with the Pechukas-Yukawa mapping of the energy eigenvalues evolution on a generalised Calogero-Sutherland model of 1D classical gas, we consider the adiabatic approximation with two different expansions of the quantum state in powers of dlambda/dt and compare them with a direct numerical simulation. We show that one of these expansions (Magnus series) is especially convenient for the description of non-adiabatic evolution of the system. Applying the expansion to the exact cover 3-satisfability problem, we obtain the occupation dynamics which provides insight on the population of states.
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In this paper we calculate the block entanglement entropies of spin models whose ground states have perfect antiferromagnetic or ferromagnetic long-range order. In the latter case the definition of entanglement entropy is extended to properly take into account the ground state degeneracy. We find in both cases the entropy grows logarithmically with the block size. Implication of our results on states with general long-range order will be discussed.
Without resorting to spin-spin coupling, we propose a scalable spin quantum computing scheme assisted with a semiconductor multiple-quantum-dot structure. The techniques of single electron transitions and the nanostructure of quantum-dot cellular automata (QCA) are used to generate charge entangled states of two electrons, which are then converted into spin entanglement states using single-spin rotations only. Deterministic two-qubit quantum gates are also manipulated using only single-spin rotations with the help of QCA. A single-shot readout of spin states can be carried out by coupling the multiple dot structure to a quantum point contact. As a result, deterministic spin-interaction-free quantum computing can be implemented in semiconductor nanostructure.
We present a quantum theory of cooling of a mechanical resonator using back-action with constant electron current. The resonator device is based on a doubly clamped nanotube, which mechanically vibrates and acts as a double quantum dot for electron transport. Mechanical vibrations and electrons are coupled electrostatically using an external gate. The fundamental eigenmode is cooled by absorbing phonons when electrons tunnel through the double quantum dot. We identify the regimes in which ground state cooling can be achieved for realistic experimental parameters.
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