22,613 research outputs found
Towards the chemical tuning of entanglement in molecular nanomagnets
Antiferromagnetic spin rings represent prototypical realizations of highly
correlated, low-dimensional systems. Here we theoretically show how the
introduction of magnetic defects by controlled chemical substitutions results
in a strong spatial modulation of spin-pair entanglement within each ring.
Entanglement between local degrees of freedom (individual spins) and collective
ones (total ring spins) are shown to coexist in exchange-coupled ring dimers,
as can be deduced from general symmetry arguments. We verify the persistence of
these features at finite temperatures, and discuss them in terms of
experimentally accessible observables.Comment: 5 pages, 4 figure
Lower bounds on concurrence and separability conditions
We obtain analytical lower bounds on the concurrence of bipartite quantum
systems in arbitrary dimensions related to the violation of separability
conditions based on local uncertainty relations and on the Bloch representation
of density matrices. We also illustrate how these results complement and
improve those recently derived [K. Chen, S. Albeverio, and S.-M. Fei, Phys.
Rev. Lett. 95, 040504 (2005)] by considering the Peres-Horodecki and the
computable cross norm or realignment criteria.Comment: 5 pages, 1 figure; minor changes, references added; final version:
minor correction in proof of lemma 1, scope of theorem 2 clarified, to appear
in PRA; mistake in proof of lemma 1 of published version corrected, results
unchange
Dynamics of Atom-Field Entanglement from Exact Solutions: Towards Strong Coupling and Non-Markovian Regimes
We examine the dynamics of bipartite entanglement between a two-level atom
and the electromagnetic field. We treat the Jaynes-Cummings model with a single
field mode and examine in detail the exact time evolution of entanglement,
including cases where the atomic state is initially mixed and the atomic
transition is detuned from resonance. We then explore the effects of other
nearby modes by calculating the exact time evolution of entanglement in more
complex systems with two, three, and five field modes. For these cases we can
obtain exact solutions which include the strong coupling regimes. Finally, we
consider the entanglement of a two-level atom with the infinite collection of
modes present in the intracavity field of a Fabre-Perot cavity. In contrast to
the usual treatment of atom-field interactions with a continuum of modes using
the Born-Markov approximation, our treatment in all cases describes the full
non-Markovian dynamics of the atomic subsystem. Only when an analytic
expression for the infinite mode case is desired do we need to make a weak
coupling assumption which at long times approximates Markovian dynamics.Comment: 12 pages, 5 figures; minor changes in grammar, wording, and
formatting. One unnecessary figure removed. Figure number revised (no longer
counts subfigures separately
Hydrogenic Spin Quantum Computing in Silicon: A Digital Approach
We suggest an architecture for quantum computing with spin-pair encoded
qubits in silicon. Electron-nuclear spin-pairs are controlled by a dc magnetic
field and electrode-switched on and off hyperfine interaction. This digital
processing is insensitive to tuning errors and easy to model. Electron
shuttling between donors enables multi-qubit logic. These hydrogenic spin
qubits are transferable to nuclear spin-pairs, which have long coherence times,
and electron spin-pairs, which are ideally suited for measurement and
initialization. The architecture is scalable to highly parallel operation.Comment: 4 pages, 5 figures; refereed and published version with improved
introductio
Mean-field dynamics of two-mode Bose-Einstein condensates in highly anisotropic potentials: Interference, dimensionality, and entanglement
We study the mean-field dynamics and the reduced-dimension character of
two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means
of perturbative techniques, we show that the tightly confined (transverse)
degrees of freedom can be decoupled from the dynamical equations at the expense
of introducing additional effective three-body, attractive, intra- and
inter-mode interactions into the dynamics of the loosely confined
(longitudinal) degrees of freedom. These effective interactions are mediated by
changes in the transverse wave function. The perturbation theory is valid as
long as the nonlinear scattering energy is small compared to the transverse
energy scales. This approach leads to reduced-dimension mean-field equations
that optimally describe the evolution of a two-mode condensate in general
quasi-1D and quasi-2D geometries. We use this model to investigate the relative
phase and density dynamics of a two-mode, cigar-shaped Rb BEC. We study
the relative-phase dynamics in the context of a nonlinear Ramsey interferometry
scheme, which has recently been proposed as a novel platform for high-precision
interferometry. Numerical integration of the coupled, time-dependent,
three-dimensional, two-mode Gross-Pitaevskii equations for various atom numbers
shows that this model gives a considerably more refined analytical account of
the mean-field evolution than an idealized quasi-1D description.Comment: 35 pages, 10 figures. Current version is as publishe
Ginsparg-Wilson-Luscher Symmetry and Ultralocality
Important recent discoveries suggest that Ginsparg-Wilson-Luscher (GWL)
symmetry has analogous dynamical consequences for the theory on the lattice as
chiral symmetry does in the continuum. While it is well known that inherent
property of lattice chiral symmetry is fermion doubling, we show here that
inherent property of GWL symmetry is that the infinitesimal symmetry
transformation couples fermionic degrees of freedom at arbitrarily large
lattice distances (non-ultralocality). The consequences of this result for
ultralocality of symmetric actions are discussed.Comment: 18 pages, LATEX. For clarity changed to infinitesimal
transformations, typos corrected, explicit hypothesis adde
Entanglement requirements for implementing bipartite unitary operations
We prove, using a new method based on map-state duality, lower bounds on
entanglement resources needed to deterministically implement a bipartite
unitary using separable (SEP) operations, which include LOCC (local operations
and classical communication) as a particular case. It is known that the Schmidt
rank of an entangled pure state resource cannot be less than the Schmidt rank
of the unitary. We prove that if these ranks are equal the resource must be
uniformly (maximally) entangled: equal nonzero Schmidt coefficients. Higher
rank resources can have less entanglement: we have found numerical examples of
Schmidt rank 2 unitaries which can be deterministically implemented, by either
SEP or LOCC, using an entangled resource of two qutrits with less than one ebit
of entanglement.Comment: 7 pages Revte
Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems
In this paper we discuss the properties of the reduced density matrix of
quantum many body systems with permutational symmetry and present basic
quantification of the entanglement in terms of the von Neumann (VNE), Renyi and
Tsallis entropies. In particular, we show, on the specific example of the spin
Heisenberg model, how the RDM acquires a block diagonal form with respect
to the quantum number fixing the polarization in the subsystem conservation
of and with respect to the irreducible representations of the
group. Analytical expression for the RDM elements and for the
RDM spectrum are derived for states of arbitrary permutational symmetry and for
arbitrary polarizations. The temperature dependence and scaling of the VNE
across a finite temperature phase transition is discussed and the RDM moments
and the R\'{e}nyi and Tsallis entropies calculated both for symmetric ground
states of the Heisenberg chain and for maximally mixed states.Comment: Festschrift in honor of the 60th birthday of Professor Vladimir
Korepin (11 pages, 5 figures
Unitarily localizable entanglement of Gaussian states
We consider generic -mode bipartitions of continuous variable
systems, and study the associated bisymmetric multimode Gaussian states. They
are defined as -mode Gaussian states invariant under local mode
permutations on the -mode and -mode subsystems. We prove that such states
are equivalent, under local unitary transformations, to the tensor product of a
two-mode state and of uncorrelated single-mode states. The entanglement
between the -mode and the -mode blocks can then be completely
concentrated on a single pair of modes by means of local unitary operations
alone. This result allows to prove that the PPT (positivity of the partial
transpose) condition is necessary and sufficient for the separability of -mode bisymmetric Gaussian states. We determine exactly their negativity and
identify a subset of bisymmetric states whose multimode entanglement of
formation can be computed analytically. We consider explicit examples of pure
and mixed bisymmetric states and study their entanglement scaling with the
number of modes.Comment: 10 pages, 2 figure
Spin Relaxation in a Quantum Dot due to Nyquist Noise
We calculate electron and nuclear spin relaxation rates in a quantum dot due
to the combined action of Nyquist noise and electron-nuclei hyperfine or
spin-orbit interactions. The relaxation rate is linear in the resistance of the
gate circuit and, in the case of spin-orbit interaction, it depends essentially
on the orientations of both the static magnetic field and the fluctuating
electric field, as well as on the ratio between Rashba and Dresselhaus
interaction constants. We provide numerical estimates of the relaxation rate
for typical system parameters, compare our results with other, previously
discussed mechanisms, and show that the Nyquist mechanism can have an
appreciable effect for experimentally relevant systems.Comment: v2: New discussion of arbitrary gate setups (1 new figure), more
Comments on experiments; 6 pages, 4 figure
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