425 research outputs found
Nonlinear dynamics of quantum dot nuclear spins
We report manifestly nonlinear dependence of quantum dot nuclear spin
polarization on applied magnetic fields. Resonant absorption and emission of
circularly polarized radiation pumps the resident quantum dot electron spin,
which in turn leads to nuclear spin polarization due to hyperfine interaction.
We observe that the resulting Overhauser field exhibits hysteresis as a
function of the external magnetic field. This hysteresis is a consequence of
the feedback of the Overhauser field on the nuclear spin cooling rate. A
semi-classical model describing the coupled nuclear and electron spin dynamics
successfully explains the observed hysteresis but leaves open questions for the
low field behaviour of the nuclear spin polarization.Comment: 7 pages, 4 figure
The parameter at three loops and elliptic integrals
We describe the analytic calculation of the master integrals required to
compute the two-mass three-loop corrections to the parameter. In
particular, we present the calculation of the master integrals for which the
corresponding differential equations do not factorize to first order. The
homogeneous solutions to these differential equations are obtained in terms of
hypergeometric functions at rational argument. These hypergeometric functions
can further be mapped to complete elliptic integrals, and the inhomogeneous
solutions are expressed in terms of a new class of integrals of combined
iterative non-iterative nature.Comment: 14 pages Latex, 7 figures, to appear in the Proceedings of "Loops and
Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018, Po
Topology by dissipation
Topological states of fermionic matter can be induced by means of a suitably
engineered dissipative dynamics. Dissipation then does not occur as a
perturbation, but rather as the main resource for many-body dynamics, providing
a targeted cooling into a topological phase starting from an arbitrary initial
state. We explore the concept of topological order in this setting, developing
and applying a general theoretical framework based on the system density matrix
which replaces the wave function appropriate for the discussion of Hamiltonian
ground-state physics. We identify key analogies and differences to the more
conventional Hamiltonian scenario. Differences mainly arise from the fact that
the properties of the spectrum and of the state of the system are not as
tightly related as in a Hamiltonian context. We provide a symmetry-based
topological classification of bulk steady states and identify the classes that
are achievable by means of quasi-local dissipative processes driving into
superfluid paired states. We also explore the fate of the bulk-edge
correspondence in the dissipative setting, and demonstrate the emergence of
Majorana edge modes. We illustrate our findings in one- and two-dimensional
models that are experimentally realistic in the context of cold atoms.Comment: 61 pages, 8 figure
Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
We calculate 3-loop master integrals for heavy quark correlators and the
3-loop QCD corrections to the -parameter. They obey non-factorizing
differential equations of second order with more than three singularities,
which cannot be factorized in Mellin- space either. The solution of the
homogeneous equations is possible in terms of convergent close integer power
series as Gau\ss{} hypergeometric functions at rational argument. In
some cases, integrals of this type can be mapped to complete elliptic integrals
at rational argument. This class of functions appears to be the next one
arising in the calculation of more complicated Feynman integrals following the
harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic
polylogarithms, square-root valued iterated integrals, and combinations
thereof, which appear in simpler cases. The inhomogeneous solution of the
corresponding differential equations can be given in terms of iterative
integrals, where the new innermost letter itself is not an iterative integral.
A new class of iterative integrals is introduced containing letters in which
(multiple) definite integrals appear as factors. For the elliptic case, we also
derive the solution in terms of integrals over modular functions and also
modular forms, using -product and series representations implied by Jacobi's
functions and Dedekind's -function. The corresponding
representations can be traced back to polynomials out of Lambert--Eisenstein
series, having representations also as elliptic polylogarithms, a -factorial
, logarithms and polylogarithms of and their -integrals.
Due to the specific form of the physical variable for different
processes, different representations do usually appear. Numerical results are
also presented.Comment: 68 pages LATEX, 10 Figure
Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations
Various of the single scale quantities in massless and massive QCD up to
3-loop order can be expressed by iterative integrals over certain classes of
alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples
are the anomalous dimensions to 3-loop order, the massless Wilson coefficients
and also different massive operator matrix elements. Starting at 3-loop order,
however, also other letters appear in the case of massive operator matrix
elements, the so called iterative non-iterative integrals, which are related to
solutions based on complete elliptic integrals or any other special function
with an integral representation that is definite but not a Volterra-type
integral. After outlining the formalism leading to iterative non-iterative
integrals,we present examples for both of these cases with the 3-loop anomalous
dimension and the structure of the principle solution in
the iterative non-interative case of the 3-loop QCD corrections to the
-parameter.Comment: 13 pages LATEX, 2 Figure
Exciton condensates in semiconductor quantum wells emit coherent light
We show that a quasi-two dimensional condensate of optically active excitons
emits coherent light even in the absence of population inversion. This allows
an unambiguous and clear experimental detection of the condensed phase. We
prove that, due to the exciton-photon coupling, quantum and thermal
fluctuations do not destroy condensation at finite temperature. Suitable
conditions to achieve condensation are temperatures of a few K for typical
exciton densities, and the use of a pulsed, and preferably circularly
polarized, laser.Comment: 5 pages, no figure
Knight Field Enabled Nuclear Spin Polarization in Single Quantum Dots
We demonstrate dynamical nuclear spin polarization in the absence of an
external magnetic field, by resonant circularly polarized optical excitation of
a single electron or hole charged quantum dot. Optical pumping of the electron
spin induces an effective inhomogeneous magnetic (Knight) field that determines
the direction along which nuclear spins could polarize and enables nuclear-spin
cooling by suppressing depolarization induced by nuclear dipole-dipole
interactions. Our observations suggest a new mechanism for spin-polarization
where spin exchange with an electron reservoir plays a crucial role. These
experiments constitute a first step towards quantum measurement of the
Overhauser field.Comment: 5 pages, 3 figure
Dynamic nuclear spin polarization in resonant laser spectroscopy of a quantum dot
Resonant optical excitation of lowest-energy excitonic transitions in
self-assembled quantum dots lead to nuclear spin polarization that is
qualitatively different from the well known optical orientation phenomena. By
carrying out a comprehensive set of experiments, we demonstrate that nuclear
spin polarization manifests itself in quantum dots subjected to finite external
magnetic field as locking of the higher energy Zeeman transition to the driving
laser field, as well as the avoidance of the resonance condition for the lower
energy Zeeman branch. We interpret our findings on the basis of dynamic nuclear
spin polarization originating from non-collinear hyperfine interaction and find
an excellent agreement between the experimental results and the theoretical
model
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