24 research outputs found
Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
Using the Algebraic Bethe Ansatz in conjunction with a simple Monte Carlo
sampling technique, we study the problem of the decoherence of a central spin
coupled to a nuclear spin bath. We describe in detail the full crossover from
strong to weak external magnetic field field, a limit where a large
non-decaying coherence factor is found. This feature is explained by
Bose-Einstein-condensate-like physics which also allows us to argue that the
corresponding zero frequency peak would not be broadened by statistical or
ensemble averaging.Comment: 5 pages, 4 figures, published versio
Spin decoherence due to a randomly fluctuating spin bath
We study the decoherence of a spin in a quantum dot due to its hyperfine
coupling to a randomly fluctuating bath of nuclear spins. The system is
modelled by the central spin model with the spin bath initially being at
infinite temperature. We calculate the spectrum and time evolution of the
coherence factor using a Monte Carlo sampling of the exact eigenstates obtained
via the algebraic Bethe ansatz. The exactness of the obtained eigenstates
allows us to study the non-perturbative regime of weak magnetic fields in a
full quantum mechanical treatment. In particular, we find a large non-decaying
fraction in the zero-field limit. The crossover from strong to weak fields is
similar to the decoherence starting from a pure initial bath state treated
previously. We compare our results to a simple semiclassical picture [Merkulov
et al., Phys. Rev. B 65, 205309 (2002)] and find surprisingly good agreement.
Finally, we discuss the effect of weakly coupled spins and show that they will
eventually lead to complete decoherence
Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin
In this work we present a determinant expression for the domain-wall boundary
condition partition function of rational (XXX) Richardson-Gaudin models which,
in addition to spins , contains one arbitrarily large spin
.
The proposed determinant representation is written in terms of a set of
variables which, from previous work, are known to define eigenstates of the
quantum integrable models belonging to this class as solutions to quadratic
Bethe equations. Such a determinant can be useful numerically since systems of
quadratic equations are much simpler to solve than the usual highly non-linear
Bethe equations. It can therefore offer significant gains in stability and
computation speed.Comment: 17 pages, 0 figure
Quadratic operator relations and Bethe equations for spin-1/2 Richardson-Gaudin models
In this work we demonstrate how one can, in a generic approach, derive a set
of simple quadratic Bethe equations for integrable Richardson-Gaudin (RG)
models built out of spins-1/2. These equations depend only on the
eigenvalues of the various conserved charges so that any solution of these
equations defines, indirectly through the corresponding set of eigenvalues, one
particular eigenstate.
The proposed construction covers the full class of integrable RG models of
the XYZ (including the subclasses of XXZ and XXX models) type realised in terms
of spins-1/2, coupled with one another through ,
, terms, including, as well,
magnetic field-like terms linear in the Pauli matrices.
The approach exclusively requires integrability, defined here only by the
requirement that conserved charges (with ) such that
exist . The result is therefore
valid, and equally simple, for models with or without symmetry, with or
without a properly defined pseudo-vacuum as well as for models with non-skew
symmetric couplings.Comment: 13 page
Non-equilibrum dynamics in the strongly excited inhomogeneous Dicke model
Using the exact eigenstates of the inhomogeneous Dicke model obtained by
numerically solving the Bethe equations, we study the decay of bosonic
excitations due to the coupling of the mode to an ensemble of two-level (spin
1/2) systems. We compare the quantum time-evolution of the bosonic mode
population with the mean field description which, for a few bosons agree up to
a relatively long Ehrenfest time. We demonstrate that additional excitations
lead to a dramatic shortening of the period of validity of the mean field
analysis. However, even in the limit where the number of bosons equal the
number of spins, the initial instability remains adequately described by the
mean-field approach leading to a finite, albeit short, Ehrenfest time. Through
finite size analysis, we also present indications that the mean field approach
could still provide an adequate description for thermodynamically large systems
even at long times. However, for mesoscopic systems one cannot expect it to
capture the behavior beyond the initial decay stage in the limit of an
extremely large number of excitations.Comment: 9 pages, 7 figures, Phys. Rev. B in pres
Integrable spin-1/2 Richardson-Gaudin XYZ models in an arbitrary magnetic field
We establish the most general class of spin-1/2 integrable Richardson-Gaudin
models including an arbitrary magnetic field, returning a fully anisotropic
(XYZ) model. The restriction to spin-1/2 relaxes the usual integrability
constraints, allowing for a general solution where the couplings between spins
lack the usual antisymmetric properties of Richardson-Gaudin models. The full
set of conserved charges are constructed explicitly and shown to satisfy a set
of quadratic equations, allowing for the numerical treatment of a fully
anisotropic central spin in an external magnetic field. While this approach
does not provide expressions for the exact eigenstates, it allows their
eigenvalues to be obtained, and expectation values of local observables can
then be calculated from the Hellmann-Feynman theorem.Comment: 11 pages, 1 figur
Bethe Ansatz approach to quench dynamics in the Richardson model
By instantaneously changing a global parameter in an extended quantum system,
an initially equilibrated state will afterwards undergo a complex
non-equilibrium unitary evolution whose description is extremely challenging. A
non-perturbative method giving a controlled error in the long time limit
remained highly desirable to understand general features of the quench induced
quantum dynamics. In this paper we show how integrability (via the algebraic
Bethe ansatz) gives one numerical access, in a nearly exact manner, to the
dynamics resulting from a global interaction quench of an ensemble of fermions
with pairing interactions (Richardson's model). This possibility is deeply
linked to the specific structure of this particular integrable model which
gives simple expressions for the scalar product of eigenstates of two different
Hamiltonians. We show how, despite the fact that a sudden quench can create
excitations at any frequency, a drastic truncation of the Hilbert space can be
carried out therefore allowing access to large systems. The small truncation
error which results does not change with time and consequently the method
grants access to a controlled description of the long time behavior which is a
hard to reach limit with other numerical approaches.Comment: Proceedings of the CRM (Montreal) workshop on Integrable Quantum
Systems and Solvable Statistical Mechanics Model
Persisting correlations of a central spin coupled to large spin baths
The decohering environment of a quantum bit is often described by the
coupling to a large bath of spins. The quantum bit itself can be seen as a spin
which is commonly called the central spin. The resulting central spin
model describes an important mechanism of decoherence. We provide
mathematically rigorous bounds for a persisting magnetization of the central
spin in this model with and without magnetic field. In particular, we show that
there is a well defined limit of infinite number of bath spins. Only if the
fraction of very weakly coupled bath spins tends to 100\% does no magnetization
persist.Comment: 19 pages, 15 figures, rigorous bounds for the central spin mode
Simulation Monte-Carlo du transport et de la relaxation des porteurs dans les structures à boîtes quantiques auto-assemblées
Ce travail de maîtrise a pour objectif la création d'un programme de simulation Monte-Carlo adapté à l'étude des propriétés de transport et de relaxation des porteurs dans les structures à boîtes quantiques auto-assemblées. Ces structures contenant à la fois des états 3D 2D et 0D, il est nécessaire de réaliser un programme permettant de traiter le comportement des porteurs dans ces trois types d'états et de décrire les processus de collision ou de recombinaison permettant aux porteurs de passer d'un état à un autre. Les résultats obtenus par simulation de l'évolution temporelle de la distribution des porteurs peuvent être comparés à des résultats expérimentaux obtenus par des études de la photoluminescence résolue en temps. Ainsi, on dispose d'une méthode permettant d'évaluer la justesse des modèles théoriques utilisés. La majorité des modélisations numériques cherchant à reproduire les résultats des expériences de photoluminescence résolue en temps sont basées sur la résolution d'un système d'équations différentielles décrivant l'évolution temporelle de la population des divers niveaux. On cherche, à l'aide du simulateur Monte-Carlo, à corriger certaines faiblesses dans la description des états 3D et 2D qui sont inhérentes à la modélisation par les équations d'évolution. Les modèles étudiés sont simples, mais permettent de réaliser rapidement quelques études. Cependant, on constate que les modèles ainsi créés ne permettent pas de reproduire efficacement les données expérimentales. On peut par contre, dans l'avenir, envisager la création de modèles plus complets dont la validité peut être testée en les étudiant avec le programme Monte-Carlo
Dynamical correlation functions of the mesoscopic pairing model
We study the dynamical correlation functions of the Richardson pairing model
(also known as the reduced or discrete-state BCS model) in the canonical
ensemble. We use the Algebraic Bethe Ansatz formalism, which gives exact
expressions for the form factors of the most important observables. By summing
these form factors over a relevant set of states, we obtain very precise
estimates of the correlation functions, as confirmed by global sum-rules
(saturation above 99% in all cases considered). Unlike the case of many other
Bethe Ansatz solvable theories, simple two-particle states are sufficient to
achieve such saturations, even in the thermodynamic limit. We provide explicit
results at half-filling, and discuss their finite-size scaling behavior