9,559 research outputs found
Stability and Dynamics of Cross Solitons in Harmonically Confined Bose-Einstein Condensates
We examine the stability and dynamics of a family of crossed dark solitons in
a harmonically confined Bose-Einstein condensate in two dimensions. Working in
a regime where the fundamental snake instability is suppressed, we show the
existence of an instability which leads to an interesting collapse and revival
of the initial state for the fundamental case of two crossed solitons. The
instability originates from the singular point where the solitons cross, and we
characterise it by examining the Bogoliubov spectrum. Finally, we extend the
treatment to systems of higher symmetry.Comment: 7 pages, 7 figure
Coexistence of qubit effects
Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained in the ranges of a single (joint) observable. Here we give several equivalent characterizations of coexistent pairs of qubit effects. We also establish the equivalence between our results and those obtained independently by other authors. Our approach makes explicit use of the Minkowski space geometry inherent in the four-dimensional real vector space of selfadjoint operators in a two-dimensional complex Hilbert space
Strongly Incompatible Quantum Devices
The fact that there are quantum observables without a simultaneous
measurement is one of the fundamental characteristics of quantum mechanics. In
this work we expand the concept of joint measurability to all kinds of possible
measurement devices, and we call this relation compatibility. Two devices are
incompatible if they cannot be implemented as parts of a single measurement
setup. We introduce also a more stringent notion of incompatibility, strong
incompatibility. Both incompatibility and strong incompatibility are rigorously
characterized and their difference is demonstrated by examples.Comment: 27 pages (AMSart), 6 figure
Maintaining Quantum Coherence in the Presence of Noise through State Monitoring
Unsharp POVM measurements allow the estimation and tracking of quantum
wavefunctions in real-time with minimal disruption of the dynamics. Here we
demonstrate that high fidelity state monitoring, and hence quantum control, is
possible even in the presence of classical dephasing and amplitude noise, by
simulating such measurements on a two-level system undergoing Rabi
oscillations. Finite estimation fidelity is found to persist indefinitely long
after the decoherence times set by the noise fields in the absence of
measurement.Comment: 5 pages, 4 figure
Alternate two-dimensional quantum walk with a single-qubit coin
We have recently proposed a two-dimensional quantum walk where the
requirement of a higher dimensionality of the coin space is substituted with
the alternance of the directions in which the walker can move [C. Di Franco, M.
Mc Gettrick, and Th. Busch, Phys. Rev. Lett. {\bf 106}, 080502 (2011)]. For a
particular initial state of the coin, this walk is able to perfectly reproduce
the spatial probability distribution of the non-localized case of the Grover
walk. Here, we present a more detailed proof of this equivalence. We also
extend the analysis to other initial states, in order to provide a more
complete picture of our walk. We show that this scheme outperforms the Grover
walk in the generation of - spatial entanglement for any initial
condition, with the maximum entanglement obtained in the case of the particular
aforementioned state. Finally, the equivalence is generalized to wider classes
of quantum walks and a limit theorem for the alternate walk in this context is
presented.Comment: 9 pages, 9 figures, RevTeX
Ion induced density bubble in a strongly correlated one dimensional gas
We consider a harmonically trapped Tonks-Girardeau gas of impenetrable bosons
in the presence of a single embedded ion, which is assumed to be tightly
confined in a RF trap. In an ultracold ion-atom collision the ion's charge
induces an electric dipole moment in the atoms which leads to an attractive
potential asymptotically. We treat the ion as a static deformation of
the harmonic trap potential and model its short range interaction with the gas
in the framework of quantum defect theory. The molecular bound states of the
ionic potential are not populated due to the lack of any possible relaxation
process in the Tonks-Girardeau regime. Armed with this knowledge we calculate
the density profile of the gas in the presence of a central ionic impurity and
show that a density \textit{bubble} of the order of a micron occurs around the
ion for typical experimental parameters. From these exact results we show that
an ionic impurity in a Tonks gas can be described using a pseudopotential,
allowing for significantly easier treatment.Comment: Accepted for publication in Physical Review A (Rapid Communications)
An eccentrically perturbed Tonks-Girardeau gas
We investigate the static and dynamic properties of a Tonks-Girardeau gas in
a harmonic trap with an eccentric -perturbation of variable strength.
For this we first find the analytic eigensolution of the single particle
problem and use this solution to calculate the spatial density and energy
profiles of the many particle gas as a function of the strength and position of
the perturbation. We find that the crystal nature of the Tonks state is
reflected in both the lowest occupation number and momentum distribution of the
gas. As a novel application of our model, we study the time evolution of the
the spatial density after a sudden removal of the perturbation. The dynamics
exhibits collapses and revivals of the original density distribution which
occur in units of the trap frequency. This is reminiscent of the Talbot effect
from classical optics.Comment: Comments and suggestions are welcom
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