11 research outputs found
Tracking down localized modes in PT-symmetric Hamiltonians under the influence of a competing nonlinearity
The relevance of parity and time reversal (PT)-symmetric structures in
optical systems is known for sometime with the correspondence existing between
the Schrodinger equation and the paraxial equation of diffraction where the
time parameter represents the propagating distance and the refractive index
acts as the complex potential. In this paper, we systematically analyze a
normalized form of the nonlinear Schrodinger system with two new families of
PT-symmetric potentials in the presence of competing nonlinearities. We
generate a class of localized eigenmodes and carry out a linear stability
analysis on the solutions. In particular, we find an interesting feature of
bifurcation charaterized by the parameter of perturbative growth rate passing
through zero where a transition to imaginary eigenvalues occurs.Comment: 10pages, To be published in Acta Polytechnic
Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations
We demonstrate the existence of complex solitary wave and periodic solutions
of the Kortweg de-vries (KdV) and modified Kortweg de-Vries (mKdV) equations.
The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and
are even (odd) under the simultaneous actions of parity () and
time-reversal () operations. The corresponding localized solitons are
hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically
vanishing intensity. The -odd complex soliton solution is shown to be
iso-spectrally connected to the fundamental solution through
supersymmetry
TRACKING DOWN LOCALIZED MODES IN PTSYMMETRIC HAMILTONIANS UNDER THE INFLUENCE OF A COMPETING NONLINEARITY
The relevance of parity and time reversal (PT)-symmetric structures in optical systems has been known for some time with the correspondence existing between the Schrödinger equation and the paraxial equation of diffraction, where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrödinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation characterized by the parameter of perturbative growth rate passing through zero, where a transition to imaginary eigenvalues occurs
Extraction of Product and Higher Moment Weak Values: Applications in Quantum State Reconstruction and Entanglement Detection
Weak measurements introduced by Aharonov, Albert and Vaidman (AAV) can
provide informations about the system with minimal back action. Weak values of
product observables (commuting) or higher moments of an observable are
informationally important in the sense that they are useful to resolve some
paradoxes, realize strange quantum effects, reconstruct density matrices, etc.
In this work, we show that it is possible to access the higher moment weak
values of an observable using weak values of that observable with pairwise
orthogonal post-selections. Although the higher moment weak values of an
observable are inaccessible with Gaussian pointer states, our method allows any
pointer state. We have calculated product weak values in a bipartite system for
any given pure and mixed pre selected states. Such product weak values can be
obtained using only the measurements of local weak values (which are defined as
single system weak values in a multi-partite system). As an application, we use
higher moment weak values and product weak values to reconstruct unknown
quantum states of single and bipartite systems, respectively. Further, we give
a necessary separability criteria for finite dimensional systems using product
weak values and certain class of entangled states violate this inequality by
cleverly choosing the product observables and the post selections. By such
choices, positive partial transpose (PPT) criteria can be achieved for these
classes of entangled states. Robustness of our method which occurs due to
inappropriate choices of quantum observables and noisy post-selections is also
discussed here. Our method can easily be generalized to the multi-partite
systems
Coherent quantum state transfer in ultra-cold chemistry
Creation and manipulation of cold molecules from atomic Bose–Einstein condensate has opened up a new dimension to study chemical reactions at ultra-cold temperature, known as ‘superchemistry,’ which is extremely useful for the quantum control of matter wave reaction at ultra-cold temperature. Here, a coherent quantum state transfer of atomic to molecular condensate is demonstrated, mediated by solitonic excitation in the mean-field geometry. It is observed that the induced photoassociation is found to control the velocity of these excitations, which in turn controls the chemical reaction fronts. Cooperative many-body effects of photoassociation on Lieb mode have also been studied through molecular dispersion, revealing degeneracy and bistable behavior. Furthermore, it is observed that the photoassociation-induced molecular energy shows oscillatory behavior, analogous to the classical reaction process
Bounding Quantum Advantages in Postselected Metrology
Weak value amplification and other postselection-based metrological protocols
can enhance precision while estimating small parameters, outperforming
postselection-free protocols. In general, these enhancements are largely
constrained because the protocols yielding higher precision are rarely obtained
due to a lower probability of successful postselection. It is shown that this
precision can further be improved with the help of quantum resources like
entanglement and negativity in the quasiprobability distribution. However,
these quantum advantages in attaining considerable success probability with
large precision are bounded irrespective of any accessible quantum resources.
Here we derive a bound of these advantages in postselected metrology,
establishing a connection with weak value optimization where the latter can be
understood in terms of geometric phase. We introduce a scheme that saturates
the bound, yielding anomalously large precision. Usually, negative
quasiprobabilities are considered essential in enabling postselection to
increase precision beyond standard optimized values. In contrast, we prove that
these advantages can indeed be achieved with positive quasiprobability
distribution. We also provide an optimal metrological scheme using three level
non-degenerate quantum system.Comment: 8+5 pages, 6 figure