A 3D topological insulator quantum dot for optically controlled quantum memory and quantum computing

We present the model of a quantum dot (QD) consisting of a spherical core-bulk heterostructure made of 3D topological insulator (TI) materials, such as PbTe/Pb$_{0.31}$Sn$_{0.69}$Te, with bound massless and helical Weyl states existing at the interface and being confined in all three dimensions. The number of bound states can be controlled by tuning the size of the QD and the magnitude of the core and bulk energy gaps, which determine the confining potential. We demonstrate that such bound Weyl states can be realized for QD sizes of few nanometers. We identify the spin locking and the Kramers pairs, both hallmarks of 3D TIs. In contrast to topologically trivial semiconductor QDs, the confined massless Weyl states in 3D TI QDs are localized at the interface of the QD and exhibit a mirror symmetry in the energy spectrum. We find strict optical selection rules satisfied by both interband and intraband transitions that depend on the polarization of electron-hole pairs and therefore give rise to the Faraday effect due to Pauli exclusion principle. We show that the semi-classical Faraday effect can be used to read out spin quantum memory. When a 3D TI QD is embedded inside a cavity, the single-photon Faraday rotation provides the possibility to implement optically mediated quantum teleportation and quantum information processing with 3D TI QDs, where the qubit is defined by either an electron-hole pair, a single electron spin, or a single hole spin in a 3D TI QD. Remarkably, the combination of inter- and intraband transition gives rise to a large dipole moment of up to 450 Debye. Therefore, the strong-coupling regime can be reached for a cavity quality factor of $Q\approx10^{4}$ in the infrared wavelength regime of around $10\:\mu$m.Comment: 19 pages, 11 figures, RevTe

Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors

Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI)---a proven lower bound on the distillable entanglement of a quantum state under one-way local operations and classical communication (LOCC), as our figure of merit. We evaluate a Gaussian lower bound on the RCI of the heralded state. We show that it can exceed the unlimited two-way LOCCassisted direct transmission entanglement distillation capacity of the pure loss channel. The optimal heralded Gaussian RCI with two quantum scissors is found to be significantly more than that with a single quantum scissors, albeit at the cost of decreased success probability. Our results fortify the possibility of a quantum repeater scheme for CV quantum states using the quantum scissors.Comment: accepted for publication in Physical Review

A New Relation between post and pre-optimal measurement states

When an optimal measurement is made on a qubit and what we call an Unbiased Mixture of the resulting ensembles is taken, then the post measurement density matrix is shown to be related to the pre-measurement density matrix through a simple and linear relation. It is shown that such a relation holds only when the measurements are made in Mutually Unbiased Bases- MUB. For Spin-1/2 it is also shown explicitly that non-orthogonal measurements fail to give such a linear relation no matter how the ensembles are mixed. The result has been proved to be true for arbitrary quantum mechanical systems of finite dimensional Hilbert spaces. The result is true irrespective of whether the initial state is pure or mixed.Comment: 4 pages in REVTE

Axial range of conjugate adaptive optics in two-photon microscopy

We describe an adaptive optics technique for two-photon microscopy in which the deformable mirror used for aberration compensation is positioned in a plane conjugate to the plane of the aberration. We demonstrate in a proof-of-principle experiment that this technique yields a large field of view advantage in comparison to standard pupil-conjugate adaptive optics. Further, we show that the extended field of view in conjugate AO is maintained over a relatively large axial translation of the deformable mirror with respect to the conjugate plane. We conclude with a discussion of limitations and prospects for the conjugate AO technique in two-photon biological microscopy

A Multi-Objective Decision-Making Approach For Mutual Fund Portfolio

Investment decision-making problems are generally multi-objective in nature such as minimization of the risk and maximization of the expected return.  These problems can be solved efficiently and effectively using multi-objective decision making (MODM) tools such as a lexicographic goal programming (LGP).  This paper applies the LGP model for selecting an optimum mutual fund portfolio for an investor, while taking into account specific parameters including risk, return, expense ratio and others.  Sensitivity analysis on the assigned weights in a priority structure of the goals identifies all possible solutions for decision-making.  The Euclidean distance method is then used, to measure distances of all possible solutions from the identified ideal solution.  The optimal solution is determined by the minimum distance between the ideal solution and other possible solutions of the problem. The associated weights with the optimal solution will be the most appropriate weights in a given priority structure.  The effectiveness and applicability of the LGP model is demonstrated via a case example from broad categories of mutual funds

Spin waves in quasi-equilibrium spin systems

Using the Landau Fermi liquid theory we have discovered a new regime for the propagation of spin waves in a quasi-equilibrium spin systems. We have determined the dispersion relation for the transverse spin waves and found that one of the modes is gapless. The gapless mode corresponds to the precessional mode of the magnetization in a paramagnetic system in the absence of an external magnetic field. One of the other modes is gapped which is associated with the precession of the spin current around the internal field. The gapless mode has a quadratic dispersion leading to some interesting thermodynamic properties including a $T^{3/2}$ contribution to the specific heat. We also show that these modes make significant contributions to the dynamic structure function.Comment: 4 pages, 3 figure