Photon temporal modes: a complete framework for quantum information science

Field-orthogonal temporal modes of photonic quantum states provide a new framework for quantum information science (QIS). They intrinsically span a high-dimensional Hilbert space and lend themselves to integration into existing single-mode fiber communication networks. We show that the three main requirements to construct a valid framework for QIS -- the controlled generation of resource states, the targeted and highly efficient manipulation of temporal modes and their efficient detection -- can be fulfilled with current technology. We suggest implementations of diverse QIS applications based on this complete set of building blocks.Comment: 17 pages, 13 figure

NS Fivebrane and Tachyon Condensation

We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained from the condensation of the tachyon on the unstable D9-brane of type IIA theory. The construction uses a combination of the descriptions of these branes as solitons of the worldvolume theory of the D9-brane. The NS5-brane, in particular, involves a gauge bundle which is operator valued, and hence is better thought of as a gerbe.Comment: 20 pages, harvma

Analysis of collaborative filtering algorithms

Recommender System is a subclass of information filtering system which predicts the rating given to an item by any user. Collaborative filtering is a key technique in recommender systems. This technique predicts the user rating of an item by collaboration of other users who have similar interests with this user. Collaborative filtering approaches can be categorized as Memory based, Model-based and Hybrid approaches. Memory-based approach can be further classified as Item-based and User-based recommendations. Pearson correlation scheme belongs to user-based scheme and Slope one family of algorithms belong to item-based scheme. Slope one family consists of Normal, Weighted and Bipolar slope one algorithms. Algorithms belonging to model-based approach are Singular value decomposition, Regularized Singular value decomposition and Probabilistic Matrix Factorization. In hybrid approach combination of memory-based and model-based approaches are used for making recommendations. In this thesis we made an attempt to analyze various algorithms in Memory-based and Model-based approaches. In model based algorithms, we analyzed Singular Value Decomposition (SVD) and Regularized Singular Value Decomposition (RSVD). By taking three different dataset sizes, we observed that RSVD outperforms SVD for all three dataset sizes. In memory based algorithms, we analyzed Pearson correlation scheme which takes the correlation between user vectors as similarity measure and Slope one family of algorithms. In slope one algorithms, we proposed an improvement to the existing scheme for determining Threshold value of Bipolar slope one algorithm. We used median and average of min-max ratings which outperforms the existing user average scheme. Finally, we made an analysis of all these algorithms and concluded that RSVD outperforms rest of the algorithms in terms of accuracy of predictions

Observation of Interaction of Spin and Intrinsic Orbital Angular Momentum of Light

Interaction of spin and intrinsic orbital angular momentum of light is observed, as evidenced by length-dependent rotations of both spatial patterns and optical polarization in a cylindrically-symmetric isotropic optical fiber. Such rotations occur in straight few-mode fiber when superpositions of two modes with parallel and anti-parallel orientation of spin and intrinsic orbital angular momentum (IOAM=$2\hslash$) are excited, resulting from a degeneracy splitting of the propagation constants of the modes.Comment: 6 pages, 5 figures, and a detailed supplement. Version 3 corrects a typo and adds the journal referenc

Theory of noise suppression in {\Lambda}-type quantum memories by means of a cavity

Quantum memories, capable of storing single photons or other quantum states of light, to be retrieved on-demand, offer a route to large-scale quantum information processing with light. A promising class of memories is based on far-off-resonant Raman absorption in ensembles of $\Lambda$-type atoms. However at room temperature these systems exhibit unwanted four-wave mixing, which is prohibitive for applications at the single-photon level. Here we show how this noise can be suppressed by placing the storage medium inside a moderate-finesse optical cavity, thereby removing the main roadblock hindering this approach to quantum memory.Comment: 10 pages, 3 figures. This paper provides the theoretical background to our recent experimental demonstration of noise suppression in a cavity-enhanced Raman-type memory ( arXiv:1510.04625 ). See also the related paper arXiv:1511.05448, which describes numerical modelling of an atom-filled cavity. Comments welcom

Non-relativistic metrics from back-reacting fermions

It has recently been pointed out that under certain circumstances the back-reaction of charged, massive Dirac fermions causes important modifications to AdS_2 spacetimes arising as the near horizon geometry of extremal black holes. In a WKB approximation, the modified geometry becomes a non-relativistic Lifshitz spacetime. In three dimensions, it is known that integrating out charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to a gravitational and Maxwell Chern-Simons theory with a cosmological constant. Motivated by this, we look for warped AdS_3 or Schrodinger metrics as exact solutions to a fully back-reacted theory containing Dirac fermions in three and four dimensions. We work out the dynamical exponent in terms of the fermion mass and generalize this result to arbitrary dimensions.Comment: 26 pages, v2: typos corrected, references added, minor change

Matrix dynamics of fuzzy spheres

We study the dynamics of fuzzy two-spheres in a matrix model which represents string theory in the presence of RR flux. We analyze the stability of known static solutions of such a theory which contain commuting matrices and SU(2) representations. We find that irreducible as well as reducible representations are stable. Since the latter are of higher energy, this stability poses a puzzle. We resolve this puzzle by noting that reducible representations have marginal directions corresponding to non-spherical deformations. We obtain new static solutions by turning on these marginal deformations. These solutions now have instability or tachyonic directions. We discuss condensation of these tachyons which correspond to classical trajectories interpolating from multiple, small fuzzy spheres to a single, large sphere. We briefly discuss spatially independent configurations of a D3/D5 system described by the same matrix model which now possesses a supergravity dual.Comment: 26 pages, 3 figures, uses JHEP.cls; (v2) references adde