Adiabatic following criterion, estimation of the nonadiabatic excitation fraction and quantum jumps

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimated quantitatively. It is shown that the limiting value to which the amplitude of the nonadiabatic part tends is equal to the Fourier component of the nonadiabatic perturbation parameter taken at the Rabi frequency of the Raman excitation. The time scale of the variation of both parts is found. While the adiabatic part of the solution varies slowly and follows the change of the nonadiabatic perturbation parameter, the nonadiabatic part appears almost instantly, revealing a jumpwise transition between the dark and bright states. This jump happens when the nonadiabatic perturbation parameter takes its maximum value.Comment: 33 pages, 8 figures, submitted to PRA on 28 Oct. 200

Pade approximations of solitary wave solutions of the Gross-Pitaevskii equation

Pade approximants are used to find approximate vortex solutions of any winding number in the context of Gross-Pitaevskii equation for a uniform condensate and condensates with axisymmetric trapping potentials. Rational function and generalised rational function approximations of axisymmetric solitary waves of the Gross-Pitaevskii equation are obtained in two and three dimensions. These approximations are used to establish a new mechanism of vortex nucleation as a result of solitary wave interactions.Comment: In press by Journal of Physics: Mathematics and Genera

Second order gradient ascent pulse engineering

We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of quantum systems. These include more accurate gradients, convergence acceleration using the BFGS quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent.Comment: Submitted for publicatio

Clusters of Exceptional Points for a Laser Control of Selective Vibrational Transfer

When a molecule is exposed to a laser field, all field-free vibrational states become resonances, with complex quasi energies calculated using Floquet theory. There are many ways to produce the coalescences of pairs of such quasi energies, with appropriate wavelength-intensity choices which define Exceptional Points (EP) in the laser parameter plane. We dress for the molecular ion H$_2^+$ an exhaustive map of these exceptional points which appear in clusters. Such clusters can be used to define several vibrational transfer scenarios implying more than a single exceptional point, exchanging single or multiple vibrational quanta. The ultimate goal is molecular vibrational cooling by transferring an initial (thermal, for instance) population on a final (ground, for instance) single vibrational state. When a molecule is exposed to a laser field, all field-free vibrational states become resonances, with complex quasi energies calculated using Floquet theory. There are many ways to produce the coalescences of pairs of such quasi energies, with appropriate wavelength-intensity choices which define Exceptional Points (EP) in the laser parameter plane. We dress for the molecular ion H$_2^+$ an exhaustive map of these exceptional points which appear in clusters. Such clusters can be used to define several vibrational transfer scenarios implying more than a single exceptional point, exchanging single or multiple vibrational quanta. The ultimate goal is molecular vibrational cooling by transferring an initial (thermal, for instance) population on a final (ground, for instance) single vibrational state.Comment: 16 pages, 7 figures, 1 tabl

Analytic pulse design for selective population transfer in many-level quantum systems: maximizing amplitude of population oscillations

State selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules or quantum dots is a the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for producing Rabi-like oscillations in the general discrete many-level quantum systems is presented.Comment: Published in Phys.Rev.A. This is the final published versio

Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate

We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at T=0K. We demonstrate that within the linear response regime, both a quantum field theory treatment and a meanfield Gross-Pitaevskii treatment lead to the same value for the mean evolution of the quasiparticle operators. The observable for Bragg spectroscopy experiments, which is the spectral response function of the momentum transferred to the condensate, can therefore be calculated in a meanfield formalism. We analyse the behaviour of this observable by carrying out numerical simulations in axially symmetric three-dimensional cases and in two dimensions. An approximate analytic expression for the observable is obtained and provides a means for identifying the relative importance of three broadening and shift mechanisms (meanfield, Doppler, and finite pulse duration) in different regimes. We show that the suppression of scattering at small values of q observed by Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the meanfield treatment, and can be interpreted in terms of the interference of the u and v quasiparticle amplitudes. We also show that, contrary to the assumptions of previous analyses, there is no regime for trapped condensates for which the spectral response function and the dynamic structure factor are equivalent. Our numerical calculations can also be performed outside the linear response regime, and show that at large laser intensities a significant decrease in the shift of the spectral response function can occur due to depletion of the initial condensate.Comment: RevTeX4 format, 16 pages plus 7 eps figures; Update to published version: minors changes and an additional figure. (To appear in Phys. Rev. A

Power Optimizations in MTJ-based Neural Networks through Stochastic Computing

Artificial Neural Networks (ANNs) have found widespread applications in tasks such as pattern recognition and image classification. However, hardware implementations of ANNs using conventional binary arithmetic units are computationally expensive, energy-intensive and have large area overheads. Stochastic Computing (SC) is an emerging paradigm which replaces these conventional units with simple logic circuits and is particularly suitable for fault-tolerant applications. Spintronic devices, such as Magnetic Tunnel Junctions (MTJs), are capable of replacing CMOS in memory and logic circuits. In this work, we propose an energy-efficient use of MTJs, which exhibit probabilistic switching behavior, as Stochastic Number Generators (SNGs), which forms the basis of our NN implementation in the SC domain. Further, error resilient target applications of NNs allow us to introduce Approximate Computing, a framework wherein accuracy of computations is traded-off for substantial reductions in power consumption. We propose approximating the synaptic weights in our MTJ-based NN implementation, in ways brought about by properties of our MTJ-SNG, to achieve energy-efficiency. We design an algorithm that can perform such approximations within a given error tolerance in a single-layer NN in an optimal way owing to the convexity of the problem formulation. We then use this algorithm and develop a heuristic approach for approximating multi-layer NNs. To give a perspective of the effectiveness of our approach, a 43% reduction in power consumption was obtained with less than 1% accuracy loss on a standard classification problem, with 26% being brought about by the proposed algorithm.Comment: Accepted in the 2017 IEEE/ACM International Conference on Low Power Electronics and Desig

Bragg spectroscopy of an accelerating condensate with solitary-wave behaviour

We present a theoretical treatment of Bragg spectroscopy of an accelerating condensate in a solitary-wave state. Our treatment is based on the Gross-Pitaevskii equation with an optical potential representing the Bragg pulse and an additional external time-dependent potential generating the solitary-wave behaviour. By transforming to a frame translating with the condensate, we derive an approximate set of equations that can be readily solved to generate approximate Bragg spectra. Our analytic method is accurate within a well defined parameter regime and provides physical insight into the structure of the spectra. We illustrate our formalism using the example of Bragg spectroscopy of a condensate in a time-averaged orbiting potential trap.Comment: 9 pages, 3 figure