Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States

The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability associated with such an arrangement allows for the study of the competition and interplay between these two, and gives rise to a whole range of interesting and rich nonlinear effects. This review covers the basic idea and overview of such nonlinear phenomena, especially those corresponding to extended states. This includes "swallowtail" loop structures of the energy band, Bloch states with multiple periodicity, and those in "nonlinear lattices", i.e., systems with the nonlinear interaction term itself being a periodic function in space.Comment: 39 pages, 21 figures; review article to be published in a Special Issue of Entropy on "Non-Linear Lattice

Quantum fluctuation theorems and power measurements

Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system's dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.Comment: 26 pages, 9 figure

Backaction-Driven Transport of Bloch Oscillating Atoms in Ring Cavities

We predict that an atomic Bose-Einstein condensate strongly coupled to an intracavity optical lattice can undergo resonant tunneling and directed transport when a constant and uniform bias force is applied. The bias force induces Bloch oscillations, causing amplitude and phase modulation of the lattice which resonantly modifies the site-to-site tunneling. For the right choice of parameters a net atomic current is generated. The transport velocity can be oriented oppositely to the bias force, with its amplitude and direction controlled by the detuning between the pump laser and the cavity. The transport can also be enhanced through imbalanced pumping of the two counter-propagating running wave cavity modes. Our results add to the cold atoms quantum simulation toolbox, with implications for quantum sensing and metrology.Comment: Published version: 5 pages, 4 figures; Supplementary Material include

Quantum Performance of Thermal Machines over Many Cycles

The performance of quantum heat engines is generally based on the analysis of a single cycle. We challenge this approach by showing that the total work performed by a quantum engine need not be proportional to the number of cycles. Furthermore, optimizing the engine over multiple cycles leads to the identification of scenarios with a quantum enhancement. We demonstrate our findings with a quantum Otto engine based on a two-level system as the working substance that supplies power to an external oscillator.Comment: 5 pages, 3 figures; published in Phys. Rev. Lett. as an Editors' Suggestio

MANAGEMENT OF VATAKAPHAJA GRIDRASI WITH URDHWA SHODANA FOLLOWED BY BASTI-A CASE REPORT

Gridrasi is one among the Vataja Nanatmaja Vyadhi with its one of the variant is Vatakaphaja. It’s Prathyatma Lakshana is Shoola radiating downwards from Sphik Pradesha upto Pada, which causes Nigraha of Sakthi Prasarana resulting in limping gait. Vata Kaphaja will present with Aruchi, Gourava along with above symptoms. Based on cardinal presentation it can be correlated to Sciatica, herniated lumbar disc being the most common cause with annual incidence of 0.5%-2%. In adults it is commonly seen in 3rd to 5th decade of life with male female ratio 2:1. The treatment protocol of Gridrasi includes Snehana, Swedana, Basti, Siravyadha and Agnikarma. Chakradatta emphasis on Urdhwashodana before administration of Basti. In this case Vatakaphaja Gridrasi initially treated with Snehana, Swedana line of treatment with no reduction in symptoms, responded very well to Basti administered after Urdhwa-shodana. Patient had significant reduction in symptoms and was able to perform his daily activities without pain

A Case Study on Dushta Vrana caused due to Vatarakta

In the present era Joint disorders are the prevailing issue and Vatarakta is one among them which is caused due to improper diet and erratic lifestyle and if the condition progresses it leads to many complications, here is one such case of complications of Uthana Vatarakta. A female patient aged 46 years presented with complaint of Ulcer in the lower 1/3rd of the left leg since 5 years, associated with pain, discharge, swelling and discolouration of the skin. Also foul smelling and slough was observed. Patient was treated with a course of mild Virechana and local treatment of Abhyanga and Dhara, Lepa with Madhu, Nimba and Tila which has a better Shodhana and Ropana action was applied, which is explained by Acharya Sushruta under 60 Upakramas for the management of Vrana. The associated symptoms of pain, slough, foul smelling, swelling were relieved and the wound was close to healing without any complications in 60 days of treatment