# Student Projects 2015

We usually have a number of projects available and details on some of the current opportunities can be found below. If any of these interest you, please get in touch for more details. Please also note that support for an internship can be obtained through the OIST Graduate School Research Internships.

#### Ultra cold atoms in artificial gauge fields

Ultra cold atomic systems have proved to be remarkable systems for realizing the fundamental models of many particle physics which are otherwise difficult to access in condensed matter systems. One of the recent advances is the demonstration of artificial magnetic fields on these systems in optical lattices as well in continuums. This adds upto the versatility of these cold atomic systems and make them an interesting playground with controllable parameters.

This project aims at theoretically studying the effect of artificially tuned magnetic fields on ultra cold atomic condensates with long range interactions in one dimension. Usually there is no effect of orbital coupling in one dimensional system, however one can use a two leg model for the one-dimensional system where such effects can be studied. The interplay between the long range interactions and the artificial magnetic field in two leg ladder systems is an open problem and would be insightful to study.

#### Shortcuts to adiabaticity for ultracold atoms

Laser techniques have been shown to be able to cool atoms to temperatures just a few microkelvins above the absolute zero and confine them in microscopical optical traps. Spatial adiabatic passage (SAP) is a quantum-mechanical technique that allows to manipulate the external degrees of freedom of such ultra cold atoms and transport them between traps, and allows for the coherent preparation of quantum states for quantum information processing.

SAP considers a system formed by three traps arranged in a straight line and, in its most basic form, it transfers an particle (such as an ultracold atom in an optical trap or an electron in a system of quantum dots) in the ground state of the first trap to the ground state of the third trap (Fig. 1). As an adiabatic technique, SAP can yield very high fidelities and is very robust (i.e., it does not require an accurate control of the system parameters), but this at the cost of being carried out over long time scales. Shortcuts to adiabaticity (STA) are techniques which allow to speed up adiabatic processes while maintaining their robustness and fidelity. The application of STA to SAP, however, requires a direct coupling between the initial and final traps, only achievable by considering two-dimensional configurations (Fig. 2).

In this project we plan to theoretically study the application of the SAP technique in a two-dimensional configuration by numerically integrating Schrödinger's equation. The aim of the project will be to gain physical insight on the transport process (with and without the STA) by means of the Bohmian formulation of quantum mechanics, which allows a clear visualisation of the two possible paths of the wave function to the final trap (1-2-3) or (1-3).

#### Hybrid systems of ions and electric-dipolar condensates

During the last two decades, scientists have developed techniques to cool down, trap, and manipulate quantum systems such as ultra cold atomic gases or chains of a handful of ions. The outstanding control over these systems has allowed to very accurately test the predictions of quantum mechanics, led to the development of ultra precise clocks, and set the foundations of experimental quantum computation. Recent experiments have demonstrated the potential and viability of hybrid systems which combine ultra cold Bose–Einstein condensates (BEC) and cold ions in a single setup. When the ions and the BEC overlap, however, because of their huge temperature difference, the main physics of the system are governed by collisions which lead to loss of atoms and cooling of the ions.

In this project we will theoretically study a novel system in which the BEC is composed of polar molecules such that its dipolar interaction with the ions can be relevant even if the BEC and the chain of ions do not overlap. This interaction can be a source of interesting physics and can be used to manipulate the ions. For instance, the polarised gas (due to the ions electric field) can act as a dielectric medium and screen the interaction between the ions.

#### Engineering Josepshon junctions with two-component Bose-Einstein condensates

Josephson junctions have proved to be a very powerful tool in the physics of superconductors and superfluids. The Josephson effect is a purely many-body quantum-mechanical phenomenon in which two superfluids or superconductors coherently tunnel back and forth though a potential barrier. In Bose-Einstein condensates, which are gaseous superfluid systems, Josephson junctions have been created by confining the atoms in a double-well potential using laser light.

The aim of this project is to propose a new scheme for a Josephson junction in an atomic Bose-Einstein condensate, using a second condensate to create the double-well structure instead of an external potential. In a first stage, we will investigate the conditions under which the second component acts as a Josephson junction. In a second stage, we will characterize the dynamics at low and high population imbalances, searching for plasma and self-trapping oscillations.

#### Bogoliubov excitations and persistent currents in coherently coupled two-component Bose-Einstein condensates

The existence of stable persistent currents (that is, flows that exist forever in the absence of rotation) is one of the main proofs of superfluidity in quantum fluids. Multicomponent Bose-Einstein condensates offer a new and exciting scenario to prove superfluidity. An interesting class of multicomponent condensates is a two-component condensate where the two components are linearly coupled via a Rabi or Raman coupling. This coherent coupling makes the system behave very differently to binary mixtures and in particular leads to a second order phase transition between a neutral and a polarized states.

In this project we will look at the stability of persistent currents in coherently coupled two-component Bose-Einstein condensates. We will explore the regimes in which persistent currents can be stabilized by studying Bogoliubov excitations in the presence of a current. While in the neutral state we will attack the problem analytically, in the polarized state numerical approaches might have to be used.