Title (Code) Fourier methods for solving the quantum well problem Degree: BSc in Physics (or Physics with any) Professor Ben Supervisor: Co-Supervisor None Murdin Room: 15ATI01 Email: b.murdin Address Phone: 9328 Group: Photonics Type: Computational Modelling You have encountered the quantum well many times in physics. The solution for the wave-function is a simple sine wave, and the higher the frequency of the wave, the higher the energy. The boundary conditions mean that only waves with nodes at both sides of the well constructively interfere and live for a long time. The result is a series of allowed states with definite energy. You have already calculated the allowed states in quantum wells using these principles, and the solutions are relatively easy and are explained in many elementary quantum mechanics courses. The main practical example quoted in such courses is the semiconductor quantum well, where a very thin layer of one semiconductor with low potential is sandwiched between layers of a high potential semiconductor. This model works well in some situations, but in real life, electrons in semiconductors are moving in a crystalline solid, with a periodic Project potential that has regular ups and downs, and the quantum well is description: usually formed by layers of different size peaks and troughs. The quantum physics problem in this case is harder to write down, and therefore harder to solve. There are many methods that have been described to solve it, and each has advantages and disadvantages. In this project you will use one of these methods, called the Fourier method. You will apply the calculation to model a research experiment being performed in the ATI on “spintronics”, where the shape of the quantum well will be used to control the electron spin. The type of quantum well in question is a new structure referred to as “the topological insulator” [see Big Bang Theory season 4 episode 14 for Sheldon’s lecture on this]. Prerequisites: Ideally you should have some knowledge of Fortran programming or Matlab or some similar computing platform. Some pen and paper mathematical theory will be necessary. Last 14/11/16 Updated: Title (Code) Nano-scale modeling of atom distributions Degree: BSc in Physics (or Physics with any) Supervisor: Professor Ben Murdin Co-Supervisor S Clowes Room: 15ATI01 Email: b.murdin Address Phone: 9328 Group: Photonics Type: Computational modelling The smallest silicon transistors in use are about 14nm (in 2014). This is nearing the size of a single donor atom (3nm), and so we can now imaging devices where single atoms are at the heart. We can even begine to imagine devices where chains of individual atoms are used, and because there are many species of donor there are a great variety of chains that can be made. As part of the £multi-M COMPASSS project at Surrey/UCL we have developed a lithography technique to position individual donors exactly where desired, but we need to start developing an understanding of how the chains might be used. The classic transistor is made of n, p and n-type regions of semiconductor, but who knows how it will work when it is reduced to the atomic scale Project and it is made of a single donor-acceptor-donor chain? description: We need to understand the statistics of nearest-neighbours. The modelling will take randomly arranged donors and examine how current passes from one to the next, for different density profiles and different combinations of species. A prior MSc project is available as a basis on which to start. Prerequisites: Successful completion of level 2 solid-state physics and the final year Light and Matter module will be a great advantage. Some computational skill will be an advantage but specific language skills are not necessary. Last 14/11/16 Updated: Title (Code) Electrical detection of atomic transitions in silicon Degree: BSc in Physics (or Physics with any) Supervisor: Professor Ben Murdin Co-Supervisor S Clowes Room: 15ATI01 Email: b.murdin Address Phone: 9328 Group: Photonics Type: experiment The donor in silicon is an analogue of hydrogen, with a ladder of 1s, 2p, states etc. The main difference between hydrogen and the donor is that the energy scale is in the infrared rather than the UV. We are trying to make electrical devices based on individual donors, which would be the smallest silicon devices. The devices are produced by implantation using the Surrey Ion Beam Centre, and we make electrical connections to the devices using the Advanced Technology Institute clean-room. These devices have many hundreds of implanted atoms, but we are working towards being able to use structures with only one atom at the heart. As part of the £multi-million COMPASSS project at Surrey/UCL we have developed a lithography technique to position individual Project donors exactly where desired, but we need to start developing an description: understanding of how to detect the state of the atoms electrically. In this project you will investigate one method of detection of the atomic state in electrical devices. The state of the atom can be controlled with laser pulses, and the capacitance of the sample changes when the atoms’ state changes due to the laser pulses. You will investigate the response of the devices to infrared excitation of the atoms from the ground state to the excited states. Prerequisites: Successful completion of level 2 solid-state physics, and level 2 experimental labs. The final year Light and Matter module will be a great advantage. Last 14/11/16 Updated: Title (Code) Quantum optical dynamics of a three level atom Degree: BSc in Physics (or Physics with any) Professor Ben Supervisor: Co-Supervisor None Murdin Room: 15ATI01 Email: b.murdin Address Phone: 9328 Group: Photonics Type: Computational Modelling When a hydrogen-like atom, i.e. a mobile electron bound to a heavy positive ion, experiences an a.c. electromagnetic wave, it can be driven into the excited state, via a superposition state like Schrodinger’s cat. The equations governing this quantum optical control are relatively simple first-order differential equations. Their derivation is described in the final year Light and Matter course, although this is not neccesry to understand. In the Photonics group we have recently been performing experiments involving driving atoms (phosphorus atoms in silicon) with pulses of light containing two different colours, and then watching the resulting motion of the electron. The orbital motion can be used to produce entanglement of the electron with the electrons on neighbouring atoms. Control over the trajectory will allow control over which atoms get entangled and how strong the entanglement is. Project description: We would like to visualise the wavefunction of the atom during the excitation, and explore the possibilities for driving the wave into useful orbits. In this project you will make a computer code to solve the quantum optical problem for two colour light pulses and three atomic levels, and follow this with rate equation solution to find which levels the electrons transfer to afterwards once the light has passed. The wavepackets will be visualised by creating movies. We will compare the results of your calculation with the experiments, and hopefully design new experiments that will be able to demonstrate the three-state superpositions that are possible. Prerequisites: Successful completion of the final year Light and Matter module will be an advantage, but is not required. You should have a good knowledge of Fortran or other programming platform. Some pen and paper mathematical theory will be helpful for checking limiting cases. Last 14/11/16 Updated: Title: Flow instabilities in complex fluids Co-Supervisor: Supervisor: James Adams None Building/Room: 14BB03 Type of Project Theoretical/Computational Email: [email protected] Project Description: Newtonian fluids such as water have a simple internal structure, so their flow behaviour is relatively easy to understand and model. By comparison complex fluids like polymer solutions, and surfactant solutions, have more internal structure – the conformation of the polymer -- than simple Newtonian fluids such as water. However, a good understanding of the relation between the stress and their flow is important for applications such as injection moulding of plastics, and the flow of drilling fluid in boreholes. Recent experiments have shown some unusual flow behaviour which has resulted in renewed interest in these materials. When subjected to a simple shear, some fluids will flow with a uniform shear rate. However, other fluids (notably polymer solutions) become unstable to the formation of shear bands. These bands can also form transiently, then decay away, and even chaotically. This project will analyse the stability in an elongational flow of some constitutive models relating to polymer solutions and liquid crystalline polymers. This will require the student to break down the constitutive equation into a set of ordinary differential equations, and solve these equations numerically. The student will then determine the eigenvalues of the stability matrix, to determine whether the equations are stable. If time permits a spatial resolved model of the flow instability can be developed. Title: Reaction-diffusion models Co-Supervisor: Supervisor: James Adams None Building/Room: 14BB03 Theoretical/Computational/literat Type of Project ure review Email: [email protected] Project Description: Reaction-diffusion models describe many different physical processes including chemical reactions and the flow of complex fluids. More recently these models have been used to describe the behaviour of a financial market [1]. The market participants can place orders to buy or sell in the order book. These orders are then cleared when the participants agree a price. This can be modelled as a one dimensional grid of length L, with the buy and sell orders represented by two particle types that can diffuse in from either side.