Postdoctoral Seminar Presentations
Two-level quantum dynamics revisited: New classes of solutions for the old Landau-Majorana-Stueckelberg-Zener problem
Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also rare. I will present a simple algorithm based on a type of partial reverse-engineering that generates an unlimited number of exact analytical solutions for a general time-dependent Hamiltonian. The method will be demonstrated with several new exact solutions that are particularly relevant to qubit control in quantum computing applications. I will further show that our formalism easily generates analytical control protocols that execute perfect Landau-Majorana-Stueckelberg-Zener interferometry and rapid adiabatic passage near the quantum speed limit.
Ultrafast creation of Schrodinger-Cat States of Motion in a Single Atom
Trapped atomic ions allow us to build up strongly interacting quantum systems one atom at a time. The internal energy levels of the ion are used to represent a spin ½ system and contain a quantum bit (qubit) of information. By applying state-dependent optical dipole forces to the chain of ions we control spin-spin couplings and can engineer interesting Hamiltonians. I will present a new method using ultrafast laser pulses to entangle pairs of ions. We engineer a short train of intense laser pulses to impart a spin-dependent kick, where each spin state receives a discrete momentum kick in opposite directions. We have realized spin-dependent kicks with a fidelity greater than 99.8%. Using a series of these spin-dependent kicks we can realize a two qubit gate. In contrast to gates using spectroscopically resolved motional sidebands, these gates may be performed faster than the trap oscillation period, making them potentially less sensitive to noise, independent of temperature, and more easily scalable to large crystals of ions. Multiple kicks can be strung together to create a “Schrodinger cat” like state, where the large separation between the two parts of the wavepacket allow us to accumulate the phase shift necessary for a gate in a shorter amount of time. We have realized kicks with 38ħk of momentum separation in a single trapped atom. I will present a realistic pulse scheme to extend this technique to two ions for an entangling gate, and our progress towards its realization.
Title: Hysteresis in a quantized, atomtronic circuit
Hysteresis is a common feature of superconducting circuits like the superconducting quantum interference device (SQUID), which is one of the world's most sensitive magnetometers. We are working to realize a neutral atom circuit that is analogous to the rf-SQUID, but is sensitive to rotation rather than magnetic fields. Our analog consists of a toroidally-shaped, Bose-Einstein condensate that is stirred by a rotating repulsive potential that serves as a weak link. The weak link induces phase slips in the superfluid between well-defined persistent current states. We have recently observed hysteresis in these transitions: the rotation frequency at which the phase slips occur changes, depending on whether the phase slip results in an increase or decrease of the persistent current. Beyond the present application of a rotation sensor, this hysteresis may prove useful in atomtronic circuits that are analogous to hysteretic electronic circuits (e.g., memory).
Presentation will be for 25 minutes and 5 minutes for questions.