Quantum mechanics with trapped motional states

The control of quantum systems has become a major issue of modern physics. In this project, we propose to use a degenerate quantum gas of neutral atoms as a model system to tackle the problem of controlling the preparation of many-body states, and to study the relaxation of non-equilibrium states. In particular, we will investigate the coherent control of collective motional states of a gas confined in a trap. In this context, the preparation of quasi one-dimensional Bose-Einstein condensates in the transverse ground state of the trap constitutes the initialization of the system in a well characterized state. Using optimal control methods, we plan to control the transfer of the system to various non-equilibrium states. These studies will be carried out on the "Rb2" experiment of the Schmiedmayer group, at the Atominstitut, TU Wien. This setup is already functional, and routinely produces quasi one-dimensional Bose-Einstein condensates with micro-fabricated chips, allowing fast modification of the trapping potentials, which is critical to this research. Capitalizing on the group`s success to transfer the full population of a Bose-Einstein condensate to the first vibrational excited state of the trap, the first step of the project will be to bring the cloud into a coherent superposition of two motional states of the trapping potential (Investigations 1). Two kinds of motional states will be considered: vibrational states along one eigen-axis of the trap, or angular momentum states in the two transverse dimensions. The transfer will be achieved either by optimal control of the trapping potential, or by two photon transitions between two low field seeking internal states (Investigations 2). Because of atomic interactions, the obtained non-equilibrium states are unstable and will decay. This decay process shows similarities with parametric down conversion, and will be investigated in order to demonstrate bosonic stimulation, and to be able to inhibit it, making the non-equilibrium states more stable (Investigation 4). With sufficiently long-lived states, we will be able to use two motional states as the two paths of an interferometer (Investigation 3). This new kind of matter-wave interferometer on a chip will be sensitive to acceleration and rotation. Finally, optimal control of the one- dimensional bosonic Josephson junction that can be created with the chip technology will enable to tailor the many-body state of the junction, which is not easily initialized with current techniques. For instance, non-classical states (number squeezed states) can be achieved. The specificities arising from the one-dimensional nature of the system (breakdown of self-trapping) will also be easier to investigate with this improved control. While the candidate will learn from the expertise of the group on the chip technology, the group will benefit from the candidate`s experience on the controlled generation of motional states of quantum gases that he developed during his PhD thesis.