Date of Completion
Heisenberg limit, double-well interferometer, quantum Fisher information
William C. Stwalley
Field of Study
Doctor of Philosophy
We theoretically study the effect of added nonlinearity from atom-atom interactions on precision of phase measurements in quantum metrology. A double-well trap with bosons inside acts as an interferometer to measure the energy difference of the atoms on the two sides of the trap. For the general case of parameter estimation, we study the generic measurement scheme using time-independent perturbation theory as the main tool, and derive an explicit expression of the best attainable measurement precision. Both the theoretical derivation and numerical computations show that nonlinearity from atom-atom interactions will not indirectly make the interferometer beat the Heisenberg limit. We study numerically the behavior of measurement precision with varying problem parameters. In many regimes of the operation, the Heisenberg limit scaling of measurement precision is preserved in spite of the combined effects of nonlinearity and arm-to-arm tunneling. Heisenberg limit can be achieved with some optimal input states of the system. We discuss theoretically Heisenberg-limited atom interferometry employing the ground state of a Bose-Einstein condensate with strong attractive atom-atom interactions in a double-well trap as the starting point. The dimensionless parameter governing the quality of the ground state for this purpose is identified. The near-degeneracy between the ground state and the first excited state offsets the advantages of an atom interferometer utilizing such near-Schrödinger Cat input states.
Chen, Han, "Optimal Measurement Precision With A Nonlinear Interferometer" (2014). Doctoral Dissertations. 494.