| Post-selection is the selection of a subset of an ensemble based on a measurement on that ensemble. In the last few years, post-selection has taken on new importance as a mechanism to induce the optical nonlinearities required for quantum logic gates. I present experiments and theory that explore post-selection in photonic systems.; First, I experimentally demonstrate effective nonlinear absorption between two single photons. I show that this photon-exchange effect can be understood as a post-selection induced nonlinearity similar to the one that occurs in Hong-Ou-Mandel interference.; I then go on to describe an experimental implementation of Hardy's Paradox, which is one of the three great thought-experiments about entanglement and correlations in quantum mechanics (the others being the EPR and GHZ "paradoxes"). In the place of the electron--positron annihilation in the original proposal, I apply, for the first time, a post-selection-based absorptive photon switch that coworkers and I had previously developed.; Weak measurement promises to be an important technique for characterizing post-selected quantum systems during their evolution. The technique minimizes disturbance to the system and therefore can be used in situ. In a third experiment, I attempt to resolve a recent debate: Which is more fundamental---complementarity or the uncertainty principle? Specifically, can interference be destroyed by a which-path measurement without transferring momentum to the particle? This question is difficult to investigate as any measurement of the momentum transfer causes collapse, severely disturbing the system. I circumvent this problem with the technique of weak measurement and show that which-path measurements do indeed induce a momentum transfer as required by the uncertainty principle.; I then proceed to develop theoretically a new method for performing multiparticle weak measurements that is unique because it does not require single-particle-level interactions. This theory provides new insight into the importance of the imaginary component of the weak measurement result.; In a fourth experiment, I use the latter theory and return to Hardy's Paradox to perform the first weak measurement of an entangled system. I post-select on the paradoxical measurement result while weakly measuring a set of observables. The results are surprising in that they no longer conflict; they now satisfy a classical-logic truth-table. |
