Quantum Back-Action Limits in Dispersively Measured Bose-Einstein Condensates

Back-action limited measurements of many-body quantum systems are a challenging topic of relevance to open quantum systems and quantum metrology. This work makes important contributions in that direction by experimentally measuring and theoretically modeling via a quantum-trajectories approach coherence in an atomic Bose-Einstein condensate coupled to a far-off-resonant laser beam. A fundamental tenet of quantum mechanics is that measurements change a system's wavefunction to that most consistent with the measurement outcome, even if no observer is present. Weak measurements produce only limited information about the system, and as a result only minimally change the system's state. Here, we theoretically and experimentally characterize quantum back-action in atomic Bose-Einstein condensates interacting with a far-from resonant laser beam. We theoretically describe this process using a quantum trajectories approach where the environment measures the scattered light and present a measurement model based on an ideal photodetection mechanism. We experimentally quantify the resulting wavefunction change in terms of the contrast of a Ramsey interferometer and control parasitic effects associated with the measurement process. The observed back-action is in good agreement with our measurement model; this result is a necessary precursor for achieving true quantum back-action limited measurements of quantum gases.