Open Quantum Dynamics of Mesoscopic Bose-Einstein ... - Physics

Chapter 3Homodyne measurements on aBose-Einstein condensate3.1 Symmetry-breaking measurementsThis chapter describes a nondestructive measurement technique that monitors Josephsonlikeoscillations between the two components of a double Bose-Einstein condensate. Theanalysis is based on the system of two spatially-separated condensates that was introducedin Ch. 2. One of the condensates is placed in an optical cavity, which is strongly driven bya coherent optical field. The cavity output field is monitored using a homodyne detectionscheme. The cavity field is well detuned from an atomic resonance, and experiencesa dispersive phase shift proportional to the number of atoms in the cavity. Thus thecoherent tunnelling oscillations in the atom distribution modulate the detected current.Even when the initial state is symmetric with respect to the two wells, back-action noisefrom the measurement induces Josephson-like oscillations; the measurement process itselfestablishes the phase.The Bose condensates that have been produced in atom traps since 1995[3, 16, 35]contain well defined numbers of atoms, even when those numbers are very large > 10 6 .For small numbers of atoms, as in the mesoscopic examples studied in this thesis, anumber state is an appropriate description. How is this reconciled to the existence ofa long-range order parameter, and its associated phase, as demonstrated in interferenceexperiments[2, 4, 74]? For a multicomponent condensate, the total number of atoms maybe definite, but there could be an uncertainty in how that number is distributed across59