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We extend our theory of Bloch oscillations of cold atoms inside an optical cavity [Venkatesh et al., Phys. Rev. A 80, 063834 (2009)) to include the effects of quantum noise arising from coupling to external modes. The noise acts as a form of quantum measurement backaction by perturbing the coupled dynamics of the atoms and the light. We take it into account by solving the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical mean fields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio, as well as heating effects. One of the hurdles we overcome in this paper is the proper treatment of fluctuations about time-dependent mean fields in the context of cold-atom cavity QED. [ABSTRACT FROM AUTHOR]

We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double-well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations, as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution, which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schrödinger-cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation. [ABSTRACT FROM AUTHOR]

We calculate the band structure of ultracold atoms located inside a laser-driven optical cavity. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (noncavity) optical lattices. However, in our case the nonlinearity derives from the cavity back-action rather than from direct interatomic interactions. We find both bi- and tristable regimes associated with the lowest band, and show that the multistability we observe can be analyzed in terms of swallowtail catastrophes. Dynamic and energetic stability of the mean-field solutions is also discussed, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the atomic band structure has important implications for proposals concerning Bloch oscillations of atoms inside optical cavities [Peden et al., Phys. Rev. A 80, 043803 (2009); Prasanna Venkatesh el at., Phys. Rev. A 80, 063834 (2009)]. [ABSTRACT FROM AUTHOR]