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Exact results for Schrodinger cats in driven-dissipative systems and their feedback control.

ABSTRACT: In quantum optics, photonic Schrödinger cats are superpositions of two coherent states with opposite phases and with a significant number of photons. Recently, these states have been observed in the transient dynamics of driven-dissipative resonators subject to engineered two-photon processes. Here we present an exact analytical solution of the steady-state density matrix for this class of systems, including one-photon losses, which are considered detrimental for the achievement of cat states. We demonstrate that the unique steady state is a statistical mixture of two cat-like states with opposite parity, in spite of significant one-photon losses. The transient dynamics to the steady state depends dramatically on the initial state and can pass through a metastable regime lasting orders of magnitudes longer than the photon lifetime. By considering individual quantum trajectories in photon-counting configuration, we find that the system intermittently jumps between two cats. Finally, we propose and study a feedback protocol based on this behaviour to generate a pure cat-like steady state.

SUBMITTER: Minganti F

PROVIDER: S-EPMC4886674 | biostudies-other | 2016

REPOSITORIES: biostudies-other

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Project description:BackgroundIn planarian flatworms, the mechanisms underlying the activity of collectively pluripotent adult stem cells (neoblasts) and their descendants can now be studied from the level of the individual gene to the entire animal. Flatworms maintain startling developmental plasticity and regenerative capacity in response to variable nutrient conditions or injury. We develop a model for cell dynamics in such animals, assuming that fully differentiated cells exert feedback control on neoblast activity.ResultsOur model predicts a number of whole organism level and general cell biological and behaviours, some of which have been empirically observed or inferred in planarians and others that have not. As previously observed empirically we find: 1) a curvilinear relationship between external food and planarian steady state size; 2) the fraction of neoblasts in the steady state is constant regardless of planarian size; 3) a burst of controlled apoptosis during regeneration after amputation as the number of differentiated cells are adjusted towards their homeostatic/steady state level. In addition our model describes the following properties that can inform and be tested by future experiments: 4) the strength of feedback control from differentiated cells to neoblasts (i.e. the activity of the signalling system) and from neoblasts on themselves in relation to absolute number depends upon the level of food in the environment; 5) planarians adjust size when food level reduces initially through increased apoptosis and then through a reduction in neoblast self-renewal activity; 6) following wounding or excision of differentiated cells, different time scales characterize both recovery of size and the two feedback functions; 7) the temporal pattern of feedback controls differs noticeably during recovery from a removal or neoblasts or a removal of differentiated cells; 8) the signaling strength for apoptosis of differentiated cells depends upon both the absolute and relative deviations of the number of differentiated cells from their homeostatic level; and 9) planaria prioritize resource use for cell divisions.ConclusionsWe offer the first analytical framework for organizing experiments on planarian flatworm stem cell dynamics in a form that allows models to be compared with quantitative cell data based on underlying molecular mechanisms and thus facilitate the interplay between empirical studies and modeling. This framework is the foundation for studying cell migration during wound repair, the determination of homeostatic levels of differentiated cells by natural selection, and stochastic effects.

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Exact results for Schrodinger cats in driven-dissipative systems and their feedback control.

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