Conditional quantum dynamics with several observers

We consider several observers who monitor different parts of the environment of a single quantum system and use their data to deduce its state. We derive a set of conditional stochastic master equations that describe the evolution of the density matrices each observer ascribes to the system under the Markov approximation, and show that this problem can be reduced to the case of a single "super-observer", who has access to all the acquired data. The key problem - consistency of the sets of data acquired by different observers - is then reduced to the probability that a given combination of data sets will be ever detected by the "super-observer". The resulting conditional master equations are applied to several physical examples: homodyne detection of phonons in quantum Brownian motion, photo-detection and homodyne detection of resonance fluorescence from a two-level atom. We introduce {\it relative purity} to quantify the correlations between the information about the system gathered by different observers from their measurements of the environment. We find that observers gain the most information about the state of the system and they agree the most about it when they measure the environment observables with eigenstates most closely correlated with the optimally predictable {\it pointer basis} of the system.Comment: Updated version: new title and contents. 22 pages, 8 figure

Unconditional Pointer States from Conditional Master Equations

When part of the environment responsible for decoherence is used to extract information about the decohering system, the preferred {\it pointer states} remain unchanged. This conclusion -- reached for a specific class of models -- is investigated in a general setting of conditional master equations using suitable generalizations of predictability sieve. We also find indications that the einselected states are easiest to infer from the measurements carried out on the environment.Comment: 4 pages, 3 .eps figures; final version to appear in Phys.Rev.Let

Topological Schr\"odinger cats: Non-local quantum superpositions of topological defects

Topological defects (such as monopoles, vortex lines, or domain walls) mark locations where disparate choices of a broken symmetry vacuum elsewhere in the system lead to irreconcilable differences. They are energetically costly (the energy density in their core reaches that of the prior symmetric vacuum) but topologically stable (the whole manifold would have to be rearranged to get rid of the defect). We show how, in a paradigmatic model of a quantum phase transition, a topological defect can be put in a non-local superposition, so that - in a region large compared to the size of its core - the order parameter of the system is "undecided" by being in a quantum superposition of conflicting choices of the broken symmetry. We demonstrate how to exhibit such a "Schr\"odinger kink" by devising a version of a double-slit experiment suitable for topological defects. Coherence detectable in such experiments will be suppressed as a consequence of interaction with the environment. We analyze environment-induced decoherence and discuss its role in symmetry breaking.Comment: 7 pages, 4 figure

A ring of BEC pools as a trap for persistent flow

Mott insulator - superfluid transition in a periodic lattice of Josephson junctions can be driven by tunneling rate increase. Resulting winding numbers $W$ of the condensate wavefunction decrease with increasing quench time in accord with the Kibble-Zurek mechanism (KZM). However, in very slow quenches Bose-Hubbard dynamics rearranges wavefunction phase so that its random walk cools, $\bar{W^2}$ decreases and eventually the wavefunction becomes too cold to overcome potential barriers separating different $W$. Thus, in contrast with KZM, in very slow quenches $\bar{W^2}$ is set by random walk with "critical" step size, independently of $\tau_Q$.Comment: Decompressed version to appear in Phys. Rev.