Cold atom dynamics in a quantum optical lattice potential

We study a generalized cold atom Bose Hubbard model, where the periodic optical potential is formed by a cavity field with quantum properties. On the one hand the common coupling of all atoms to the same mode introduces cavity mediated long range atom-atom interactions and on the other hand atomic backaction on the field introduces atom-field entanglement. This modifies the properties of the associated quantum phase transitions and allows for new correlated atom-field states including superposition of different atomic quantum phases. After deriving an approximative Hamiltonian including the new long range interaction terms we exhibit central physical phenomena at generic configurations of few atoms in few wells. We find strong modifications of population fluctuations and next-nearest neighbor correlations near the phase transition point.Comment: 4 pages, 5 figures, corrected typo

Cavity enhanced light scattering in optical lattices to probe atomic quantum statistics

Different quantum states of atoms in optical lattices can be nondestructively monitored by off-resonant collective light scattering into a cavity. Angle resolved measurements of photon number and variance give information about atom-number fluctuations and pair correlations without single-site access. Observation at angles of diffraction minima provides information on quantum fluctuations insensitive to classical noise. For transverse probing, no photon is scattered into a cavity from a Mott insulator phase, while the photon number is proportional to the atom number for a superfluid.Comment: 4 pages, 3 figures, to published in Phys. Rev. Lett. (March 2007

Light scattering from ultracold atoms in optical lattices as an optical probe of quantum statistics

We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without an optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum non-demolition (QND) measurement of various atomic variables by observing light.Comment: 15 pages, 5 figure

Microscopic physics of quantum self-organisation of optical lattices in cavities

We study quantum particles at zero temperature in an optical lattice coupled to a resonant cavity mode. The cavity field substantially modifies the particle dynamics in the lattice, and for strong particle-field coupling leads to a quantum phase with only every second site occupied. We study the growth of this new order out of a homogeneous initial distribution for few particles as the microscopic physics underlying a quantum phase transition. Simulations reveal that the growth dynamics crucially depends on the initial quantum many-body state of the particles and can be monitored via the cavity fluorescence. Studying the relaxation time of the ordering reveals inhibited tunnelling, which indicates that the effective mass of the particles is increased by the interaction with the cavity field. However, the relaxation becomes very quick for large coupling.Comment: 14 pages 6 figure

Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity QED

Studies of ultracold atoms in optical lattices link various disciplines, providing a playground where fundamental quantum many-body concepts, formulated in condensed-matter physics, can be tested in much better controllable atomic systems, e.g., strongly correlated phases, quantum information processing. Standard methods to measure quantum properties of Bose-Einstein condensates (BECs) are based on matter-wave interference between atoms released from traps which destroys the system. Here we propose a nondestructive method based on optical measurements, and prove that atomic statistics can be mapped on transmission spectra of a high-Q cavity. This can be extremely useful for studying phase transitions between Mott insulator and superfluid states, since various phases show qualitatively distinct light scattering. Joining the paradigms of cavity quantum electrodynamics (QED) and ultracold gases will enable conceptually new investigations of both light and matter at ultimate quantum levels, which only recently became experimentally possible. Here we predict effects accessible in such novel setups.Comment: 6 pages, 3 figure

Links across ecological scales: Plant biomass responses to elevated CO2_2

The degree to which elevated CO$_2$ concentrations (e[CO$_2$]) increase the amount of carbon (C) assimilated by vegetation plays a key role in climate change. However, due to the short-term nature of CO$_2$ enrichment experiments and the lack of reconciliation between different ecological scales, the effect of e[CO$_2$] on plant biomass stocks remains a major uncertainty in future climate projections. Here, we review the effect of e[CO$_2$] on plant biomass across multiple levels of ecological organization, scaling from physiological responses to changes in population-, community-, ecosystem-, and global-scale dynamics. We find that evidence for a sustained biomass response to e[CO$_2$] varies across ecological scales, leading to diverging conclusions about the responses of individuals, populations, communities, and ecosystems. While the distinct focus of every scale reveals new mechanisms driving biomass accumulation under e[CO$_2$], none of them provides a full picture of all relevant processes. For example, while physiological evidence suggests a possible long-term basis for increased biomass accumulation under e[CO$_2$] through sustained photosynthetic stimulation, population-scale evidence indicates that a possible e[CO$_2$]-induced increase in mortality rates might potentially outweigh the effect of increases in plant growth rates on biomass levels. Evidence at the global scale may indicate that e[CO$_2$] has contributed to increased biomass cover over recent decades, but due to the difficulty to disentangle the effect of e[CO$_2$] from a variety of climatic and land-use-related drivers of plant biomass stocks, it remains unclear whether nutrient limitations or other ecological mechanisms operating at finer scales will dampen the e[CO$_2$] effect over time. By exploring these discrepancies, we identify key research gaps in our understanding of the effect of e[CO$_2$] on plant biomass and highlight the need to integrate knowledge across scales of ecological organization so that large-scale modeling can represent the finer-scale mechanisms needed to constrain our understanding of future terrestrial C storage.ISSN:1354-1013ISSN:1365-248