Christoph Maschler

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.

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

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

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.

Ultracold atoms in optical lattices generated by quantized light fields

Abstract.We study an ultracold gas of neutral atoms subject to the periodic optical potential generated by a high-Q cavity mode. In the limit of very low temperatures, cavity field and atomic dynamics require a quantum description. Starting from a cavity QED single atom Hamiltonian we use different routes to derive approximative multiparticle Hamiltonians in Bose-Hubbard form with rescaled or even dynamical parameters. In the limit of large enough cavity damping the different models agree. Compared to free space optical lattices, quantum uncertainties of the potential and the possibility of atom-field entanglement lead to modified phase transition characteristics, the appearance of new phases or even quantum superpositions of different phases. Using a corresponding effective master equation, which can be numerically solved for few particles, we can study time evolution including dissipation. As an example we exhibit the microscopic processes behind the transition dynamics from a Mott insulator like state to a self-ordered superradiant state of the atoms, which appears as steady state for transverse atomic pumping.

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 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 nondemolition measurement of various atomic variables by observing light.

Microscopic physics of quantum self-organization 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 self-organization of the particles, a configuration with only every second site occupied. We study the growth of this order out of a homogeneous initial distribution for few particles. 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 due to the interaction with the cavity field. However, the relaxation becomes very quick for strong coupling.

Cavity QED with ultracold gases: Probing quantum phases in optical lattices by light scattering

We consider collective light scattering from ultracold atoms trapped in a deep optical lattice. Different atomic quantum states were shown to exhibit qualitatively different light scattering. This suggests a novel nondestructive method to probe atomic quantum statistics and characterize quantum phase transitions, e.g., between Mott insulator and superfluid states. The method is based on measurements of light fields only, in contrast to the standard methods based on matter-field interference, which destroys the system.