Brandon Peden

Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices

The notion of quasi-angular momentum is introduced to label the eigenstates of a Hamiltonian with a discrete rotational symmetry. This concept is recast in an operatorial form where the creation and annihilation operators of a Hubbard Hamiltonian carry units of quasi-angular momentum. Using this formalism, the ground states of ultracold gases of non-interacting fermions in rotating optical lattices are studied as a function of rotation, and transitions between states of different quasi-angular momentum are identified. In addition, previous results for strongly-interacting bosons are re-examined and compared to the results for non-interacting fermions. Quasi-angular momentum can be used to distinguish between these two cases. Finally, an experimentally accessible signature of quasi-angular momentum is identified in the momentum distributions of single-particle eigenstates.

Quantized vortex states of strongly interacting bosons in a rotating optical lattice

Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of up to one atom per lattice site. The entry of vortices into the system is characterized by jumps of

Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms

2\ensuremath{\pi}

Two-state Bogoliubov theory of a molecular Bose gas

in the phase winding of the condensate wave function. A lattice of size

Spin waves and dielectric softening of polar molecule condensates.

L\ifmmode\times\else\texttimes\fi{}L

Resonantly enhanced tunneling and transport of ultracold atoms on tilted optical lattices

can have at most

Effects of Contact Interactions in Molecular Bose-Einstein Condensates

L\ensuremath{-}1

Bose-Einstein condensate of rigid rotor molecules

quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasiangular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasiangular momentum of the ground state changes.

Low-energy excitations of a Bose-Einstein condensate of rigid rotor molecules

We describe a scheme for probing a gas of ultracold atoms trapped in an optical lattice and moving in the presence of an external potential. The probe is nondestructive and uses the existing lattice fields as the measurement device. Two counterpropagating cavity fields simultaneously set up a conservative lattice potential and a weak quantum probe of the atomic motion. Balanced heterodyne detection of the probe field at the cavity output along with integration in time and across the atomic cloud yield information about the atomic dynamics in a single run. The scheme is applied to a measurement of the Bloch oscillation frequency for atoms moving in the presence of the local gravitational potential. Signal-to-noise ratios are estimated to be as high as 10{sup 4}.

Spin Waves and Dielectric Softening of Polar Molecule Condensates

We present an analytic Bogoliubov description of a Bose-Einstein condensate of polar molecules trapped in a quasi-two-dimensional geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and static structure factors. This method can be applied to any homogeneous, two-component system with linear coupling and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. The nature of these instabilities is clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave responses in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs,