Roberto B. Diener

Quantum fluctuations in the superfluid state of the BCS-BEC crossover

We determine the effects of quantum fluctuations about the T=0 mean-field solution of the BCS-BEC crossover in a dilute Fermi gas using the functional integral method. These fluctuations are described in terms of the zero-point motion of collective modes and the virtual scattering of gapped quasiparticles. We calculate their effects on various measurable properties, including chemical potential, ground-state energy, the gap, the speed of sound and the Landau critical velocity. At unitarity, we find excellent agreement with quantum Monte Carlo and experimental results. In the BCS limit, we show analytically that we obtain Fermi liquid interaction corrections to thermodynamics including the Hartree shift. In the Bose-Einstein condensation (BEC) limit, we show that the theory leads to an approximate description of the reduction of the scattering length for bosonic molecules and also obtain quantum depletion of the Lee-Yang form. At the end of the paper, we describe a method to include feedback of quantum fluctuations into the gap equation, and discuss the problems of self-consistent calculations in satisfying Goldstones theorem and obtaining ultraviolet finite results at unitarity.

Bloch waves and bloch bands of Bose-Einstein condensates in optical lattices

Bloch waves and Bloch bands of Bose-Einstein condensates in optical lattices are studied. We provide further evidence for the loop structure in the Bloch band, and compute the critical values of the mean-field interaction strength for the Landau instability and the dynamical instability.

Quantum Tweezer for Atoms

We propose a quantum tweezer for extracting a desired number of neutral atoms from a reservoir. A trapped Bose-Einstein condensate is used as the reservoir, taking advantage of its coherent nature, which can guarantee a constant outcome. The tweezer is an attractive quantum dot, which may be generated by red-detuned laser light. By moving at certain speeds, the dot can extract a desired number of atoms from the condensate through Landau-Zener tunneling. The feasibility of our quantum tweezer is demonstrated through realistic and extensive model calculations.

Criterion for Bosonic Superfluidity in an Optical Lattice

We show that the current method of determining superfluidity in optical lattices based on a visibly sharp bosonic momentum distribution n(k) can be misleading, for even a normal Bose gas can have a similarly sharp n(k). We show that superfluidity in a homogeneous system can be detected from the so-called visibility (v) of n(k)--that v must be 1 within O(N(-2/3)), where N is the number of bosons. We also show that the T=0 visibility of trapped lattice bosons is far higher than what is obtained in some current experiments, suggesting strong temperature effects and that these states can be normal. These normal states allow one to explore the physics in the quantum critical region.

Quantum step heights in hysteresis loops of molecular magnets

We present an analytical theory on the heights of the quantum steps observed in the hysteresis loops of molecular magnets. By considering the dipolar interaction between molecular spins, our theory successfully yields the step heights measured in experiments, and reveals a scaling law for the dependence of the heights on the sweeping rates hidden in the experimental data. With this theory, we show how to accurately determine the tunnel splitting of a single molecular spin from the step heights and the sample geometry.

Fermions in Optical Lattices Swept across Feshbach Resonances

We point out that the recent experiments at ETH on fermions in optical lattices, where a band insulator evolves continuously into states occupying many bands as the system is swept adiabatically across Feshbach resonance, have implications on a wide range of fundamental issues in condensed matter. We derive the effective Hamiltonian of these systems, obtain expressions for their energies and band populations, and point out the increasing quantum entanglement of the ground state during the adiabatic sweep. Our results also explain why only specific regions in k space can be populated after the sweep as found at ETH.

BCS-BEC crossover with unequal-mass fermions

We investigate the crossover from BCS pairing to molecular Bose-Einstein condensation (BEC) in an atomic gas with two fermion species with masses m↑ � m↓ tuned through a Feshbach resonance. We present results for the T = 0 equation of state as a function of the scattering length including the effects of Gaussian fluctuations about the mean field ground state. We compute the ground state energy as a function of m↑/m↓ at unitarity and find excellent agreement with the quantum Monte Carlo result for m↑/m↓ = 6.67 for a 40 K- 6 Li mixture. We show that the dimer scattering length in the BEC limit as a function of m↑/m↓ compares well with the exact four-body results of Petrov et al. [J. Phys. B 38, S645 (2005)]. We also derive the condition for trapping frequencies to obtain an unpolarized gas in a harmonic trap.

Comment on 'Feshbach resonances in an optical lattice'

We point out some logical inconsistencies in the model proposed in [Phys. Rev. A 71, 043604 (2005)] as well as in the calculations performed on it. The proposed model is not able to describe Feshbach resonances in optical lattices.

The dynamical generation of two-dimensional matter-wave discrete solitons

We suggest a method to experimentally obtain two-dimensional matter-wave discrete solitons with a self-repulsive Bose–Einstein condensate in optical lattices. At the edge of the Brillouin zone, a wavepacket effective mass is negative, which could be treated as an inversion of the nonlinearity sign. Above critical nonlinearity this makes the wavepackets collapse partially into localized modes with a chemical potential located in the gap between the first and the second bands. This critical nonlinearity is also associated with the smallest nonlinearity for which the discrete solitons are possible in the gap. Extensive numerical simulations for square and asymmetric honeycomb lattices in the continuous model illustrate every stage of the process.

AC and DC fields in optical lattices: quasienergy band structure

We study the effects of both AC and DC fields in the quasienergy band structure of cold atoms in optical lattices. The effects studied include Rabi oscillations between Bloch bands and dynamical band collapse in AC fields, which have already been observed experimentally. We also present some new results regarding the location of Wannier-Stark ladders in DC fields and the band structure of fractional Wannier-Stark ladders in DC/AC fields.