The potential energy of a 40^{40}K Fermi gas in the BCS-BEC crossover

We present a measurement of the potential energy of an ultracold trapped gas of $^{40}$K atoms in the BCS-BEC crossover and investigate the temperature dependence of this energy at a wide Feshbach resonance, where the gas is in the unitarity limit. In particular, we study the ratio of the potential energy in the region of the unitarity limit to that of a non-interacting gas, and in the T=0 limit we extract the universal many-body parameter $\beta$. We find $\beta = -0.54^{+0.05}_{-0.12}$; this value is consistent with previous measurements using $^{6}$Li atoms and also with recent theory and Monte Carlo calculations. This result demonstrates the universality of ultracold Fermi gases in the strongly interacting regime

Cavity optomechanics with Si3N4 membranes at cryogenic temperatures

We describe a cryogenic cavity-optomechanical system that combines Si3N4 membranes with a mechanically-rigid Fabry-Perot cavity. The extremely high quality-factor frequency products of the membranes allow us to cool a MHz mechanical mode to a phonon occupation of less than 10, starting at a bath temperature of 5 kelvin. We show that even at cold temperatures thermally-occupied mechanical modes of the cavity elements can be a limitation, and we discuss methods to reduce these effects sufficiently to achieve ground state cooling. This promising new platform should have versatile uses for hybrid devices and searches for radiation pressure shot noise.Comment: 19 pages, 5 figures, submitted to New Journal of Physic

From Cavity Electromechanics to Cavity Optomechanics

We present an overview of experimental work to embed high-Q mesoscopic mechanical oscillators in microwave and optical cavities. Based upon recent progress, the prospect for a broad field of "cavity quantum mechanics" is very real. These systems introduce mesoscopic mechanical oscillators as a new quantum resource and also inherently couple their motion to photons throughout the electromagnetic spectrum.Comment: 8 pages, 6 figures, ICAP proceedings submissio

Modulation spectroscopy with ultracold fermions in an optical lattice

We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time dependent density-matrix renormalization group method that the position of the peak in the spectrum of the induced double occupancy gives the pairing energy in a superfluid and the interaction energy in a Mott-insulator, respectively. In the Mott-insulator we relate the spectral weight of the peak to the spin ordering at finite temperature using perturbative calculations

Tensile strained InxGa1−xPIn_{x}Ga_{1-x}P membranes for cavity optomechanics

We investigate the optomechanical properties of tensile-strained ternary InGaP nanomembranes grown on GaAs. This material system combines the benefits of highly strained membranes based on stoichiometric silicon nitride, with the unique properties of thin-film semiconductor single crystals, as previously demonstrated with suspended GaAs. Here we employ lattice mismatch in epitaxial growth to impart an intrinsic tensile strain to a monocrystalline thin film (approximately 30 nm thick). These structures exhibit mechanical quality factors of 2*10^6 or beyond at room temperature and 17 K for eigenfrequencies up to 1 MHz, yielding Q*f products of 2*10^12 Hz for a tensile stress of ~170 MPa. Incorporating such membranes in a high finesse Fabry-Perot cavity, we extract an upper limit to the total optical loss (including both absorption and scatter) of 40 ppm at 1064 nm and room temperature. Further reductions of the In content of this alloy will enable tensile stress levels of 1 GPa, with the potential for a significant increase in the Q*f product, assuming no deterioration in the mechanical loss at this composition and strain level. This materials system is a promising candidate for the integration of strained semiconductor membrane structures with low-loss semiconductor mirrors and for realizing stacks of membranes for enhanced optomechanical coupling.Comment: 10 pages, 3 figure

Signatures of Superfluidity in Dilute Fermi Gases near a Feshbach Resonance

We present a brief account of the most salient properties of vortices in dilute atomic Fermi superfluids near a Feshbach resonance.Comment: 6 pages, 1 figure, and jltp.cls. Several typos and a couple of inaccuracies have been correcte

Determination of the Fermion Pair Size in a Resonantly Interacting Superfluid

Fermionic superfluidity requires the formation of pairs. The actual size of these fermion pairs varies by orders of magnitude from the femtometer scale in neutron stars and nuclei to the micrometer range in conventional superconductors. Many properties of the superfluid depend on the pair size relative to the interparticle spacing. This is expressed in BCS-BEC crossover theories, describing the crossover from a Bardeen-Cooper-Schrieffer (BCS) type superfluid of loosely bound and large Cooper pairs to Bose-Einstein condensation (BEC) of tightly bound molecules. Such a crossover superfluid has been realized in ultracold atomic gases where high temperature superfluidity has been observed. The microscopic properties of the fermion pairs can be probed with radio-frequency (rf) spectroscopy. Previous work was difficult to interpret due to strong and not well understood final state interactions. Here we realize a new superfluid spin mixture where such interactions have negligible influence and present fermion-pair dissociation spectra that reveal the underlying pairing correlations. This allows us to determine the spectroscopic pair size in the resonantly interacting gas to be 2.6(2)/kF (kF is the Fermi wave number). The pairs are therefore smaller than the interparticle spacing and the smallest pairs observed in fermionic superfluids. This finding highlights the importance of small fermion pairs for superfluidity at high critical temperatures. We have also identified transitions from fermion pairs into bound molecular states and into many-body bound states in the case of strong final state interactions.Comment: 8 pages, 7 figures; Figures updated; New Figures added; Updated discussion of fit function

Momentum distribution of a trapped Fermi gas with large scattering length

Using a scattering length parametrization of the BCS-BEC crossover as well as the local density approximation for the density profile, we calculate the momentum distribution of a harmonically trapped atomic Fermi gas at zero temperature. Various interaction regimes are considered, including the BCS phase, the unitarity limit and the molecular regime. We show that the relevant parameter which characterizes the crossover is given by the dimensionless combination $N^{1/6}a/a_{ho}$, where $N$ is the number of atoms, $a$ is the scattering length and $a_{ho}$ is the oscillator length. The width of the momentum distribution is shown to depend in a crucial way on the value and sign of this parameter. Our predictions can be relevant for experiments on ultracold atomic Fermi gases near a Feshbach resonance.Comment: 6 pages, 2 figures. Submitted to Phys. Rev. A. Added reference

Production of cold molecules via magnetically tunable Feshbach resonances

Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose as well as two spin component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled channels theory provides the rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, as well as the classification in terms of entrance- and closed-channel dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic field sweeps in cold Bose and Fermi gases as well as pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean field as well as beyond mean field approaches are reviewed in detail, including the associated ranges of validity.Comment: 50 pages, 26 figures, to be published in Reviews of Modern Physics, final version with updated reference