Superfluid phase transition and strong-coupling effects in an ultracold Fermi gas with mass imbalance

We investigate the superfluid phase transition and effects of mass imbalance in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an cold Fermi gas. We point out that the Gaussian fluctuation theory developed by Nozi\`eres and Schmitt-Rink and the $T$-matrix theory, that are now widely used to study strong-coupling physics of cold Fermi gases, give unphysical results in the presence of mass imbalance. To overcome this problem, we extend the $T$-matrix theory to include higher-order pairing fluctuations. Using this, we examine how the mass imbalance affects the superfluid phase transition. Since the mass imbalance is an important key in various Fermi superfluids, such as $^{40}$K-$^6$Li Fermi gas mixture, exciton condensate, and color superconductivity in a dense quark matter, our results would be useful for the study of these recently developing superfluid systems.Comment: 7 pages, 4 figures, Proceedings of QFS-201

Tests with a Carlina-type diluted telescope; Primary coherencing

Studies are under way to propose a new generation of post-VLTI interferometers. The Carlina concept studied at the Haute- Provence Observatory is one of the proposed solutions. It consists in an optical interferometer configured like a diluted version of the Arecibo radio telescope: above the diluted primary mirror made of fixed cospherical segments, a helium balloon (or cables suspended between two mountains), carries a gondola containing the focal optics. Since 2003, we have been building a technical demonstrator of this diluted telescope. First fringes were obtained in May 2004 with two closely-spaced primary segments and a CCD on the focal gondola. We have been testing the whole optical train with three primary mirrors. The main aim of this article is to describe the metrology that we have conceived, and tested under the helium balloon to align the primary mirrors separate by 5-10 m on the ground with an accuracy of a few microns. The servo loop stabilizes the mirror of metrology under the helium balloon with an accuracy better than 5 mm while it moves horizontally by 30 cm in open loop by 10-20 km/h of wind. We have obtained the white fringes of metrology; i.e., the three mirrors are aligned (cospherized) with an accuracy of {\approx} 1 micron. We show data proving the stability of fringes over 15 minutes, therefore providing evidence that the mechanical parts are stabilized within a few microns. This is an important step that demonstrates the feasibility of building a diluted telescope using cables strained between cliffs or under a balloon. Carlina, like the MMT or LBT, could be one of the first members of a new class of telescopes named diluted telescopes.Comment: 18 pages, 17 figures, A&A, accepte

The Carlina-type diluted telescope: Stellar fringes on Deneb

Context. The performance of interferometers has largely been increased over the last ten years. But the number of observable objects is still limited due to the low sensitivity and imaging capability of the current facilities. Studies have been done to propose a new generation of interferometers. Aims. The Carlina concept studied at the Haute-Provence Observatory consists in an optical interferometer configured as a diluted version of the Arecibo radio telescope: above the diluted primary mirror made of fixed co-spherical segments, a helium balloon or cables suspended between two mountains and/or pylons, carries a gondola containing the focal optics. This concept does not require delay lines. Methods. Since 2003, we have been building a technical demonstrator of this diluted telescope. The main goals of this project were to find the opto-mechanical solutions to stabilize the optics attached under cables at several tens of meters above the ground, and to characterize this diluted telescope under real conditions. In 2012, we have obtained metrology fringes, and co-spherized the primary mirrors within one micron accuracy. In 2013, we have tested the whole optical train: servo loop, metrology, and the focal gondola. Results. We obtained stellar fringes on Deneb in September 2013. In this paper, we present the characteristics of these observations: quality of the guiding, S /N reached, and possible improvements for a future system. Conclusions. It is an important step that demonstrates the feasibility of building a diluted telescope using cables strained between cliffs or pylons. Carlina, like the MMT or LBT, could be one of the first members of a new class of telescopes named Large Diluted Telescopes. Its optical architecture has many advantages for future projects: Planet Formation Imager, Post-ELTs, Interferometer in space.Comment: 8 pages, 7 figures, Astronomy & Astrophysic

Ultrasensitive force and displacement detection using trapped ions

The ability to detect extremely small forces is vital for a variety of disciplines including precision spin-resonance imaging, microscopy, and tests of fundamental physical phenomena. Current force-detection sensitivity limits have surpassed 1 $aN/\sqrt{Hz}$ (atto $=10^{-18}$) through coupling of micro or nanofabricated mechanical resonators to a variety of physical systems including single-electron transistors, superconducting microwave cavities, and individual spins. These experiments have allowed for probing studies of a variety of phenomena, but sensitivity requirements are ever-increasing as new regimes of physical interactions are considered. Here we show that trapped atomic ions are exquisitely sensitive force detectors, with a measured sensitivity more than three orders of magnitude better than existing reports. We demonstrate detection of forces as small as 174 $yN$ (yocto $=10^{-24}$), with a sensitivity 390$\pm150$ $yN/\sqrt{Hz}$ using crystals of $n=60$ $^{9}$Be$^{+}$ ions in a Penning trap. Our technique is based on the excitation of normal motional modes in an ion trap by externally applied electric fields, detection via and phase-coherent Doppler velocimetry, which allows for the discrimination of ion motion with amplitudes on the scale of nanometers. These experimental results and extracted force-detection sensitivities in the single-ion limit validate proposals suggesting that trapped atomic ions are capable of detecting of forces with sensitivity approaching 1 $yN/\sqrt{Hz}$. We anticipate that this demonstration will be strongly motivational for the development of a new class of deployable trapped-ion-based sensors, and will permit scientists to access new regimes in materials science.Comment: Expanded introduction and analysis. Methods section added. Subject to press embarg

Stamp transferred suspended graphene mechanical resonators for radio-frequency electrical readout

We present a simple micromanipulation technique to transfer suspended graphene flakes onto any substrate and to assemble them with small localized gates into mechanical resonators. The mechanical motion of the graphene is detected using an electrical, radio-frequency (RF) reflection readout scheme where the time-varying graphene capacitor reflects a RF carrier at f=5-6 GHz producing modulation sidebands at f +/- fm. A mechanical resonance frequency up to fm=178 MHz is demonstrated. We find both hardening/softening Duffing effects on different samples, and obtain a critical amplitude of ~40 pm for the onset of nonlinearity in graphene mechanical resonators. Measurements of the quality factor of the mechanical resonance as a function of DC bias voltage Vdc indicate that dissipation due to motion-induced displacement currents in graphene electrode is important at high frequencies and large Vdc

Control of microwave signals using circuit nano-electromechanics

Waveguide resonators are crucial elements in sensitive astrophysical detectors [1] and circuit quantum electrodynamics (cQED) [2]. Coupled to artificial atoms in the form of superconducting qubits [3, 4], they now provide a technologically promising and scalable platform for quantum information processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots [13] or mechanical oscillators [14, 15] has been explored to realize hybrid systems with extended functionality. Here, we couple a superconducting coplanar waveguide resonator to a nano-coshmechanical oscillator, and demonstrate all-microwave field controlled slowing, advancing and switching of microwave signals. This is enabled by utilizing electromechanically induced transparency [16-18], an effect analogous to electromagnetically induced transparency (EIT) in atomic physics [19]. The exquisite temporal control gained over this phenomenon provides a route towards realizing advanced protocols for storage of both classical and quantum microwave signals [20-22], extending the toolbox of control techniques of the microwave field.Comment: 9 figure

Finite temperature phase diagram of a polarised Fermi condensate

The two-component Fermi gas is the simplest fermion system displaying superfluidity, and as such finds applications ranging from the theory of superconductivity to QCD. Ultracold atomic gases provide an exceptionally clean realization of this system, where the interatomic interaction and the atom species population are both independent, tuneable parameters. This allows one to investigate the Fermi gas with imbalanced spin populations, which had previously been experimentally elusive, and this prospect has stimulated much theoretical activity. Here we show that the finite temperature phase diagram contains a region of phase separation between the superfluid and normal states that touches the boundary of second-order superfluid transitions at a tricritical point, reminiscent of the phase diagram of $^3$He-$^4$He mixtures. A variation of interaction strength then results in a line of tricritical points that terminates at zero temperature on the molecular Bose-Einstein condensate (BEC) side. On this basis, we argue that tricritical points will play an important role in the recent experiments on polarised atomic Fermi gases.Comment: 6 pages, 4 figures. Manuscript extended and figures modified. For final version, see Nature Physic

Imbalanced Superfluid Phase of a Trapped Fermi Gas in the BCS-BEC Crossover Regime

We theoretically investigate the ground state of trapped neutral fermions with population imbalance in the BCS-BEC crossover regime. On the basis of the single-channel Hamiltonian, we perform full numerical calculations of the Bogoliubov-de Gennes equation coupled with the regularized gap and number equations. The zero-temperature phase diagram in the crossover regime is presented, where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state governs the weak-coupling BCS region of a resonance. It is found that the FFLO oscillation vanishes in the BEC side, in which the system under population imbalance turns into a phase separation (PS) between locally binding superfluid and fully polarized spin domains. We also demonstrate numerical calculations with a large particle number O(10^5), comparable to that observed in recent experiments. The resulting density profile on a resonance yields the PS, which is in good agreement with the recent experiments, while the FFLO modulation exists in the pairing field. It is also proposed that the most favorable location for the detection of the FFLO oscillation is in the vicinity of the critical population imbalance in the weak coupling BCS regime, where the oscillation periodicity becomes much larger than the interparticle spacing. Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalanced system. The clear difference in the RF spectroscopy between BCS and BEC sides reveals the structure of the pairing field and local ``magnetization''.Comment: 16 pages, 13 figures, replaced by the version to appear in J. Phys. Soc. Jp

Relativistic quantum effects of Dirac particles simulated by ultracold atoms

Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.Comment: 22 pages, review article in Frontiers of Physics: Proceedings on Quantum Dynamics of Ultracold Atom

Many-Body Physics with Ultracold Gases

This article reviews recent experimental and theoretical progress on many-body phenomena in dilute, ultracold gases. Its focus are effects beyond standard weak-coupling descriptions, like the Mott-Hubbard-transition in optical lattices, strongly interacting gases in one and two dimensions or lowest Landau level physics in quasi two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near Feshbach resonances in the BCS-BEC crossover.Comment: revised version, accepted for publication in Rev. Mod. Phy