Effect of the particle-hole channel on BCS--Bose-Einstein condensation crossover in atomic Fermi gases

BCS--Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel. Here we study the effect of the particle-hole channel on the zero $T$ gap $\Delta(0)$, superfluid transition temperature $T_{\text{c}}$ and the pseudogap at $T_{\text{c}}$, as well as the mean-field ratio $2\Delta(0)/T_{\text{c}}^{\text{MF}}$, from BCS through BEC regimes, in the framework of a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs. These pairs necessarily lead to a pseudogap in single particle excitation spectrum above and below $T_{\text{c}}$. We sum over the infinite particle-hole ladder diagrams so that the particle-particle and particle-hole $T$-matrices are entangled with each other. We find that the particle-hole susceptibility has a complex dynamical structure, with strong momentum and frequency dependencies, and is sensitive to temperature, gap size and interaction strength. We conclude that neglecting the self-energy feedback causes a serious over-estimate of the particle-hole susceptibility. In the BCS limit, the particle-hole channel effect may be approximated by the same reduction in the overall pairing strength so that the ratio $2\Delta(0)/T_{\text{c}}$ is unaffected, in agreement with Gor'kov \textit{et al.} to the leading order. However, the effect becomes more complex and pronounced in the crossover regime, where the particle-hole susceptibility is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We propose that precision measurements of the magnetic field for Feshbach resonance at low temperatures as a function of density can be used to quantify the particle-hole susceptibility and test different theories.Comment: Substantial rewriting of the theory section and the discussion of Tc/E_F at unitarit

Investigation of Diamond Nucleation under Very Low Pressure in Chemical Vapor Deposition

Diamond nucleation under very low pressure (0.1-1.0 torr) was obtained at very high nucleation densities and very rapid rates using hot-filament chemical vapor deposition (HFCVD). The density on mirror-polished silicon was as high as 10^10 - 10^11 cm^{-2}, equivalent to the highest density in a microwave-plasma CVD system. That on scratched silicon substrates was up to 10^9 cm^{-2}, 1-2 orders of magnitude higher than that obtained under conventionally low pressure (tens of torr, 10^7 - 10^8 cm^{-2}). Also, the density on scratched titanium substrates was as high as 10^10 cm^{-2}. The samples were characterized using scanning electron microscopy (SEM) and Raman spectroscopy. The mechanism is investigated in detail, revealing that, under very low pressure, very long mean free path of the gas species, strong electron emission from the hot filament, and high efficiency of decomposition of hydrocarbon species by the filament greatly increase the concentration of reactive hydrocarbon radicals and atomic hydrogen on the substrate surface, and therefore, dramatically enhance the nucleation eventually. This work has great practical applications and theoretical significance.Comment: 8 pages, 8 figures in JPEG compressed form, containing 10 photos, REVTeX, in publication forma

Population of closed-channel molecules in trapped Fermi gases with broad Feshbach resonances

We compute the fraction of closed-channel molecules in trapped atomic Fermi gases, over the entire range of accessible fields and temperatures. We use a two-channel model of BCS--Bose-Einstein condensation (BEC) crossover theory at general temperature $T$, and show that this fraction provides a measure of the $T$ dependent pairing gap. Our calculations, containing no free parameters, are in good quantitative agreement with recent low $T$ measurements in $^6$Li. We present readily testable predictions for the dependencies of the closed-channel fraction on temperature and Fermi momentum.Comment: 4 pages, 3 figures, published in PR

Pseudogap phenomena in ultracold atomic Fermi gases

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high $T_c$ superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum simulator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high $T_c$ superconductivity. One obstacle to the ultimate understanding of high $T_c$ superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics community, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fluctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high $T_c$ superconductivity.Comment: Invited review article, 32 Figures, 29 page

Finite Temperature Effects in Ultracold Fermi Gases

This article is written as a Lecture given in the 2006 Varenna Summer School on "Ultracold Fermi Gases". Here we present a review of BCS--Bose Einstein condensation (BEC) crossover theory with emphasis on finite temperature effects. We discuss the role of temperature $T$ as it enters a theoretical formalism which is based on the standard BCS-Leggett ground state. We also discuss the role of temperature in the context of experiments ranging from thermometric issues to signatures of superfluidity. Particularly important to this discussion is the novel normal state associated with the crossover regime, intermediate between BCS and BEC. The experimental evidence for this unusual normal state (associated with pre-formed pairs) and its counterpart below $T_c$ (associated with non-condensed pairs) is presented in the context of different experiments. We end with a discussion of finite temperature effects in spin polarized superfluids, where $T$ is found to play a crucial role in both theory and experiment.Comment: Lecture given at the International School of Physics "Enrico Fermi" -- the 2006 Varenna Summer School on "Ultracold Fermi Gases", 27 pages, 17 figure

Mechanism of Diamond Nucleation on Titanium Substrate under Very Low Pressure

Nucleation and its mechanism of diamond on titanium substrates under very low pressure was studied using hot-filament chemical vapor deposition. Very high nucleation rates and densities (10^8-10^{10} cm^{-2}) were obtained under 1 torr, which were 1-3 orders of magnitude higher than the counterpart (10^7 cm^{-2}) under conventionally low pressure (tens of torr). The effects of substrate temperature and methane concentration under very low pressure were also investigated, revealing that, overly high substrate temperature leads to a relatively low nucleation density, and that higher CH_4 concentration gives rise to a higher density and a higher rate. The nucleation mechanism is discussed in detail. While a large amount of atomic hydrogen creates nucleating sites, sufficient supersaturation of carbon and/or hydrocarbon species on/near the substrate surface is the key factor for nucleation, in competition against the rapid formation of carbide. Very low pressure leads to long mean free path and other benefiting effects, and hence, is critical for rapid, high-density nucleation. Effects of substrate temperature and CH_4 concentration are also important. This further implies that C_2H_x (x<6) and CH_4 also contribute to nucleation, but CH_{1-3} dominates under very low pressure. The very-low-pressure method seems to be the only candidate to make diamond deposition on titanium films applicable. It also sheds light on how to increase the diamond growth rate.Comment: 8 pages (REVTeX) plus 4 (PostScript) figures with 14 photos, Ghostscript 4.02 or higher may be needed to view the PS files. But they print OK; Resubmit to fix the HTML tags in the abstract fiel

What can ultracold Fermi gases teach us about high TcT_c superconductors and vice versa?

We review recent developments in the field of ultracold atomic Fermi gases. As the cold atom system evolves from BCS to Bose-Einstein condensation (BEC), the behavior of the thermodynamics, and the particle density profiles evolves smoothly in a way which can be well understood theoretically. In the interesting "unitary" regime, we show that these and other data necessarily requires the introduction of a pseudogap in the fermionic spectrum which exhibits many striking similarities to its counterpart in underdoped high $T_c$ superconductors. We emphasize these similarities, giving an overview of the experimental tools and key issues of common interest in both systems.Comment: 4 pages, 6 figures, to appear in a special issue of Physica C for the M2S-HTSC VIII Conference Proceeding

Particle Density Distributions in Fermi Gas Superfluids: Molecular Boson Effects

We show how to describe the $T \neq 0$ behavior associated with the usual BCS- Bose Einstein condensation (BEC) crossover ground state. We confine our attention here to the BEC and near-BEC regime where analytical calculations are possible. At finite $T$, non-condensed fermion pairs must be included, although they have been generally ignored in the literature. Within this BEC regime we compute the equations of state for the one and two channel models; these two cases correspond to whether Feshbach resonance effects are omitted or included. Differences between these two cases can be traced to differences between the nature of a Cooper pair and bosonic condensate. Our results are also compared with the Gross Pitaevskii equations of state for true bosons. Differences found here are associated with the underlying fermionic character of the system. Finally, the particle density distribution functions for a trap containing superfluid fermionic atoms are computed using a Thomas-Fermi approach. The one and two channel behavior is found to be very different; we find a narrowing of the density profile as a result of Feshbach resonance effects. Importantly, we infer that the ratio between bosonic and fermionic scattering lengths depends on the magnetic detuning and is generally smaller than 2. Future experiments will be required to determine to what extent this ratio varies with magnetic fields.Comment: 8 pages, 2 figure, Revtex 4, submitted to PRA; manuscript expanded, figure adde

Reentrant Superfluidity and Pair Density Wave in Single Component Dipolar Fermi Gases

We study the superfluidity of single component dipolar Fermi gases in three dimensions within a pairing fluctuation theory. The transition temperature $T_{c}$ for the dominant $p_z$ wave superfluidity exhibits a remarkable re-entrant behavior as a function of the pairing strength induced by the dipole-dipole interaction (DDI), which leads to an anisotropic pair dispersion. The anisotropy and the long range nature of the DDI cause $T_c$ to vanish for a narrow range of intermediate interaction strengths, where a pair density wave state emerges as the ground state. The superfluid density and thermodynamics below $T_{c}$, along with the density profiles in a harmonic trap, are investigated as well, throughout the BCS-BEC crossover. Implications for experiments are discussed.Comment: 6 pages, 6 color figures; replaced with the final published versio

Applying BCS-BEC Crossover Theory To High Temperature Superconductors and Ultracold Atomic Fermi Gases

This review is written at the time of the twentieth anniversary of the discovery of high temperature superconductors, which, nearly coincides with the important discovery of the superfluid phases of ultracold trapped fermionic atoms. We show how these two subjects have much in common. Both have been addressed from the perspective of the BCS-Bose Einstein condensation (BEC) crossover scenario, which is designed to treat short coherence length superfluids with transition temperatures which are "high", with respect to the Fermi energy. A generalized mean field treatment of BCS-BEC crossover at general temperatures $T$, based on the BCS-Leggett ground state, has met with remarkable success in the fermionic atomic systems. Here we summarize this success in the context of four different cold atom experiments, all of which provide indications, direct or indirect, for the existence of a pseudogap. This scenario also provides a physical picture of the pseudogap phase in the underdoped cuprates which is a central focus of high $T_c$ research. We summarize successful applications of BCS-BEC crossover to key experiments in high $T_c$ systems including the phase diagram, specific heat, and vortex core STM data, along with the Nernst effect, and exciting recent data on the superfluid density in very underdoped samples,Comment: Review article for the 20th anniversary of high Tc superconductivity, 20 pages, 25 figures, to appear in J Low Temp Phy