Theory of ultracold atomic Fermi gases
TL;DR: In this article, the physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective, focusing on the effect of interactions that bring the gas into a superfluid phase at low temperature.
Abstract: The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the $s$-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
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Proceedings Article•
14 Jul 1996TL;DR: The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of ~2µK.
Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.
3,530 citations
TL;DR: Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases and have found numerous experimental applications, opening up the way to important breakthroughs as mentioned in this paper.
Abstract: Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
2,642 citations
TL;DR: In this paper, a review of advances in this field is presented and discussed the possibilities offered by this approach to quantum simulation, as well as the possibilities of quantum simulation with ultracold quantum gases.
Abstract: Experiments with ultracold quantum gases provide a platform for creating many-body systems that can be well controlled and whose parameters can be tuned over a wide range. These properties put these systems in an ideal position for simulating problems that are out of reach for classical computers. This review surveys key advances in this field and discusses the possibilities offered by this approach to quantum simulation.
1,914 citations
01 May 2009
TL;DR: Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases and have found numerous experimental applications, opening up the way to important breakthroughs as mentioned in this paper.
Abstract: Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
1,531 citations
Cites background from "Theory of ultracold atomic Fermi ga..."
...For reviews on the theory of degenerate quantum gases of bosons and fermions see (Dalfovo et al., 1999) and (Giorgini et al., 2008), respectively, and the textbooks by (Stringari and Pitaevskii, 2003) and (Pethick and Smith, 2008). the underlying two-body physics and on models to describe Feshbach…...
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TL;DR: In this paper, a review of recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems is presented, from the superfluid flow around a defect at low speeds to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles.
Abstract: This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.
1,469 citations
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TL;DR: In this article, a theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, and it is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction.
Abstract: A theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, $\ensuremath{\hbar}\ensuremath{\omega}$. It is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction. The normal phase is described by the Bloch individual-particle model. The ground state of a superconductor, formed from a linear combination of normal state configurations in which electrons are virtually excited in pairs of opposite spin and momentum, is lower in energy than the normal state by amount proportional to an average ${(\ensuremath{\hbar}\ensuremath{\omega})}^{2}$, consistent with the isotope effect. A mutually orthogonal set of excited states in one-to-one correspondence with those of the normal phase is obtained by specifying occupation of certain Bloch states and by using the rest to form a linear combination of virtual pair configurations. The theory yields a second-order phase transition and a Meissner effect in the form suggested by Pippard. Calculated values of specific heats and penetration depths and their temperature variation are in good agreement with experiment. There is an energy gap for individual-particle excitations which decreases from about $3.5k{T}_{c}$ at $T=0\ifmmode^\circ\else\textdegree\fi{}$K to zero at ${T}_{c}$. Tables of matrix elements of single-particle operators between the excited-state superconducting wave functions, useful for perturbation expansions and calculations of transition probabilities, are given.
9,619 citations
TL;DR: In this paper, a theoretical analysis of the shape of the 2s2p^{1}P resonance of He observed in the inelastic scattering of electrons is presented. But the analysis is restricted to the case of one discrete level with two or more continua and of a set of discrete levels with one continuum.
Abstract: The interference of a discrete autoionized state with a continuum gives rise to characteristically asymmetric peaks in excitation spectra. The earlier qualitative interpretation of this phenomenon is extended and revised. A theoretical formula is fitted to the shape of the $2s2p^{1}P$ resonance of He observed in the inelastic scattering of electrons. The fitting determines the parameters of the $2s2p^{1}P$ resonance as follows: $E=60.1$ ev, $\ensuremath{\Gamma}\ensuremath{\sim}0.04$ ev, $f\ensuremath{\sim}2 \mathrm{to} 4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. The theory is extended to the interaction of one discrete level with two or more continua and of a set of discrete levels with one continuum. The theory can also give the position and intensity shifts produced in a Rydberg series of discrete levels by interaction with a level of another configuration. The connection with the nuclear theory of resonance scattering is indicated.
8,210 citations
"Theory of ultracold atomic Fermi ga..." refers background in this paper
...This situation exists near the so called Fano-Feshbach resonances (Fano, 1961; Feshbach, 1962)....
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TL;DR: A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled and exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.
Abstract: A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 x 10 12 per cubic centimeter and could be preserved for more than 15 seconds. Three primary signatures of Bose-Einstein condensation were seen. (i) On top of a broad thermal velocity distribution, a narrow peak appeared that was centered at zero velocity. (ii) The fraction of the atoms that were in this low-velocity peak increased abruptly as the sample temperature was lowered. (iii) The peak exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.
6,074 citations
"Theory of ultracold atomic Fermi ga..." refers background in this paper
...The first realization of Bose-Einstein condensation (BEC) in dilute vapours of alkali atoms (Anderson et al., 1995; Bradley et al., 1995; Davis et al., 1995) has in fact opened new stimulating perspectives in this area of research....
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Book•
01 Jan 1980
TL;DR: In this paper, the Hartree-Fock method pairing correlations and superfluid nuclei was used to restore broken symmetries in the generator coordinate method of the generator-coordinate method.
Abstract: The liquid drop model the shell model rotation and single-particle motion nuclear forces the Hartree-Fock method pairing correlations and superfluid nuclei the generalized single-particle model (HFB theory) harmonic vibrations boson expansion methods the generator coordinate method restoration of broken symmetries the time dependent Hartree-Fock method (TDHF) semiclassical methods in nuclear physics. Appendices: angular momentum algebra in the laboratory and the body-fixed system electromagnetic moments and transitions second quantization density matrices theorems concerning product wave functions many-body green's functions.
5,259 citations
"Theory of ultracold atomic Fermi ga..." refers background in this paper
...By combining these two relations, one obtains the following expression for the gap (see, e.g., Ring and Schuck, 1980) ∆gap = 1 2 [2E(N/2 ± 1, N/2) (30) − E(N/2 ± 1, N/2± 1) − E(N/2, N/2)] ....
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...(11) is the consequence of the absence of collisions during the expansion and reflects the isotropy of the momentum distribution (10)....
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TL;DR: In this paper, the Hartree-Fock approximation of the correlation problem for the d-and f-bands was applied to a simple, approximate model for the interaction of electrons in narrow energy bands.
Abstract: It is pointed out that one of the main effects of correlation phenomena in d- and f-bands is to give rise to behaviour characteristic of the atomic or Heitler-London model. To investigate this situation a simple, approximate model for the interaction of electrons in narrow energy bands is introduced. The results of applying the Hartree-Fock approximation to this model are examined. Using a Green function technique an approximate solution of the correlation problem for this model is obtained. This solution has the property of reducing to the exact atomic solution in the appropriate limit and to the ordinary uncorrelated band picture in the opposite limit. The condition for ferromagnetism of this solution is discussed. To clarify the physical meaning of the solution a two-electron example is examined.
5,151 citations