Ultracold Fermions and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>Hubbard Model

Honerkamp, Carsten; Hofstetter, Walter

doi:10.1103/physrevlett.92.170403

Cited by 304 publications

(413 citation statements)

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“…As an interesting consequence of these many-body corrections we predict in a spatially varying confining potential (typically harmonic trap) the appearance of superfluid shell structures even in the absence of population imbalance (polarization) of the components. These shell structures are due to many-body effects only and therefore fundamentally different from earlier predictions of shell structures due to population, mass, or trapping potential imbalance [23,24] We also point out that many body effects due to the third component provide a new way to tune the effective interaction between the two other fermions and that this contribution can dominate over the usual GM contribution.Earlier, intriquing results have been found experimentally for the critical temperature of iron-based multiband superconductors [25] and degenerate three-component Fermi gases have been studied theoretically in a lattice [26,27]. Furthermore, pairing [23,28,29], stability [30], and breached pairing [31] have recently been studied in a three-component fermionic mixtures.…”

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confidence: 95%

Induced Interactions and the Superfluid Transition Temperature in a Three-Component Fermi Gas

et al. 2009

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We study many-body contributions to the effective interaction between fermions in a threecomponent Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a 6 Li mixture which can deviate strongly from the one in a weakly interacting two-component system.By using Feshbach resonances to change the effective interaction between ultracold atoms several groups have probed the crossover from the Bardeen-CooperSchrieffer (BCS) superfluid to a Bose-Einstein condensate of molecules [1][2][3][4][5][6][7][8][9][10]. Studies of the crossover have provided important insights into fermionic superfluids around the unitarity limit of strong interactions. Importantly, it has become experimentally feasible to study also more complicated mixtures than Fermi gases with two different atomic internal states. Bose-Fermi mixtures [11,12] and Bose-Einstein condensates with many components have been created using many different setups [13,14]. Also, heteronuclear Fermi-Fermi mixtures [15,16] and even heteronuclear Fermi-Fermi-Bose mixtures [17] have been recently demonstrated. In yet another breakthrough a three-component Fermi mixture of atoms in the three lowest hyperfine states of 6 Li [18,19] has also been demonstrated. Such multicomponent systems have some intriguing similarities with quark matter counterparts where color superconductivity may appear [20].The purpose of this Letter is to explore how the induced interactions due to the third component modify the expected behavior of three-component mixtures. This is important because, depending on parameters, the many-body effects can change the effective interaction between atoms substantially and on occasion even change the relative magnitudes of couplings between different components. Such changes imply that phase diagrams predicted using only two-body scattering properties can be incorrect. Also, even when the corrections to the effective interactions are weak, they can cause large changes to the critical temperature for the BCS transition. Indeed, for a two component system Gorkov and MelikBarkhudarov (GM) showed [21] that the perturbative correction to the effective interaction can reduce the critical temperature by a constant factor of (4e) 1/3 ≈ 2.22 in the weak-coupling limit. Also in spin-density imbalanced systems such corrections have been shown to have a considerable effect [22]. Here we will analyze the effects of analogous corrections on the three component system and find important changes to the GM result. As an interesting consequence of these many-body corrections we predict in a spatially varying confining potential (typically harmonic trap) the appearance of superfluid shell structures even in the absence of population imbalance (polarization)...

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Induced Interactions and the Superfluid Transition Temperature in a Three-Component Fermi Gas

et al. 2009

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“…The three-body decay rates, however, decrease by more than an order of magnitude between 690 and 830 G for a ternary mixture, which may reflect interesting three-body physics. The lifetime of 30 ms at 691 G might be sufficient for studies involving all three hyperfine states [29] with the potential for experiments on pairing competition in multi-component Fermi gases and spinor Fermi superfluids.…”

Section: Figmentioning

confidence: 99%

Determination of the fermion pair size in a resonantly interacting superfluid

Schunck

Shin

Schirotzek

et al. 2008

Nature

126

161

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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 [1,2,3], 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 [4,5]. The microscopic properties of the fermion pairs can be probed with radiofrequency (rf) spectroscopy. Previous work [6,7,8] 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 fermions 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 [9]. 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.The properties of pairs are revealed in a dissociation spectrum, where pair dissociation is monitored as a function of the applied energy E. The spectrum has a sharp onset at the pair's binding energy E b , where the fragments have zero kinetic energy, and then spreads out to higher energy. Since a rf photon has negligible momentum, the allowed momenta for the fragments reflect the Fourier transform Φ(k) of the pair wavefunction φ(r), which has a width on the order of 1/ξ where ξ is the pair size. Thus the pair size can be estimated from the spectral line width E w as ξ 2 ∼ 2 /mE w (m is the mass of the particles and is Planck's constant h divided by 2π).The conceptually simplest pairs in the BCS-BEC crossover are the weakly bound molecules in the BEC limit, which are described by a spatial wavefunction φ m (r) ∝ e −r/b /r with a binding energy E b = 2 /mb 2 . When the molecules are dissociated into noninteracting free particles, the spectral response is I m ∝ √ E − E b /E 2 , showing a highly asymmetric line shape with a steep rise at the molecular binding energy E b and a long "tail" to higher energies (Fig. 1a) [5,10]. This general behavior of the dissociation spectrum holds also in the BCS limit where pairing is a many-body effect [5,11]. The rf dissociation process discussed below, in the limit of negligible final state interactions, can be considered as breaking a Cooper pair into...

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“…Although the problem of two coupled two-component fermionic chains has been extensively studied, and some results on the two-dimensional SU(n) Hubbard model are known, 3,27 to the best of our knowledge the properties of two coupled SU(n) symmetric fermionic chains have not been discussed. For this reason, in this paper, we will present the results obtained for a ladder built up from two n-component fermion systems.…”

Section: Introductionmentioning

confidence: 99%

Possible phases of two coupledn-component fermionic chains determined using an analytic renormalization group method

Szirmai¹,

Sólyom²

2006

Phys. Rev. B

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A two-leg ladder with n-component fermionic fields in the chains has been considered using an analytic renormalization group method. The fixed points and possible phases have been determined for generic filling as well as for a half-filled system and for the case when one of the subbands is half filled. A weak-coupling Luttinger-liquid phase and several strong-coupling gapped phases have been found. In the Luttinger liquid phase, for the most general spin dependence of the couplings, all 2n modes have different velocities if the interband scattering processes are scaled out, while n doubly degenerate modes appear if the interband scattering processes remain finite. The role of backward-scattering, charge-transfer and umklapp processes has been analysed using their bosonic form and the possible phases are characterized by the number of gapless modes. As a special case the SU(n) symmetric Hubbard ladder has been investigated numerically. It was found that this model does not scale to the Luttinger liquid fixed point. Even for generic filling gaps open up in the spectrum of the spin or charge modes, and the system is always insulator in the presence of umklapp processes.

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Ultracold Fermions and theSU(N)Hubbard Model

Cited by 304 publications

References 34 publications

Induced Interactions and the Superfluid Transition Temperature in a Three-Component Fermi Gas

Induced Interactions and the Superfluid Transition Temperature in a Three-Component Fermi Gas

Determination of the fermion pair size in a resonantly interacting superfluid

Possible phases of two coupledn-component fermionic chains determined using an analytic renormalization group method

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