1
|
Schlawin F, Jaksch D. Cavity-Mediated Unconventional Pairing in Ultracold Fermionic Atoms. PHYSICAL REVIEW LETTERS 2019; 123:133601. [PMID: 31697538 DOI: 10.1103/physrevlett.123.133601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Indexed: 06/10/2023]
Abstract
We investigate long-range pairing interactions between ultracold fermionic atoms confined in an optical lattice which are mediated by the coupling to a cavity. In the absence of other perturbations, we find three degenerate pairing symmetries for a two-dimensional square lattice. By tuning a weak local atomic interaction via a Feshbach resonance or by tuning a weak magnetic field, the superfluid system can be driven from a topologically trivial s wave to topologically ordered, chiral superfluids containing Majorana edge states. Our work points out a novel path towards the creation of exotic superfluid states by exploiting the competition between long-range and short-range interactions.
Collapse
Affiliation(s)
- Frank Schlawin
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Dieter Jaksch
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| |
Collapse
|
2
|
Challis KJ, Ballagh RJ, Gardiner CW. Bragg scattering of cooper pairs in an ultracold Fermi gas. PHYSICAL REVIEW LETTERS 2007; 98:093002. [PMID: 17359154 DOI: 10.1103/physrevlett.98.093002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2006] [Indexed: 05/14/2023]
Abstract
We present a theoretical treatment of Bragg scattering of a degenerate Fermi gas in the weakly interacting BCS regime. Our numerical calculations predict correlated scattering of Cooper pairs into a spherical shell in momentum space. The scattered shell of correlated atoms is centered at half the usual Bragg momentum transfer, and can be clearly distinguished from atoms scattered by the usual single-particle Bragg mechanism. We develop an analytic model that explains key features of the correlated-pair Bragg scattering, and determine the dependence of that scattering on the initial pair correlations in the gas.
Collapse
Affiliation(s)
- K J Challis
- Jack Dodd Centre for Photonics and Ultra-Cold Atoms, Department of Physics, University of Otago, P.O. Box 56, Dunedin, New Zealand
| | | | | |
Collapse
|
3
|
Zwierlein MW, Schunck CH, Schirotzek A, Ketterle W. Direct observation of the superfluid phase transition in ultracold Fermi gases. Nature 2006; 442:54-8. [PMID: 16823447 DOI: 10.1038/nature04936] [Citation(s) in RCA: 289] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2006] [Accepted: 05/23/2006] [Indexed: 11/09/2022]
Abstract
Phase transitions are dramatic phenomena: water freezes into ice, atomic spins spontaneously align in a magnet, and liquid helium becomes superfluid. Sometimes, such a drastic change in behaviour is accompanied by a visible change in appearance. The hallmark of Bose-Einstein condensation and superfluidity in trapped, weakly interacting Bose gases is the sudden formation of a dense central core inside a thermal cloud. However, in strongly interacting gases--such as the recently observed fermionic superfluids--there is no longer a clear separation between the superfluid and the normal parts of the cloud. The detection of fermion pair condensates has required magnetic field sweeps into the weakly interacting regime, and the quantitative description of these sweeps presents a major theoretical challenge. Here we report the direct observation of the superfluid phase transition in a strongly interacting gas of 6Li fermions, through sudden changes in the shape of the clouds--in complete analogy to the case of weakly interacting Bose gases. By preparing unequal mixtures of the two spin components involved in the pairing, we greatly enhance the contrast between the superfluid core and the normal component. Furthermore, the distribution of non-interacting excess atoms serves as a direct and reliable thermometer. Even in the normal state, strong interactions significantly deform the density profile of the majority spin component. We show that it is these interactions that drive the normal-to-superfluid transition at the critical population imbalance of 70 +/- 5 per cent (ref. 12).
Collapse
Affiliation(s)
- Martin W Zwierlein
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, Massachusetts 02139, USA.
| | | | | | | |
Collapse
|
4
|
Stajic J, Chen Q, Levin K. Density profiles of strongly interacting trapped fermi gases. PHYSICAL REVIEW LETTERS 2005; 94:060401. [PMID: 15783708 DOI: 10.1103/physrevlett.94.060401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2004] [Revised: 11/10/2004] [Indexed: 05/24/2023]
Abstract
We study density profiles in trapped fermionic gases, near Feshbach resonances, at all T< or =Tc and in the near Bose-Einstein condensation and unitary regimes. For the latter, we characterize and quantify the generally neglected contribution from noncondensed Cooper pairs. As a consequence of these pairs, our profiles are rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature.
Collapse
Affiliation(s)
- Jelena Stajic
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | | | | |
Collapse
|
5
|
Lee C. Bose-Einstein condensation of particle-hole pairs in ultracold fermionic atoms trapped within optical lattices. PHYSICAL REVIEW LETTERS 2004; 93:120406. [PMID: 15447239 DOI: 10.1103/physrevlett.93.120406] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2004] [Indexed: 05/24/2023]
Abstract
We investigate the Bose-Einstein condensation (BEC, superfluidity) of particle-hole pairs in ultracold fermionic atoms with repulsive interactions and arbitrary polarization, which are trapped within optical lattices. In the strongly repulsive limit, the dynamics of particle-hole pairs can be described by a hard-core Bose-Hubbard model. The insulator-superfluid and charge-density-wave- (CDW) superfluid phase transitions can be induced by decreasing and increasing the potential depths with controlling the trapping laser intensity, respectively. The parameter and polarization dependence of the critical temperatures for the ordered states (BEC and/or CDW) are discussed simultaneously.
Collapse
Affiliation(s)
- Chaohong Lee
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
| |
Collapse
|
6
|
Kinnunen J, Rodríguez M, Törmä P. Pairing Gap and In-Gap Excitations in Trapped Fermionic Superfluids. Science 2004; 305:1131-3. [PMID: 15272124 DOI: 10.1126/science.1100782] [Citation(s) in RCA: 114] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
We consider trapped atomic Fermi gases with Feshbach-resonance enhanced interactions in pseudogap and superfluid temperatures. We calculate the spectrum of radio-frequency (or laser) excitations for transitions that transfer atoms out of the superfluid state. The spectrum displays the pairing gap and also the contribution of unpaired atoms, that is, in-gap excitations. The results support the conclusion that a superfluid, in which pairing is a manybody effect, was observed in recent experiments on radio-frequency spectroscopy of the pairing gap.
Collapse
Affiliation(s)
- J Kinnunen
- Department of Physics, NanoScience Center, Post Office Box 35, FIN-40014, University of Jyväskylä, Finland
| | | | | |
Collapse
|
7
|
Perali A, Pieri P, Pisani L, Strinati GC. BCS-BEC crossover at finite temperature for superfluid trapped Fermi atoms. PHYSICAL REVIEW LETTERS 2004; 92:220404. [PMID: 15245204 DOI: 10.1103/physrevlett.92.220404] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2003] [Indexed: 05/24/2023]
Abstract
We consider the BCS-BEC (Bose-Einstein-condensate) crossover for a system of trapped Fermi atoms at finite temperature, both below and above the superfluid critical temperature, by including fluctuations beyond mean field. We determine the superfluid critical temperature and the pair-breaking temperature as functions of the attractive interaction between Fermi atoms, from the weak- to the strong-coupling limit (where bosonic molecules form as bound-fermion pairs). Density profiles in the trap are also obtained for all temperatures and couplings.
Collapse
Affiliation(s)
- A Perali
- Dipartimento di Fisica, UdR INFM, Università di Camerino, I-62032 Camerino, Italy
| | | | | | | |
Collapse
|
8
|
Csordás A, Szépfalusy P, Szoke E. Clustering of Fermi particles with arbitrary spin. PHYSICAL REVIEW LETTERS 2004; 92:090401. [PMID: 15089455 DOI: 10.1103/physrevlett.92.090401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2003] [Indexed: 05/24/2023]
Abstract
A single l-shell model is investigated for a system of fermions of spin s and an attractive s-wave, spin channel independent, interaction. The spectra and eigenvectors are determined exactly for different l,s values and particle numbers N. As a generalization of Cooper pairing it is shown that when N=mu(2s+1), mu=1,2,..., 2l+1, the ground state consists of clusters of (2s+1) particles. The relevance of the results for more general situations including the homogeneous system is briefly discussed.
Collapse
Affiliation(s)
- András Csordás
- Research Group for Statistical Physics of the Hungarian Academy of Sciences, Pázmány P. Sétány 1/A, H-1117 Budapest, Hungary
| | | | | |
Collapse
|
9
|
Ho TL. Universal thermodynamics of degenerate quantum gases in the unitarity limit. PHYSICAL REVIEW LETTERS 2004; 92:090402. [PMID: 15089456 DOI: 10.1103/physrevlett.92.090402] [Citation(s) in RCA: 102] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2003] [Indexed: 05/24/2023]
Abstract
We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study is based on a "universality hypothesis" for the relevant energy scales which is supported by experiments and can be proven in the Boltzmann regime. It implies a universal form for the grand potential, which is specified by only a few universal numbers in the degenerate limit. This hypothesis provides a simple way to determine the density profile of a trapped fermion superfluid. It implies a superfluid bump in the density and gives the general expression of the second sound velocity of a homogeneous superfluid at unitarity.
Collapse
Affiliation(s)
- Tin-Lun Ho
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| |
Collapse
|
10
|
Domanski T, Ranninger J. Bogoliubov shadow bands in the normal state of superconducting systems with strong pair fluctuations. PHYSICAL REVIEW LETTERS 2003; 91:255301. [PMID: 14754123 DOI: 10.1103/physrevlett.91.255301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2003] [Indexed: 05/24/2023]
Abstract
On the basis of a scenario where electron pairing is induced by resonant two-particle scattering (the boson-fermion model), we show how precursors of the superconducting state-in the form of overdamped Bogoliubov modes-emerge in the normal state upon approaching the transition temperature from above. This result is obtained by a renormalization technique based on continuous unitary transformations (the flow equations), projecting out the coherent contributions in the electron spectral function from an incoherent background.
Collapse
Affiliation(s)
- T Domanski
- Centre de Recherches sur les Très Basses Températures associé à l'Université Joseph Fourier, CNRS, BP 166, 38042 Grenoble-Cédex 9, France
| | | |
Collapse
|
11
|
Jochim S, Bartenstein M, Altmeyer A, Hendl G, Chin C, Hecker Denschlag J, Grimm R. Pure gas of optically trapped molecules created from fermionic atoms. PHYSICAL REVIEW LETTERS 2003; 91:240402. [PMID: 14683094 DOI: 10.1103/physrevlett.91.240402] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2003] [Indexed: 05/24/2023]
Abstract
We report on the production of a pure sample of up to 3 x 10(5) optically trapped molecules from a Fermi gas of 6Li atoms. The dimers are formed by three-body recombination near a Feshbach resonance. For purification, a Stern-Gerlach selection technique is used that efficiently removes all trapped atoms from the atom-molecule mixture. The behavior of the purified molecular sample shows a striking dependence on the applied magnetic field. For very weakly bound molecules near the Feshbach resonance, the gas exhibits a remarkable stability with respect to collisional decay.
Collapse
Affiliation(s)
- S Jochim
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | | | | | | | | | | | | |
Collapse
|
12
|
Presilla C, Onofrio R. Cooling dynamics of ultracold two-species Fermi-Bose mixtures. PHYSICAL REVIEW LETTERS 2003; 90:030404. [PMID: 12570476 DOI: 10.1103/physrevlett.90.030404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2002] [Indexed: 05/24/2023]
Abstract
We compare strategies for evaporative and sympathetic cooling of two-species Fermi-Bose mixtures in single-color and two-color optical dipole traps. We show that in the latter case a large heat capacity of the bosonic species can be maintained during the entire cooling process. This could allow one to efficiently achieve a deep Fermi degeneracy regime having at the same time a significant thermal fraction for the Bose gas, crucial for a precise thermometry of the mixture. Two possible signatures of a superfluid phase transition for the Fermi species are discussed.
Collapse
Affiliation(s)
- Carlo Presilla
- Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, Roma 00185, Italy
| | | |
Collapse
|
13
|
Jochim S, Bartenstein M, Hendl G, Denschlag JH, Grimm R, Mosk A, Weidemüller M. Magnetic field control of elastic scattering in a cold gas of fermionic lithium atoms. PHYSICAL REVIEW LETTERS 2002; 89:273202. [PMID: 12513205 DOI: 10.1103/physrevlett.89.273202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2002] [Indexed: 05/24/2023]
Abstract
We study elastic collisions in an optically trapped spin mixture of fermionic lithium atoms in the presence of magnetic fields up to 1.5 kG by measuring evaporative loss. Our experiments confirm the expected magnetic tunability of the scattering length by showing the main features of elastic scattering according to recent calculations. We measure the zero crossing of the scattering length at 530(3) G which is associated with a predicted Feshbach resonance at approximately 850 G. Beyond the resonance we observe the expected large cross section in the triplet scattering regime.
Collapse
Affiliation(s)
- S Jochim
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | | | | | | | | | | | | |
Collapse
|
14
|
Menotti C, Pedri P, Stringari S. Expansion of an interacting fermi gas. PHYSICAL REVIEW LETTERS 2002; 89:250402. [PMID: 12484869 DOI: 10.1103/physrevlett.89.250402] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2002] [Indexed: 05/24/2023]
Abstract
We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.
Collapse
Affiliation(s)
- C Menotti
- Dipartimento di Fisica, Università di Trento and BEC-INFM, I-38050 Povo, Italy
| | | | | |
Collapse
|
15
|
Ohashi Y, Griffin A. BCS-BEC crossover in a gas of Fermi atoms with a Feshbach resonance. PHYSICAL REVIEW LETTERS 2002; 89:130402. [PMID: 12225012 DOI: 10.1103/physrevlett.89.130402] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2002] [Indexed: 05/23/2023]
Abstract
We discuss the BCS-BEC crossover in a degenerate Fermi gas of two hyperfine states interacting close to a Feshbach resonance. We show that, by including fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink, the character of the superfluid phase transition continuously changes from the BCS-type to the BEC-type, as the threshold of the quasimolecular band is lowered. In the BEC regime, the superfluid phase transition is interpreted in terms of molecules associated with both the Feshbach resonance and Cooper pairing.
Collapse
Affiliation(s)
- Y Ohashi
- Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
| | | |
Collapse
|
16
|
Onofrio R, Presilla C. Reaching fermi degeneracy in two-species optical dipole traps. PHYSICAL REVIEW LETTERS 2002; 89:100401. [PMID: 12225175 DOI: 10.1103/physrevlett.89.100401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2002] [Indexed: 05/23/2023]
Abstract
We propose the use of a combined optical dipole trap to achieve Fermi degeneracy by sympathetic cooling with a different bosonic species. Two far-detuned pairs of laser beams focused on the atomic clouds are used to confine the two atomic species with different trapping strengths. We show that a deep Fermi degeneracy regime can be potentially achieved earlier than Bose-Einstein condensation, as discussed in the favorable situation of a 6Li-23Na mixture. This opens up the possibility of experimentally investigating a mixture of superfluid Fermi and normal Bose gases.
Collapse
Affiliation(s)
- Roberto Onofrio
- Dipartimento di Fisica G. Galilei, Università di Padova, Via Marzolo 8, Italy
| | | |
Collapse
|
17
|
Loftus T, Regal CA, Ticknor C, Bohn JL, Jin DS. Resonant control of elastic collisions in an optically trapped fermi gas of atoms. PHYSICAL REVIEW LETTERS 2002; 88:173201. [PMID: 12005753 DOI: 10.1103/physrevlett.88.173201] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2001] [Indexed: 05/23/2023]
Abstract
We have loaded an ultracold gas of fermionic atoms into a far-off resonance optical dipole trap and precisely controlled the spin composition of the trapped gas. We have measured a magnetic-field Feshbach resonance between atoms in the two lowest energy spin states, /9/2,-9/2> and /9/2,-7/2>. The resonance peaks at a magnetic field of 201.5+/-1.4 G and has a width of 8.0+/-1.1 G. Using this resonance, we have changed the elastic collision cross section in the gas by nearly 3 orders of magnitude.
Collapse
Affiliation(s)
- T Loftus
- JILA, National Institute of Standards and Technology, University of Colorado, Boulder, Colorado 80309, USA
| | | | | | | | | |
Collapse
|