51
|
A Mott insulator of fermionic atoms in an optical lattice. Nature 2008; 455:204-7. [DOI: 10.1038/nature07244] [Citation(s) in RCA: 778] [Impact Index Per Article: 48.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2008] [Accepted: 07/09/2008] [Indexed: 11/09/2022]
|
52
|
|
53
|
Titvinidze I, Snoek M, Hofstetter W. Supersolid bose-fermi mixtures in optical lattices. PHYSICAL REVIEW LETTERS 2008; 100:100401. [PMID: 18352164 DOI: 10.1103/physrevlett.100.100401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2007] [Indexed: 05/26/2023]
Abstract
We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.
Collapse
Affiliation(s)
- I Titvinidze
- Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, 60438 Frankfurt am Main, Germany
| | | | | |
Collapse
|
54
|
Abstract
Ultracold quantum gases are proving to be a powerful model system for strongly interacting electronic many-body systems. This Perspective explores how such atomic ensembles can help to unravel some of the outstanding open questions in the field.
Collapse
|
55
|
Seibold G, Becca F, Lorenzana J. Theory of antibound states in partially filled narrow band systems. PHYSICAL REVIEW LETTERS 2008; 100:016405. [PMID: 18232796 DOI: 10.1103/physrevlett.100.016405] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2007] [Indexed: 05/25/2023]
Abstract
We present a theory of the dynamical two-particle response function in the Hubbard model based on the time-dependent Gutzwiller approximation. The results are in excellent agreement with exact diagonalization on small clusters and are reliable even for high densities, where the usual ladder approximation breaks down. We apply the theory to the computation of antibound states relevant for Auger spectroscopy and cold atom physics.
Collapse
Affiliation(s)
- G Seibold
- Institut für Physik, BTU Cottbus, P.O. Box 101344, 03013 Cottbus, Germany
| | | | | |
Collapse
|
56
|
Strohmaier N, Takasu Y, Günter K, Jördens R, Köhl M, Moritz H, Esslinger T. Interaction-controlled transport of an ultracold fermi gas. PHYSICAL REVIEW LETTERS 2007; 99:220601. [PMID: 18233274 DOI: 10.1103/physrevlett.99.220601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2007] [Revised: 10/09/2007] [Indexed: 05/25/2023]
Abstract
We explore the transport properties of an interacting Fermi gas in a three-dimensional optical lattice. The center of mass dynamics of the atoms after a sudden displacement of the trap minimum is monitored for different interaction strengths and lattice fillings. With increasingly strong attractive interactions the weakly damped oscillation, observed for the noninteracting case, turns into a slow relaxational drift. Tuning the interaction strength during the evolution allows us to dynamically control the transport behavior. Strong attraction between the atoms leads to the formation of local pairs with a reduced tunneling rate. The interpretation in terms of pair formation is supported by a measurement of the number of doubly occupied lattice sites. This quantity also allows us to determine the temperature of the noninteracting gas in the lattice to be as low as (27+/-2)% of the Fermi temperature.
Collapse
Affiliation(s)
- Niels Strohmaier
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | | | | | | | | | | | | |
Collapse
|
57
|
Rapp A, Zaránd G, Honerkamp C, Hofstetter W. Color superfluidity and "baryon" formation in ultracold fermions. PHYSICAL REVIEW LETTERS 2007; 98:160405. [PMID: 17501400 DOI: 10.1103/physrevlett.98.160405] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2006] [Indexed: 05/15/2023]
Abstract
We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, U<0. Using a variational calculation for equal color densities and small couplings, |U|<|UC|, a color superfluid state emerges with a tendency to domain formation. For |U|>|UC|, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.
Collapse
Affiliation(s)
- Akos Rapp
- Theoretical Physics Department, Institute of Physics, Budapest University of Technology and Economy, Budapest, H-1521, Hungary
| | | | | | | |
Collapse
|
58
|
Rom T, Best T, van Oosten D, Schneider U, Fölling S, Paredes B, Bloch I. Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice. Nature 2006; 444:733-6. [PMID: 17151662 DOI: 10.1038/nature05319] [Citation(s) in RCA: 211] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2006] [Accepted: 10/06/2006] [Indexed: 11/09/2022]
Abstract
Noise in a quantum system is fundamentally governed by the statistics and the many-body state of the underlying particles. The correlated noise observed for bosonic particles (for example, photons or bosonic neutral atoms) can be explained within a classical field description with fluctuating phases; however, the anticorrelations ('antibunching') observed in the detection of fermionic particles have no classical analogue. Observations of such fermionic antibunching are scarce and have been confined to electrons and neutrons. Here we report the direct observation of antibunching of neutral fermionic atoms. By analysing the atomic shot noise in a set of standard absorption images of a gas of fermionic (40)K atoms released from an optical lattice, we find reduced correlations for distances related to the original spacing of the trapped atoms. The detection of such quantum statistical correlations has allowed us to characterize the ordering and temperature of the Fermi gas in the lattice. Moreover, our findings are an important step towards revealing fundamental fermionic many-body quantum phases in periodic potentials, which are at the focus of current research.
Collapse
Affiliation(s)
- T Rom
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | | | | | | | | | | | | |
Collapse
|
59
|
Chin JK, Miller DE, Liu Y, Stan C, Setiawan W, Sanner C, Xu K, Ketterle W. Evidence for superfluidity of ultracold fermions in an optical lattice. Nature 2006; 443:961-4. [PMID: 17066028 DOI: 10.1038/nature05224] [Citation(s) in RCA: 305] [Impact Index Per Article: 16.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2006] [Accepted: 08/25/2006] [Indexed: 11/08/2022]
Abstract
The study of superfluid fermion pairs in a periodic potential has important ramifications for understanding superconductivity in crystalline materials. By using cold atomic gases, various models of condensed matter can be studied in a highly controllable environment. Weakly repulsive fermions in an optical lattice could undergo d-wave pairing at low temperatures, a possible mechanism for high temperature superconductivity in the copper oxides. The lattice potential could also strongly increase the critical temperature for s-wave superfluidity. Recent experimental advances in bulk atomic gases include the observation of fermion-pair condensates and high-temperature superfluidity. Experiments with fermions and bosonic bound pairs in optical lattices have been reported but have not yet addressed superfluid behaviour. Here we report the observation of distinct interference peaks when a condensate of fermionic atom pairs is released from an optical lattice, implying long-range order (a property of a superfluid). Conceptually, this means that s-wave pairing and coherence of fermion pairs have now been established in a lattice potential, in which the transport of atoms occurs by quantum mechanical tunnelling and not by simple propagation. These observations were made for interactions on both sides of a Feshbach resonance. For larger lattice depths, the coherence was lost in a reversible manner, possibly as a result of a transition from superfluid to insulator. Such strongly interacting fermions in an optical lattice can be used to study a new class of hamiltonians with interband and atom-molecule couplings.
Collapse
Affiliation(s)
- J K Chin
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
| | | | | | | | | | | | | | | |
Collapse
|
60
|
Kollath C, Iucci A, Giamarchi T, Hofstetter W, Schollwöck U. Spectroscopy of ultracold atoms by periodic lattice modulations. PHYSICAL REVIEW LETTERS 2006; 97:050402. [PMID: 17026081 DOI: 10.1103/physrevlett.97.050402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2006] [Indexed: 05/12/2023]
Abstract
We present a nonperturbative analysis of a new experimental technique for probing ultracold bosons in an optical lattice by periodic lattice depth modulations. This is done using the time-dependent density-matrix renormalization group method. We find that sharp energy absorption peaks are not unique to the Mott insulating phase at commensurate filling but also exist for superfluids at incommensurate filling. For strong interactions, the peak structure provides an experimental measure of the interaction strength. Moreover, the peak height of the peaks at Planck's omega > or approximately 2U can be employed as a measure of the incommensurability of the system.
Collapse
Affiliation(s)
- C Kollath
- Université de Genève, 24 Quai Ernest-Ansermet, CH-1211 Genèva, Switzerland
| | | | | | | | | |
Collapse
|
61
|
Trebst S, Schollwöck U, Troyer M, Zoller P. d-Wave resonating valence bond states of fermionic atoms in optical lattices. PHYSICAL REVIEW LETTERS 2006; 96:250402. [PMID: 16907290 DOI: 10.1103/physrevlett.96.250402] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2005] [Indexed: 05/11/2023]
Abstract
We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by a change of the lattice parameters. Results of exact time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on a time scale smaller than typical experimental decoherence times.
Collapse
Affiliation(s)
- Simon Trebst
- Theoretische Physik, Eidgenössische Technische Hochschule Zürich, CH-8093 Zürich, Switzerland
| | | | | | | |
Collapse
|
62
|
Winkler K, Thalhammer G, Lang F, Grimm R, Denschlag JH, Daley AJ, Kantian A, Büchler HP, Zoller P. Repulsively bound atom pairs in an optical lattice. Nature 2006; 441:853-6. [PMID: 16778884 DOI: 10.1038/nature04918] [Citation(s) in RCA: 443] [Impact Index Per Article: 24.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2006] [Accepted: 05/18/2006] [Indexed: 11/10/2022]
Abstract
Throughout physics, stable composite objects are usually formed by way of attractive forces, which allow the constituents to lower their energy by binding together. Repulsive forces separate particles in free space. However, in a structured environment such as a periodic potential and in the absence of dissipation, stable composite objects can exist even for repulsive interactions. Here we report the observation of such an exotic bound state, which comprises a pair of ultracold rubidium atoms in an optical lattice. Consistent with our theoretical analysis, these repulsively bound pairs exhibit long lifetimes, even under conditions when they collide with one another. Signatures of the pairs are also recognized in the characteristic momentum distribution and through spectroscopic measurements. There is no analogue in traditional condensed matter systems of such repulsively bound pairs, owing to the presence of strong decay channels. Our results exemplify the strong correspondence between the optical lattice physics of ultracold bosonic atoms and the Bose-Hubbard model-a link that is vital for future applications of these systems to the study of strongly correlated condensed matter and to quantum information.
Collapse
Affiliation(s)
- K Winkler
- Institute for Experimental Physics, Innsbruck, Austria
| | | | | | | | | | | | | | | | | |
Collapse
|
63
|
Günter K, Stöferle T, Moritz H, Köhl M, Esslinger T. Bose-fermi mixtures in a three-dimensional optical lattice. PHYSICAL REVIEW LETTERS 2006; 96:180402. [PMID: 16712345 DOI: 10.1103/physrevlett.96.180402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2006] [Indexed: 05/09/2023]
Abstract
We have studied mixtures of fermionic (40)K and bosonic (87)Rb quantum gases in a three-dimensional optical lattice. We observe that an increasing admixture of the fermionic species diminishes the phase coherence of the bosonic atoms as measured by studying both the visibility of the matter wave interference pattern and the coherence length of the bosons. Moreover, we find that the attractive interactions between bosons and fermions lead to an increase of the boson density in the lattice which we measure by studying three-body recombination in the lattice. In our data, we do not observe three-body loss of the fermionic atoms. An analysis of the thermodynamics of a noninteracting Bose-Fermi mixture in the lattice suggests a mechanism for sympathetic cooling of the fermions in the lattice.
Collapse
Affiliation(s)
- Kenneth Günter
- Institute of Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland
| | | | | | | | | |
Collapse
|
64
|
Duan LM. Detecting correlation functions of ultracold atoms through fourier sampling of time-of-flight images. PHYSICAL REVIEW LETTERS 2006; 96:103201. [PMID: 16605731 DOI: 10.1103/physrevlett.96.103201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2005] [Indexed: 05/08/2023]
Abstract
We propose a detection method for ultracold atoms which allows reconstruction of the full one-particle and two-particle correlation functions from the measurements. The method is based on Fourier sampling of the time-of-flight images through two consecutive impulsive Raman pulses. For applications of this method, we discuss a few examples, including detection of phase separation between superfluid and Mott insulators, various types of spin or superfluid orders, entanglement, exotic or fluctuating orders.
Collapse
Affiliation(s)
- L-M Duan
- FOCUS Center and MCTP, Department of Physics, University of Michigan, Ann Arbor, 48109, USA
| |
Collapse
|
65
|
Stöferle T, Moritz H, Günter K, Köhl M, Esslinger T. Molecules of fermionic atoms in an optical lattice. PHYSICAL REVIEW LETTERS 2006; 96:030401. [PMID: 16486668 DOI: 10.1103/physrevlett.96.030401] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2005] [Indexed: 05/06/2023]
Abstract
We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunneling, the individual wells can be regarded as independent three-dimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.
Collapse
Affiliation(s)
- Thilo Stöferle
- Institute of Quantum Electronics, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland
| | | | | | | | | |
Collapse
|
66
|
Orso G, Shlyapnikov GV. Superfluid fermi gas in a 1D optical lattice. PHYSICAL REVIEW LETTERS 2005; 95:260402. [PMID: 16486318 DOI: 10.1103/physrevlett.95.260402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2005] [Indexed: 05/06/2023]
Abstract
We calculate the superfluid transition temperature for a two-component 3D Fermi gas in a 1D tight optical lattice and discuss a dimensional crossover from the 3D to quasi-2D regime. For the geometry of finite size discs in the 1D lattice, we find that even for a large number of atoms per disc the critical effective tunneling rate for a quantum transition to the Mott insulator state can be large compared to the loss rate caused by three-body recombination. This allows the observation of the Mott transition, in contrast to the case of Bose-condensed gases in the same geometry.
Collapse
Affiliation(s)
- G Orso
- BEC-INFM and Dipartimento di Fisica, Universitá di Trento, Povo, Italy
| | | |
Collapse
|
67
|
Lecheminant P, Boulat E, Azaria P. Confinement and superfluidity in one-dimensional degenerate fermionic cold atoms. PHYSICAL REVIEW LETTERS 2005; 95:240402. [PMID: 16384355 DOI: 10.1103/physrevlett.95.240402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2005] [Indexed: 05/05/2023]
Abstract
The physical properties of arbitrary half-integer spins F = N - (1/2) fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for F > or = (3/2) depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular-superfluid instability made of 2N fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the Z(N) generalized Ising universality class. We discuss the possible Mott phases at (1/2) filling.
Collapse
Affiliation(s)
- P Lecheminant
- Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, Université de Cergy-Pontoise, Site de Saint-Martin, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France
| | | | | |
Collapse
|
68
|
Günter K, Stöferle T, Moritz H, Köhl M, Esslinger T. p-Wave interactions in low-dimensional fermionic gases. PHYSICAL REVIEW LETTERS 2005; 95:230401. [PMID: 16384278 DOI: 10.1103/physrevlett.95.230401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2005] [Indexed: 05/05/2023]
Abstract
We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of /m/ = 1 (or m = 0) can be inhibited. In two and three dimensions, we observe the doublet structure of the p-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.
Collapse
Affiliation(s)
- Kenneth Günter
- Institute of Quantum Electronics, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland
| | | | | | | | | |
Collapse
|
69
|
Cazalilla MA, Ho AF, Giamarchi T. Two-component Fermi gas on internal-state-dependent optical lattices. PHYSICAL REVIEW LETTERS 2005; 95:226402. [PMID: 16384247 DOI: 10.1103/physrevlett.95.226402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2005] [Indexed: 05/05/2023]
Abstract
We study the phase diagram of a one-dimensional, two-component (i.e., pseudo-"spin"-(1/2)) ultracold atomic Fermi gas. The two atom species can have different hopping or mass. A very rich phase diagram for equal densities of the species is found, containing Mott insulators and superfluids. We also discuss coupling such 1D systems and the experimental signatures of the phases. In particular, we compute the spin-structure factor at small momentum, which should reveal a spin gap.
Collapse
Affiliation(s)
- M A Cazalilla
- Donostia Int'l Physics Center, Manuel de Lardizabal, 4. 20018-Donostia, Spain
| | | | | |
Collapse
|
70
|
Kinoshita T, Wenger T, Weiss DS. Local pair correlations in one-dimensional Bose gases. PHYSICAL REVIEW LETTERS 2005; 95:190406. [PMID: 16383965 DOI: 10.1103/physrevlett.95.190406] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2005] [Indexed: 05/05/2023]
Abstract
We measure photoassociation rates in one-dimensional Bose gases, and so determine the local pair correlation function over a wide range of coupling strengths. As bosons become more strongly coupled, we observe a tenfold decrease in their wave function overlap, thus directly observing the fermionization of bosons.
Collapse
Affiliation(s)
- Toshiya Kinoshita
- Department of Physics, The Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802, USA
| | | | | |
Collapse
|
71
|
Damski B, Everts HU, Honecker A, Fehrmann H, Santos L, Lewenstein M. Atomic Fermi gas in the trimerized kagomé lattice at 2/3 filling. PHYSICAL REVIEW LETTERS 2005; 95:060403. [PMID: 16090930 DOI: 10.1103/physrevlett.95.060403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2004] [Indexed: 05/03/2023]
Abstract
We study low temperature properties of a spinless interacting Fermi gas in the trimerized kagomé lattice. The case of two fermions per trimer is described by a quantum spin 1/2 model on the triangular lattice with couplings depending on the bond directions. Using exact diagonalizations we show that the system exhibits nonstandard properties of a quantum spin-liquid crystal, combining a planar antiferromagnetic order with an exceptionally large number of low-energy excitations.
Collapse
Affiliation(s)
- B Damski
- Institut für Theoretische Physik, Universität Hannover, Appelstrasse 2, D-30167 Hannover, Germany
| | | | | | | | | | | |
Collapse
|
72
|
Werner F, Parcollet O, Georges A, Hassan SR. Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices. PHYSICAL REVIEW LETTERS 2005; 95:056401. [PMID: 16090895 DOI: 10.1103/physrevlett.95.056401] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2005] [Indexed: 05/03/2023]
Abstract
We propose an interaction-induced cooling mechanism for two-component cold fermions in an optical lattice. It is based on an increase of the spin entropy upon localization, an analogue of the Pomeranchuk effect in liquid helium 3. We discuss its application to the experimental realization of the antiferromagnetic phase. We illustrate our arguments with dynamical mean-field theory calculations.
Collapse
Affiliation(s)
- F Werner
- LKB, Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
| | | | | | | |
Collapse
|
73
|
Dickerscheid DBM, van Oosten D, Tillema EJ, Stoof HTC. Quantum phases in a resonantly interacting boson-fermion mixture. PHYSICAL REVIEW LETTERS 2005; 94:230404. [PMID: 16090448 DOI: 10.1103/physrevlett.94.230404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2005] [Indexed: 05/03/2023]
Abstract
We consider a resonantly interacting boson-fermion mixture of 40K and 87Rb atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for 40K and 87Rb atoms, and 40K-87Rb molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.
Collapse
Affiliation(s)
- D B M Dickerscheid
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
| | | | | | | |
Collapse
|
74
|
Troyer M, Wiese UJ. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. PHYSICAL REVIEW LETTERS 2005; 94:170201. [PMID: 15904269 DOI: 10.1103/physrevlett.94.170201] [Citation(s) in RCA: 221] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2004] [Indexed: 05/02/2023]
Abstract
Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem" when applied to fermions--causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show that such a solution is almost certainly unattainable by proving that the sign problem is nondeterministic polynomial (NP) hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP in polynomial time.
Collapse
Affiliation(s)
- Matthias Troyer
- Theoretische Physik, ETH Zürich, CH-8093 Zürich, Switzerland
| | | |
Collapse
|
75
|
Fölling S, Gerbier F, Widera A, Mandel O, Gericke T, Bloch I. Spatial quantum noise interferometry in expanding ultracold atom clouds. Nature 2005; 434:481-4. [PMID: 15791249 DOI: 10.1038/nature03500] [Citation(s) in RCA: 446] [Impact Index Per Article: 23.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2005] [Accepted: 02/28/2005] [Indexed: 11/09/2022]
Abstract
In a pioneering experiment, Hanbury Brown and Twiss (HBT) demonstrated that noise correlations could be used to probe the properties of a (bosonic) particle source through quantum statistics; the effect relies on quantum interference between possible detection paths for two indistinguishable particles. HBT correlations--together with their fermionic counterparts--find numerous applications, ranging from quantum optics to nuclear and elementary particle physics. Spatial HBT interferometry has been suggested as a means to probe hidden order in strongly correlated phases of ultracold atoms. Here we report such a measurement on the Mott insulator phase of a rubidium Bose gas as it is released from an optical lattice trap. We show that strong periodic quantum correlations exist between density fluctuations in the expanding atom cloud. These spatial correlations reflect the underlying ordering in the lattice, and find a natural interpretation in terms of a multiple-wave HBT interference effect. The method should provide a useful tool for identifying complex quantum phases of ultracold bosonic and fermionic atoms.
Collapse
Affiliation(s)
- Simon Fölling
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, D-55099 Mainz, Germany
| | | | | | | | | | | |
Collapse
|
76
|
Köhl M, Moritz H, Stöferle T, Günter K, Esslinger T. Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions. PHYSICAL REVIEW LETTERS 2005; 94:080403. [PMID: 15783869 DOI: 10.1103/physrevlett.94.080403] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2004] [Indexed: 05/24/2023]
Abstract
We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.
Collapse
Affiliation(s)
- Michael Köhl
- Institute of Quantum Electronics, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland.
| | | | | | | | | |
Collapse
|
77
|
Byczuk K, Hofstetter W, Vollhardt D. Mott-Hubbard transition versus Anderson localization in correlated electron systems with disorder. PHYSICAL REVIEW LETTERS 2005; 94:056404. [PMID: 15783669 DOI: 10.1103/physrevlett.94.056404] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2004] [Indexed: 05/24/2023]
Abstract
The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged ("typical") local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.
Collapse
Affiliation(s)
- Krzysztof Byczuk
- Institute of Theoretical Physics, Warsaw University, ulica Hoza 69, PL-00-681 Warszawa, Poland
| | | | | |
Collapse
|
78
|
Feder DL. Vortex arrays in a rotating superfluid Fermi gas. PHYSICAL REVIEW LETTERS 2004; 93:200406. [PMID: 15600906 DOI: 10.1103/physrevlett.93.200406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2004] [Indexed: 05/24/2023]
Abstract
The behavior of a dilute two-component neutral superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the triangular vortex arrays become increasingly irregular, indicating a quantum melting transition.
Collapse
Affiliation(s)
- David L Feder
- Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada
| |
Collapse
|
79
|
Machida M, Yamada S, Ohashi Y, Matsumoto H. Novel superfluidity in a trapped gas of Fermi atoms with repulsive interaction loaded on an optical lattice. PHYSICAL REVIEW LETTERS 2004; 93:200402. [PMID: 15600902 DOI: 10.1103/physrevlett.93.200402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2004] [Indexed: 05/24/2023]
Abstract
We investigate a possibility of superfluidity in a trapped gas of Fermi atoms with a repulsive interaction in the presence of an optical lattice. Applying the exact diagonalization method to a one-dimensional Hubbard model including the trap potential, we find that, when the strength of the repulsive interaction exceeds a critical value, the binding energy of two Fermi atoms becomes negative below the half-filling case, indicating that an attractive interaction effectively works between Fermi atoms. In this case, a "Mott insulating core" appears in the center of the trap, where each site is occupied by one atom. The Cooper-pair correlation strongly develops between atoms in the left- and right-hand sides of this core.
Collapse
Affiliation(s)
- M Machida
- CCSE, Japan Atomic Energy Research Institute, 6-9-3 Higashi-Ueno, Taito-ku, Tokyo 110-0015, Japan
| | | | | | | |
Collapse
|
80
|
Cramer M, Eisert J, Illuminati F. Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices. PHYSICAL REVIEW LETTERS 2004; 93:190405. [PMID: 15600816 DOI: 10.1103/physrevlett.93.190405] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2003] [Indexed: 05/24/2023]
Abstract
We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.
Collapse
Affiliation(s)
- M Cramer
- Institut für Physik, Universität Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany
| | | | | |
Collapse
|
81
|
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
|
82
|
Pezzè L, Pitaevskii L, Smerzi A, Stringari S, Modugno G, de Mirandes E, Ferlaino F, Ott H, Roati G, Inguscio M. Insulating behavior of a trapped ideal Fermi gas. PHYSICAL REVIEW LETTERS 2004; 93:120401. [PMID: 15447234 DOI: 10.1103/physrevlett.93.120401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2004] [Indexed: 05/24/2023]
Abstract
We investigate theoretically and experimentally the center-of-mass motion of an ideal Fermi gas in a combined periodic and harmonic potential. We find a crossover from a conducting to an insulating regime as the Fermi energy moves from the first Bloch band into the band gap of the lattice. The conducting regime is characterized by an oscillation of the cloud about the potential minimum, while in the insulating case the center of mass remains on one side of the potential.
Collapse
Affiliation(s)
- L Pezzè
- Istituto Nazionale per la Fisica della Materia BEC-CRS and Dipartimento di Fisica, Università di Trento, I-38050 Povo, Italy
| | | | | | | | | | | | | | | | | | | |
Collapse
|
83
|
Illuminati F, Albus A. High-temperature atomic superfluidity in lattice Bose-Fermi mixtures. PHYSICAL REVIEW LETTERS 2004; 93:090406. [PMID: 15447082 DOI: 10.1103/physrevlett.93.090406] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2003] [Revised: 03/01/2004] [Indexed: 05/24/2023]
Abstract
We consider atomic Bose-Fermi mixtures in optical lattices and study the superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion interactions. We prove that the induced fermion-fermion coupling is always attractive if the boson-boson on-site interaction is repulsive, and predict the existence of an enhanced BEC-BCS crossover as the strength of the lattice potential is varied. We show that for direct on-site fermion-fermion repulsion, the induced attraction can give rise to superfluidity via s-wave pairing at striking variance with the case of pure systems of fermionic atoms with direct repulsive interactions.
Collapse
Affiliation(s)
- Fabrizio Illuminati
- Dipartimento di Fisica, Università di Salerno, INFM--UdR di Salerno, and INFN, Sezione di Napoli--Gruppo Collegato di Salerno, Via S. Allende, I-84081 Baronissi (SA), Italy
| | | |
Collapse
|
84
|
Büchler HP, Zoller P, Zwerger W. Spectroscopy of superfluid pairing in atomic fermi gases. PHYSICAL REVIEW LETTERS 2004; 93:080401. [PMID: 15447158 DOI: 10.1103/physrevlett.93.080401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2004] [Indexed: 05/24/2023]
Abstract
We study the dynamic structure factor for density and spin within the crossover from BCS superfluidity of atomic fermions to the Bose-Einstein condensation of molecules. Both structure factors are experimentally accessible via Bragg spectroscopy and allow for the identification of the pairing mechanism: the spin structure factor allows for the determination of the two particle gap, while the collective sound mode in the density structure reveals the superfluid state.
Collapse
Affiliation(s)
- H P Büchler
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Science, 6020 Innsbruck, Austria
| | | | | |
Collapse
|
85
|
Baranov MA, Dobrek Ł, Lewenstein M. Superfluidity of trapped dipolar fermi gases. PHYSICAL REVIEW LETTERS 2004; 92:250403. [PMID: 15244988 DOI: 10.1103/physrevlett.92.250403] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2003] [Indexed: 05/24/2023]
Abstract
We derive the phase diagram for ultracold trapped dipolar Fermi gases. Below the critical value of the dipole-dipole interaction energy, the BCS transition into a superfluid phase ceases to exist. The critical dipole strength is obtained as a function of the trap aspect ratio. Alternatively, for a given dipole strength there is a critical value of the trap anisotropy for the BCS state to appear. The order parameter exhibits a novel nonmonotonic behavior at the criticality.
Collapse
Affiliation(s)
- M A Baranov
- Institut für Theoretische Physik, Universität Hannover, D-30167 Hannover, Germany
| | | | | |
Collapse
|
86
|
Honerkamp C, Hofstetter W. Ultracold fermions and the SU(N) Hubbard model. PHYSICAL REVIEW LETTERS 2004; 92:170403. [PMID: 15169134 DOI: 10.1103/physrevlett.92.170403] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2003] [Indexed: 05/24/2023]
Abstract
We investigate the fermionic SU(N) Hubbard model on the two-dimensional square lattice for weak to moderate interactions using renormalization group and mean-field methods. For the repulsive case U>0 at half filling and small N the dominant tendency is towards breaking of the SU(N) symmetry. For N>6 staggered flux order takes over as the dominant instability, in agreement with the large-N limit. Away from half filling for N=3 two flavors remain half filled by cannibalizing the third flavor. For U<0 and odd N a full Fermi surface coexists with a superconductor. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.
Collapse
Affiliation(s)
- Carsten Honerkamp
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | |
Collapse
|
87
|
Hadzibabic Z, Gupta S, Stan CA, Schunck CH, Zwierlein MW, Dieckmann K, Ketterle W. Fiftyfold improvement in the number of quantum degenerate fermionic atoms. PHYSICAL REVIEW LETTERS 2003; 91:160401. [PMID: 14611386 DOI: 10.1103/physrevlett.91.160401] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2003] [Indexed: 05/24/2023]
Abstract
We have produced a quantum degenerate 6Li Fermi gas with up to 7 x 10(7) atoms, an improvement by a factor of 50 over all previous experiments with degenerate Fermi gases. This was achieved by sympathetic cooling with bosonic 23Na in the F=2, upper hyperfine ground state. We have also achieved Bose-Einstein condensation of F=2 sodium atoms by direct evaporation.
Collapse
Affiliation(s)
- Z Hadzibabic
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, Massachusetts 02139, USA
| | | | | | | | | | | | | |
Collapse
|
88
|
Rabl P, Daley AJ, Fedichev PO, Cirac JI, Zoller P. Defect-suppressed atomic crystals in an optical lattice. PHYSICAL REVIEW LETTERS 2003; 91:110403. [PMID: 14525407 DOI: 10.1103/physrevlett.91.110403] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2003] [Indexed: 05/24/2023]
Abstract
We present a coherent filtering scheme which dramatically reduces the site occupation number defects for atoms in an optical lattice by transferring a chosen number of atoms to a different internal state via adiabatic passage. With the addition of superlattices it is possible to engineer states with a specific number of atoms per site (atomic crystals), which are required for quantum computation and the realization of models from condensed matter physics, including doping and spatial patterns. The same techniques can be used to measure two-body spatial correlation functions.
Collapse
Affiliation(s)
- P Rabl
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | | | | | | | | |
Collapse
|
89
|
Duan LM, Demler E, Lukin MD. Controlling spin exchange interactions of ultracold atoms in optical lattices. PHYSICAL REVIEW LETTERS 2003; 91:090402. [PMID: 14525163 DOI: 10.1103/physrevlett.91.090402] [Citation(s) in RCA: 212] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2002] [Indexed: 05/24/2023]
Abstract
We describe a general technique that allows one to induce and control strong interaction between spin states of neighboring atoms in an optical lattice. We show that the properties of spin exchange interactions, such as magnitude, sign, and anisotropy, can be designed by adjusting the optical potentials. We illustrate how this technique can be used to efficiently "engineer" quantum spin systems with desired properties, for specific examples ranging from scalable quantum computation to probing a model with complex topological order that supports exotic anyonic excitations.
Collapse
Affiliation(s)
- L-M Duan
- Institute for Quantum Information, California Institute of Technology, mc 107-81, Pasadena, CA 91125, USA
| | | | | |
Collapse
|
90
|
|
91
|
Regal CA, Jin DS. Measurement of positive and negative scattering lengths in a Fermi gas of atoms. PHYSICAL REVIEW LETTERS 2003; 90:230404. [PMID: 12857243 DOI: 10.1103/physrevlett.90.230404] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2003] [Indexed: 05/24/2023]
Abstract
We report on progress toward realizing a predicted superfluid phase in a Fermi gas of atoms. We present measurements of both large positive and large negative scattering lengths in a quantum degenerate Fermi gas of atoms near a magnetic-field Feshbach resonance. We employ an rf spectroscopy technique to directly measure the mean-field interaction energy, which is proportional to the s-wave scattering length. Near the peak of the resonance we observe a saturation of the interaction energy; it is in this strongly interacting regime that superfluidity is predicted to occur. We have also observed anisotropic expansion of the gas, which has recently been suggested as a signature of superfluidity. However, we find that this can be attributed to a purely collisional effect.
Collapse
Affiliation(s)
- C A Regal
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, CO 80309-0440, USA
| | | |
Collapse
|
92
|
Idziaszek Z, Santos L, Baranov M, Lewenstein M. Laser cooling of trapped Fermi gases. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/1464-4266/5/2/379] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
93
|
|