1
|
Vogler A, Labouvie R, Barontini G, Eggert S, Guarrera V, Ott H. Dimensional phase transition from an array of 1D Luttinger liquids to a 3D Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2014; 113:215301. [PMID: 25479499 DOI: 10.1103/physrevlett.113.215301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2014] [Indexed: 06/04/2023]
Abstract
We study the thermodynamic properties of a 2D array of coupled one-dimensional Bose gases. The system is realized with ultracold bosonic atoms loaded in the potential tubes of a two-dimensional optical lattice. For negligible coupling strength, each tube is an independent weakly interacting 1D Bose gas featuring Tomonaga Luttinger liquid behavior. By decreasing the lattice depth, we increase the coupling strength between the 1D gases and allow for the phase transition into a 3D condensate. We extract the phase diagram for such a system and compare our results with theoretical predictions. Because of the high effective mass across the periodic potential and the increased 1D interaction strength, the phase transition is shifted to large positive values of the chemical potential. Our results are prototypical to a variety of low-dimensional systems, where the coupling between the subsystems is realized in a higher spatial dimension such as coupled spin chains in magnetic insulators.
Collapse
Affiliation(s)
- Andreas Vogler
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Ralf Labouvie
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Giovanni Barontini
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Sebastian Eggert
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Vera Guarrera
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Herwig Ott
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| |
Collapse
|
2
|
Bissbort U, Götze S, Li Y, Heinze J, Krauser JS, Weinberg M, Becker C, Sengstock K, Hofstetter W. Detecting the amplitude mode of strongly interacting lattice bosons by Bragg scattering. PHYSICAL REVIEW LETTERS 2011; 106:205303. [PMID: 21668240 DOI: 10.1103/physrevlett.106.205303] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2010] [Indexed: 05/30/2023]
Abstract
We report the first detection of the Higgs-type amplitude mode using Bragg spectroscopy in a strongly interacting condensate of ultracold atoms in an optical lattice. By the comparison of our experimental data with a spatially resolved, time-dependent bosonic Gutzwiller calculation, we obtain good quantitative agreement. This allows for a clear identification of the amplitude mode, showing that it can be detected with full momentum resolution by going beyond the linear response regime. A systematic shift of the sound and amplitude modes' resonance frequencies due to the finite Bragg beam intensity is observed.
Collapse
Affiliation(s)
- Ulf Bissbort
- Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, 60438 Frankfurt/Main, Germany
| | | | | | | | | | | | | | | | | |
Collapse
|
3
|
De Grandi C, Barankov RA, Polkovnikov A. Adiabatic nonlinear probes of one-dimensional bose gases. PHYSICAL REVIEW LETTERS 2008; 101:230402. [PMID: 19113528 DOI: 10.1103/physrevlett.101.230402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2008] [Indexed: 05/27/2023]
Abstract
We discuss two complimentary problems: adiabatic loading of one-dimensional bosons into an optical lattice and merging two one-dimensional Bose systems. Both problems can be mapped to the sine-Gordon model. This mapping allows us to find power-law scalings for the number of excitations with the ramping rate in the regime where the conventional linear response approach fails. We show that the exponent of this power law is sensitive to the interaction strength. In particular, the response is larger, or less adiabatic, for strongly (weakly) interacting bosons for the loading (merging) problem. Our results illustrate that in general the nonlinear response to slow relevant perturbations can be a powerful tool for characterizing properties of interacting systems.
Collapse
Affiliation(s)
- C De Grandi
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
| | | | | |
Collapse
|
4
|
Lal S, Laad MS. From frustrated insulators to correlated anisotropic metals: charge-ordering and quantum criticality in coupled chain systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:235213. [PMID: 21694304 DOI: 10.1088/0953-8984/20/23/235213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
By following the ideas of Emery and Noguera, a recent study revealed the dynamics of the charge sector of a one-dimensional quarter-filled electronic system with extended Hubbard interactions to be that of an effective pseudospin transverse-field Ising model (TFIM) in the strong-coupling limit. With the twin motivations of studying the co-existing charge and spin order found in strongly correlated chain systems and the effects of interchain couplings, we investigate the phase diagram of coupled effective (TFIM) systems. A bosonization and renormalization group (RG) analysis for a two-leg TFIM ladder yields a rich phase diagram showing Wigner/Peierls charge order and Néel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Kosterlitz-Thouless transitions are found to lead from the gapless phase to either of the charge-ordered phases. A detailed analysis is also carried out for the dimensional crossover physics when many such pseudospin systems are coupled to one another. Importantly, the analysis reveals the key role of critical quantum fluctuations in driving the strong dispersion in the transverse directions, as well as a T = 0 deconfinement transition. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled chain and ladder systems.
Collapse
Affiliation(s)
- Siddhartha Lal
- The Abdus Salam ICTP, Strada Costiera 11, Trieste 34014, Italy
| | | |
Collapse
|
5
|
Bergkvist S, Rosengren A, Saers R, Lundh E, Rehn M, Kastberg A. Transition from a two-dimensional superfluid to a one-dimensional Mott insulator. PHYSICAL REVIEW LETTERS 2007; 99:110401. [PMID: 17930414 DOI: 10.1103/physrevlett.99.110401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2007] [Revised: 06/21/2007] [Indexed: 05/25/2023]
Abstract
A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.
Collapse
Affiliation(s)
- Sara Bergkvist
- Department of Theoretical Physics, Royal Institute of Technology, AlbaNova, SE-106 91 Stockholm, Sweden
| | | | | | | | | | | |
Collapse
|
6
|
Benfatto L, Castellani C, Giamarchi T. Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex core energy. PHYSICAL REVIEW LETTERS 2007; 98:117008. [PMID: 17501083 DOI: 10.1103/physrevlett.98.117008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2006] [Indexed: 05/15/2023]
Abstract
In layered superconductors (SC) with small interlayer Josephson coupling vortex-antivortex phase fluctuations characteristic of quasi two-dimensional (2D) Kosterlitz-Thouless behavior are expected to be observable at some energy scale T(d). While in the 2D case T(d) is uniquely identified by the KT temperature T(KT) where the universal value of the superfluid density is reached, we show that in a generic anisotropic 3D system T(d) is controlled by the vortex-core energy, and can be significantly larger than the 2D scale T(KT). These results are discussed in relation to recent experiments in cuprates, which represent a typical experimental realization of layered anisotropic SC.
Collapse
Affiliation(s)
- L Benfatto
- Centro Studi e Ricerche Enrico Fermi, via Panisperna 89/A, I-00184, Rome, Italy
| | | | | |
Collapse
|
7
|
Gangardt DM, Pedri P, Santos L, Shlyapnikov GV. Mott-insulator phase of coupled one-dimensional atomic gases in a two-dimensional optical lattice. PHYSICAL REVIEW LETTERS 2006; 96:040403. [PMID: 16486794 DOI: 10.1103/physrevlett.96.040403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2004] [Indexed: 05/06/2023]
Abstract
We consider the 2D Mott-insulator state of a 2D array of coupled finite size 1D Bose gases. It is shown that the momentum distribution in the lattice plane is very sensitive to the interaction regime in the 1D tubes. In particular, we find that the disappearance of the interference pattern in time-of-flight experiments is a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes.
Collapse
Affiliation(s)
- D M Gangardt
- Laboratoire Physique Théorique et Modèles Statistiques, Université Paris Sud, Bâtiment 100, 91405 Orsay Cedex, France
| | | | | | | |
Collapse
|
8
|
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
|
9
|
Majumdar K, Fertig HA. Deconfinement and phase diagram of bosons in a linear optical lattice with a particle reservoir. PHYSICAL REVIEW LETTERS 2005; 94:220402. [PMID: 16090369 DOI: 10.1103/physrevlett.94.220402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2004] [Indexed: 05/03/2023]
Abstract
We investigate the zero-temperature phases of bosons in a one-dimensional optical lattice with an explicit tunnel coupling to a Bose-condensed particle reservoir. Renormalization group analysis of this system is shown to reveal three phases: one in which the linear system is fully phase locked to the reservoir; one in which Josephson vortices between the one-dimensional system and the particle reservoir deconfine due to quantum fluctuations, leading to a decoupled state in which the one-dimensional system is metallic; and one in which the one-dimensional system is in a Mott insulating state.
Collapse
|
10
|
Abstract
We report the observation of a one-dimensional (1D) Tonks-Girardeau (TG) gas of bosons moving freely in 1D. Although TG gas bosons are strongly interacting, they behave very much like noninteracting fermions. We enter the TG regime with cold rubidium-87 atoms by trapping them with a combination of two light traps. By changing the trap intensities, and hence the atomic interaction strength, the atoms can be made to act either like a Bose-Einstein condensate or like a TG gas. We measure the total 1D energy and the length of the gas. With no free parameters and over a wide range of coupling strengths, our data fit the exact solution for the ground state of a 1D Bose gas.
Collapse
Affiliation(s)
- Toshiya Kinoshita
- Physics Department, Pennsylvania State University, University Park, PA 16802, USA
| | | | | |
Collapse
|