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Hertkorn J, Böttcher F, Guo M, Schmidt JN, Langen T, Büchler HP, Pfau T. Fate of the Amplitude Mode in a Trapped Dipolar Supersolid. PHYSICAL REVIEW LETTERS 2019; 123:193002. [PMID: 31765213 DOI: 10.1103/physrevlett.123.193002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2019] [Revised: 09/13/2019] [Indexed: 06/10/2023]
Abstract
We theoretically investigate the spectrum of elementary excitations of a trapped dipolar quantum gas across the BEC-supersolid phase transition. Our calculations reveal the existence of distinct Higgs amplitude and Nambu-Goldstone modes that emerge from the softening roton modes of the dipolar BEC at the phase transition point. On the supersolid side of the transition, the energy of the Higgs amplitude mode increases rapidly, leading to a strong coupling to higher-lying modes. Our Letter highlights how the symmetry-breaking nature of the supersolid state translates to finite-size systems.
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Affiliation(s)
- J Hertkorn
- 5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universitt Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - F Böttcher
- 5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universitt Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - M Guo
- 5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universitt Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - J N Schmidt
- 5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universitt Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - T Langen
- 5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universitt Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - H P Büchler
- Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, Universitt Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - T Pfau
- 5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universitt Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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Gazit S, Podolsky D, Nonne H, Auerbach A, Arovas DP. Collective Modes in a Quantum Solid. PHYSICAL REVIEW LETTERS 2016; 117:085302. [PMID: 27588863 DOI: 10.1103/physrevlett.117.085302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2015] [Indexed: 06/06/2023]
Abstract
We provide a theoretical explanation for the optical modes observed in inelastic neutron scattering on the bcc solid phase of helium 4 [T. Markovich et al., Phys. Rev. Lett. 88, 195301 (2002)]. We argue that these excitations are amplitude (Higgs) modes associated with fluctuations of the crystal order parameter within the unit cell. We present an analysis of the modes based on an effective Ginzburg-Landau model, classify them according to their symmetry properties, and compute their signature in inelastic neutron scattering experiments. In addition, we calculate the dynamical structure factor by means of an ab intio quantum Monte Carlo simulation and find a finite frequency excitation at zero relative momentum.
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Affiliation(s)
- Snir Gazit
- Department of Physics, University of California, Berkeley, California 94720, USA
- Physics Department, Technion, 32000 Haifa, Israel
| | | | | | | | - Daniel P Arovas
- Department of Physics, University of California at San Diego, La Jolla, California 92093, USA
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Cea T, Castellani C, Seibold G, Benfatto L. Nonrelativistic Dynamics of the Amplitude (Higgs) Mode in Superconductors. PHYSICAL REVIEW LETTERS 2015; 115:157002. [PMID: 26550746 DOI: 10.1103/physrevlett.115.157002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Indexed: 06/05/2023]
Abstract
Despite the formal analogy with the Higgs particle, the amplitude fluctuations of the order parameter in weakly coupled superconductors do not identify a real mode with a Lorentz-invariant dynamics. Indeed, its resonance occurs at 2Δ_{0}, which coincides with the threshold 2E_{gap} for quasiparticle excitations that spoil any relativistic dynamics. Here we investigate the fate of the Higgs mode in the unconventional case where 2E_{gap} becomes larger than 2Δ_{0}, as due to strong coupling or strong disorder. We show that also in this situation, the amplitude fluctuations never identify a real mode at 2Δ_{0}, since such a "bosonic" limit is always reached via strong mixing with the phase fluctuations, which dominate the low-energy part of the spectrum. Our results have direct implications for the interpretation of the subgap optical absorption in disordered superconductors.
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Affiliation(s)
- T Cea
- ISC-CNR and Department of Physics, "Sapienza" University of Rome, P.le A. Moro 5, 00185 Rome, Italy
| | - C Castellani
- ISC-CNR and Department of Physics, "Sapienza" University of Rome, P.le A. Moro 5, 00185 Rome, Italy
| | - G Seibold
- Institut Für Physik, BTU Cottbus-Senftenberg, P.O. Box 101344, 03013 Cottbus, Germany
| | - L Benfatto
- ISC-CNR and Department of Physics, "Sapienza" University of Rome, P.le A. Moro 5, 00185 Rome, Italy
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4
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Kobayashi M, Nitta M. Interpolating relativistic and nonrelativistic Nambu-Goldstone and Higgs modes. Int J Clin Exp Med 2015. [DOI: 10.1103/physrevd.92.045028] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chen K, Liu L, Deng Y, Pollet L, Prokof'ev N. Universal properties of the Higgs resonance in (2+1)-dimensional U(1) critical systems. PHYSICAL REVIEW LETTERS 2013; 110:170403. [PMID: 23679688 DOI: 10.1103/physrevlett.110.170403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2013] [Revised: 02/07/2013] [Indexed: 06/02/2023]
Abstract
We present spectral functions for the magnitude squared of the order parameter in the scaling limit of the two-dimensional superfluid to Mott insulator quantum phase transition at constant density, which has emergent particle-hole symmetry and Lorentz invariance. The universal functions for the superfluid, Mott insulator, and normal liquid phases reveal a low-frequency resonance which is relatively sharp and is followed by a damped oscillation (in the first two phases only) before saturating to the quantum critical plateau. The counterintuitive resonance feature in the insulating and normal phases calls for deeper understanding of collective modes in the strongly coupled (2+1)-dimensional relativistic field theory. Our results are derived from analytically continued correlation functions obtained from path-integral Monte Carlo simulations of the Bose-Hubbard model.
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Affiliation(s)
- Kun Chen
- National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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Endres M, Fukuhara T, Pekker D, Cheneau M, Schauβ P, Gross C, Demler E, Kuhr S, Bloch I. The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition. Nature 2012; 487:454-8. [DOI: 10.1038/nature11255] [Citation(s) in RCA: 241] [Impact Index Per Article: 20.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2012] [Accepted: 05/16/2012] [Indexed: 11/10/2022]
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Pollet L, Prokof'ev N. Higgs mode in a two-dimensional superfluid. PHYSICAL REVIEW LETTERS 2012; 109:010401. [PMID: 23031091 DOI: 10.1103/physrevlett.109.010401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2012] [Indexed: 06/01/2023]
Abstract
We present solid evidence for the existence of a well-defined Higgs amplitude mode in two-dimensional relativistic field theories based on analytically continued results from quantum Monte Carlo simulations of the Bose-Hubbard model in the vicinity of the superfluid-Mott insulator quantum critical point, featuring emergent particle-hole symmetry and Lorentz invariance. The Higgs boson, seen as a well-defined low-frequency resonance in the spectral density, is quickly pushed to high energies in the superfluid phase and disappears by merging with the broad secondary peak at the characteristic interaction scale. Simulations of a trapped system of ultracold (87)Rb atoms demonstrate that the low-frequency resonance is lost for typical experimental parameters, while the characteristic frequency for the onset of a strong response is preserved.
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Affiliation(s)
- L Pollet
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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Huber SD, Lindner NH. Topological transitions for lattice bosons in a magnetic field. Proc Natl Acad Sci U S A 2011; 108:19925-30. [PMID: 22109548 PMCID: PMC3250117 DOI: 10.1073/pnas.1110813108] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The Hall response provides an important characterization of strongly correlated phases of matter. We study the Hall conductivity of interacting bosons on a lattice subjected to a magnetic field. We show that for any density or interaction strength, the Hall conductivity is characterized by an integer. We find that the phase diagram is intersected by topological transitions between different values of this integer. These transitions lead to surprising effects, including sign reversal of the Hall conductivity and extensive regions in the phase diagram where it acquires a negative sign, which implies that flux flow is reversed in these regions--vortices there flow upstream. Our findings have immediate applications to a wide range of phenomena in condensed matter physics, which are effectively described in terms of lattice bosons.
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Affiliation(s)
- Sebastian D. Huber
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Netanel H. Lindner
- Institute for Quantum Information, California Institute of Technology, Pasadena, CA 91125; and
- Department of Physics, California Institute of Technology, Pasadena, CA 91125
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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.
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Affiliation(s)
- Ulf Bissbort
- Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, 60438 Frankfurt/Main, Germany
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Silberberg Y, Lahini Y, Bromberg Y, Small E, Morandotti R. Universal correlations in a nonlinear periodic 1D system. PHYSICAL REVIEW LETTERS 2009; 102:233904. [PMID: 19658937 DOI: 10.1103/physrevlett.102.233904] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2008] [Indexed: 05/28/2023]
Abstract
When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when the system is nonlinear, correlations are spontaneously formed. We find that for strong nonlinearities, the intensity histograms approach a narrow Gaussian distributed around their mean and phase correlations are formed between neighboring sites. Sites tend to be out of phase for a positive nonlinearity and in phase for a negative one. Most impressively, the field correlation takes a universal shape independent of parameters. These results are relevant to bosonic gas in 1D optical lattices as well as to nonlinear optical waveguide arrays, which are used to demonstrate experimentally some of the features of this equilibrium state.
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Affiliation(s)
- Yaron Silberberg
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
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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]
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