DOCSLIB.ORG

Quantum Hydrodynamics for Supersolid Crystals and Quasicrystals

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Hydrodynamics for Supersolid Crystals and Quasicrystals Quantum hydrodynamics for supersolid crystals and quasicrystals The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Heinonen, Vili et al. "Quantum hydrodynamics for supersolid crystals and quasicrystals." Physical Review A 99, 6 (June 2019): 063621 © 2019 American Physical Society As Published http://dx.doi.org/10.1103/physreva.99.063621 Publisher American Physical Society (APS) Version Final published version Citable link https://hdl.handle.net/1721.1/123298 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. PHYSICAL REVIEW A 99, 063621 (2019) Quantum hydrodynamics for supersolid crystals and quasicrystals Vili Heinonen,1,* Keaton J. Burns,2 and Jörn Dunkel1,† 1Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA (Received 3 August 2018; published 24 June 2019) Supersolids are theoretically predicted quantum states that break the continuous rotational and translational symmetries of liquids while preserving superfluid transport properties. Over the last decade, much progress has been made in understanding and characterizing supersolid phases through numerical simulations for specific interaction potentials. The formulation of an analytically tractable framework for generic interactions still poses theoretical challenges. By going beyond the usually considered quadratic truncations, we derive a systematic higher-order generalization of the Gross-Pitaevskii mean-field model in conceptual similarity with the Swift- Hohenberg theory of pattern formation. We demonstrate the tractability of this broadly applicable approach by determining the ground-state phase diagram and the dispersion relations for the supersolid lattice vibrations in terms of the potential parameters. Our analytical predictions agree well with numerical results from direct hydrodynamic simulations and earlier quantum Monte Carlo studies. The underlying framework is universal and can be extended to anisotropic pair potentials with a complex Fourier-space structure. DOI: 10.1103/PhysRevA.99.063621 I. INTRODUCTION surface crystals [22], and active fluids [23–25]. Whereas higher PDEs are often postulated as effective phenomenologi- Supersolids are superfluids in which the local density spon- cal descriptions of systems with crystalline or quasicrystalline taneously arranges in a state of crystalline order. The existence order [26], it turns out that such equations can be derived of supersolid quantum states was proposed in the late 1960s directly within the established GP framework. The resulting by Andreev, Lifshitz, and Chester [1,2] but the realization in mean-field theory yields analytical predictions that agree with the laboratory has proven extremely difficult [3]. Recent ex- direct quantum hydrodynamic and recent qMC simulations perimental breakthroughs in the control of ultracold quantum [12,27] and specify the experimental conditions for realizing gases [4–7] suggest that it may indeed be possible to design periodic supersolids and coexistence phases, as well as super- quantum matter that combines dissipationless flow with the solid states exhibiting quasicrystalline symmetry (Sec. V). intrinsic stiffness of solids. Important theoretical insights into the expected properties of supersolids and experimental II. MEAN-FIELD THEORY candidate systems have come from numerical mean-field calculations and quantum Monte Carlo (qMC) simulations As in the classical GP theory [13,14], we assume that a for specific particle interaction potentials [8–12]. What is system of spinless particles can be described by a complex still lacking, however, is a general analytically tractable scalar field (t, x) and that quantum fluctuations about the framework that allows the simultaneous characterization of mean density n(t, x) =||2 are negligible. Considering an whole classes of potentials as well as the direct computation isotropic pairwise interaction potential u(|x − x |), the total of ground-state phase diagrams and dispersion relations for potential energy density is given by a spatial convolution supersolid lattice vibrations in terms of the relevant potential integral which can be expressed as a sum over Fourier-mode parameters. contributions ∝ uˆ|nˆ|2, where hats denote Fourier transforms To help overcome such conceptual and practical limita- (see Appendix A for a detailed derivation). If u is isotropic tions, we introduce here a generalization of the classical with finite moments, then its Fourier expansion can be written = ∞ 2 j =| | Gross-Pitaveskii (GP) mean-field model [13,14]bydrawing asu ˆ(k) j=0 g2 jk [28], where k k is the modulus guidance from the Swift-Hohenberg theory [15], which uses of the wave vector, yielding the potential energy density 1 ∞ − j ∇2 j ∇2 fourth-order partial differential equations (PDEs) to describe 2 n j=0( 1) g2 j ( ) n, with denoting the spatial Lapla- pattern formation in Rayleigh-Bénard convection. Our ap- cian. The constant Fourier coefficients g2 j encode the spatial proach is motivated by the successful application of higher- structure of the potential. Variation of the total energy func- than-second-order PDE models to describe classical solidifi- tional with respect to yields the generalized GP equation cation phenomena [16–18], electrostatic correlations in con- (Appendix A) centrated electrolytes and ionic liquids [19,20], nonuniform ⎡ ⎛ ⎞⎤ 2 ∞ FFLO superconductors [21], symmetry breaking in elastic h¯ ih¯∂ = ⎣− ∇2 + ⎝ (−1)jg (∇2 ) j||2⎠⎦. (1) t 2m 2 j j=0 *[email protected] The classical GP model, corresponding to repulsive point † [email protected] interactions u = g0δ(x − x ), is recovered for g0 > 0 and 2469-9926/2019/99(6)/063621(16) 063621-1 ©2019 American Physical Society HEINONEN, BURNS, AND DUNKEL PHYSICAL REVIEW A 99, 063621 (2019) g2 j = 0 otherwise. The authors of Ref. [29] studied the case the interaction parameter (Appendix C). In an infinite domain, g0, g2 > 0 and g2 j4 = 0, keeping partial information about the internal energy U[ρ] is completely parameterized by αu long-range (k → 0) hydrodynamic interactions by effectively and the average densityρ ¯ = ρdx/ dx. For the Rydberg- 2 −1 adding a surface energy term ∝|∇n| to the energy density. dressed BEC in Ref. [27], which has q0 = 1.87 μm , corre- However, as we see shortly, to describe supersolid states, the sponding to a hexagonal lattice spacing of 3.88 μm, one finds long-wavelength expansion has to be carried out at least to αu =−0.043 andρ ¯ ≈ 9.4 (Appendix G). order k4. To show this explicitly, it is convenient to express the III. GROUND-STATE STRUCTURE complex√ dynamics, (1), in real Madelung form [31]. Writing = n exp(iS) and defining the irrotational velocity field An advantageous aspect of the above framework is that ρ α , ρ v = (¯h/m)∇S,Eq.(1) can be recast as the quantum hydro- the ground-state structure of U[ ]inthe( u ¯ )-phase plane dynamic equations (Appendix C; see also [32]) can be explored both analytically and numerically in a fairly straightforward manner (Fig. 1). Standard linear stability anal- ysis (Appendix D3) for uniform constant-density solutions ∂t n =−∇·(nv), (2) predicts a symmetry-breaking transition at αu =−1 when ρ¯ 1/8 and m(∂t + v ·∇)v =−∇(δU/δn), (3) 1 − 16¯ρ 4 α = whenρ> ¯ 1/8, (7) with the effective potential energy U[n] to order O(k ), u 64¯ρ2 h¯2 |∇n|2 g g g indicated by the thin dashed line in Fig. 1(a). Refined analyt- = + 0 2 + 2 |∇ |2 + 4 ∇2 2 . U dx n n ( n) (4) ical estimates for the ground-state phases can be obtained by 8m n 2 2 2 ρ = ρ + φ · considering the Fourier ansatz ¯ j j exp (iq j x). +∇2 2 The first term is the kinetic quantum potential [31] and the The pattern forming operator (1 ) penalizes modes with 2 | | = kinetic energy is K = (m/2) dx nv . For nonleaky boundary q j 1, suggesting that single-wavelength expansions can conditions, Eqs. (2) and (3) conserve the total particle number yield useful approximations for the ground-state solutions. N = dx n and energy E[n, v] = K[n, v] + U[n]. The quan- Conceptually similar studies for classical phase field models tum hydrodynamics defined by Eqs. (2)–(4) is Hamiltonian [18] imply that 2D and 1D close-packing structures realizing in terms of the momentum density mnv = hn¯ ∇S, thereby hexagonal and stripe patterns are promising candidates. The differing, for example, from generalized Ginzburg-Landau one-mode approximation ansatz for a hexagonal lattice reads theories for nonuniform FFLO superconductors [21] and 3 finite-temperature hydrodynamic approaches [1,33–35]. ρ = ρ¯ + φ [exp (iq · x) + c.c.], (8) , ≡ 0 j Local minima of E[n v] have zero flow, v 0, and hence j=1 the corresponding density fields must minimize U[n]. As- · suming short-range repulsion g0 > 0, we see that uniform where the lattice vectors q j form the “first star” with qi = 2 = − 2/ constant-density solutions minimize U[n] when g2 0 and q j q ,ifi j and q 2 otherwise (c.c. denotes complex g = 0 (Appendix F); this case was studied in Ref. [29]. If, conjugate terms). Similarly, the stripe phase is defined by 4 ρ = ρ + φ + however, we consider the more general class of pair inter- ¯ [ 0 exp (iqx1) c.c.]. These trial functions have to φ action potentials with g2 ≷ 0, then short-wavelength stabil- be minimized with respect to the amplitudes 0 and the 4 ity at order k requires that g4 > 0. This situation arises, magnitudes q of the reciprocal lattice vectors, which can be for example, for the two-dimensional (2D) Rydberg-dressed done analytically (Appendix D4). Our analytical calculations Bose-Einstein condensate (BEC) studied in Ref. [27], which predict four distinct pure ground-state types, which can be 2 2 2 has g0 = 0.189¯h /m, g2 =−0.113 (¯h /m) μm , and g4 = identified as uniform (U), supersolid (SS), normal solid– 2 4 / 0.016 (¯h /m) μm (Appendix G).
Load more

Recommended publications
  • A New Framework for Understanding Supersolidity in 4He
    A New Framework for Understanding Supersolidity in 4He David S. Weiss Physics Department, The Pennsylvania State University, University Park, PA 16802, USA Recent experiments have detected 4He supersolidity, but the observed transition is rather unusual. In this paper, we describe a supersolid as a normal lattice suffused by a Bose gas. With this approach, we can explain the central aspects of the recent observations as well as previous experimental results. We conclude that detailed balance is violated in part of the 4He phase diagram, so that even in steady state contact with a thermal reservoir, the material is not in equilibrium. (submitted June 28, 2004) 67.80-s 1 The possibility that quantum solids exhibit supersolidity has been debated for 45 years1,2. The experimental search for the phenomenon culminated in the recent observations of Kim and Chan that the moment of inertia of solid 4He decreases at low temperature, both in porous media3 and in bulk4. These experiments strongly suggest a quantum phase transition to a supersolid state, especially because the effect is absent in solid 3He or when the annulus of their sample is blocked. However, the behavior of the transition is unexpected. It is gradual as a function of temperature, instead of sharp. The non-classical inertial effect starts to disappear at a very low critical velocity. When the supersolid is slightly doped with 3He, the reduction in inertia decreases, but the apparent transition temperature actually increases. In this paper, we present a new framework for understanding supersolidity in 4He. While consistent with earlier theoretical conceptions5,6, our framework allows for an interpretation of all available experimental data and for prediction of new phenomena.
    [Show full text]
  • Density Fluctuations Across the Superfluid-Supersolid Phase Transition in a Dipolar Quantum Gas
    PHYSICAL REVIEW X 11, 011037 (2021) Density Fluctuations across the Superfluid-Supersolid Phase Transition in a Dipolar Quantum Gas J. Hertkorn ,1,* J.-N. Schmidt,1,* F. Böttcher ,1 M. Guo,1 M. Schmidt,1 K. S. H. Ng,1 S. D. Graham,1 † H. P. Büchler,2 T. Langen ,1 M. Zwierlein,3 and T. Pfau1, 15. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany 2Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany 3MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 15 October 2020; accepted 8 January 2021; published 23 February 2021) Phase transitions share the universal feature of enhanced fluctuations near the transition point. Here, we show that density fluctuations reveal how a Bose-Einstein condensate of dipolar atoms spontaneously breaks its translation symmetry and enters the supersolid state of matter—a phase that combines superfluidity with crystalline order. We report on the first direct in situ measurement of density fluctuations across the superfluid-supersolid phase transition. This measurement allows us to introduce a general and straightforward way to extract the static structure factor, estimate the spectrum of elementary excitations, and image the dominant fluctuation patterns. We observe a strong response in the static structure factor and infer a distinct roton minimum in the dispersion relation. Furthermore, we show that the characteristic fluctuations correspond to elementary excitations such as the roton modes, which are theoretically predicted to be dominant at the quantum critical point, and that the supersolid state supports both superfluid as well as crystal phonons.
    [Show full text]
  • Sounds of a Supersolid A
    NEWS & VIEWS RESEARCH hypothesis came from extensive population humans, implying possible mosquito exposure long-distance spread of insecticide-resistant time-series analysis from that earlier study5, to malaria parasites and the potential to spread mosquitoes, worsening an already dire situ- which showed beyond reasonable doubt that infection over great distances. ation, given the current spread of insecticide a mosquito vector species called Anopheles However, the authors failed to detect resistance in mosquito populations. This would coluzzii persists locally in the dry season in parasite infections in their aerially sampled be a matter of great concern because insecticides as-yet-undiscovered places. However, the malaria vectors, a result that they assert is to be are the best means of malaria control currently data were not consistent with this outcome for expected given the small sample size and the low available8. However, long-distance migration other malaria vectors in the study area — the parasite-infection rates typical of populations of could facilitate the desirable spread of mosqui- species Anopheles gambiae and Anopheles ara- malaria vectors. A problem with this argument toes for gene-based methods of malaria-vector biensis — leaving wind-powered long-distance is that the typical infection rates they mention control. One thing is certain, Huestis and col- migration as the only remaining possibility to are based on one specific mosquito body part leagues have permanently transformed our explain the data5. (salivary glands), rather than the unknown but understanding of African malaria vectors and Both modelling6 and genetic studies7 undoubtedly much higher infection rates that what it will take to conquer malaria.
    [Show full text]
  • Defects in Novel Superfluids: Supersolid Helium and Cold Gases
    DEFECTS IN NOVEL SUPERFLUIDS: SUPERSOLID HELIUM AND COLD GASES By KINJAL DASBISWAS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012 ⃝c 2012 Kinjal Dasbiswas 2 To my parents, both physicians, who have always supported and nurtured my ambitions to be a physicist 3 ACKNOWLEDGMENTS I am grateful to my adviser, Professor Alan T. Dorsey, for the pivotal role he has played as a mentor in my PhD He introduced me to many topics in condensed matter physics, particularly the novel topic of supersolid helium. I have learned a number of techniques through working with him, but equally importantly, he has taught me to choose my problems carefully and to present my results in a coherent manner. I would like to thank Professors Peter J. Hirschfeld, Amlan Biswas, H.-P. Cheng and Susan B. Sinnott for useful discussions and for serving on my committee. I would also like to acknowledge Professors Y. -S. Lee and Pradeep Kumar for their valuable inputs about the supersolid problem, Professors D. L. Maslov, Richard Woodard, S. L. Shabanov, and K. A. Muttalib for their inspiring teaching, and the Max Planck Institute in Dresden for giving me the opportunity to attend a summer school on Bose-Einstein condensates. I am indebted to some of my graduate student colleagues for stimulating discussions and for ensuring a collegial environment in the department. I am grateful to K. Nichola and P. Marlin for their generous assistance with the administrative aspects of my graduate program.
    [Show full text]
  • Superfluid Density in a Two-Dimensional Model of Supersolid
    Eur. Phys. J. B 78, 439–447 (2010) DOI: 10.1140/epjb/e2010-10176-y THE EUROPEAN PHYSICAL JOURNAL B Regular Article Superfluid density in a two-dimensional model of supersolid N. Sep´ulveda1,2,C.Josserand2,a, and S. Rica3,4 1 Laboratoire de Physique Statistique, Ecole´ Normale Sup´erieure, UPMC Paris 06, Universit´eParisDiderot,CNRS, 24 rue Lhomond, 75005 Paris, France 2 Institut Jean Le Rond D’Alembert, UMR 7190 CNRS-UPMC, 4 place Jussieu, 75005 Paris, France 3 Facultad de Ingenier´ıa y Ciencias, Universidad Adolfo Ib´a˜nez, Avda. Diagonal las Torres 2640, Pe˜nalol´en, Santiago, Chile 4 INLN, CNRS-UNSA, 1361 route des Lucioles, 06560 Valbonne, France Received 28 February 2010 / Received in final form 27 October 2010 Published online 6 December 2010 – c EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2010 Abstract. We study in 2-dimensions the superfluid density of periodically modulated states in the frame- work of the mean-field Gross-Pitaevskiˇı model of a quantum solid. We obtain a full agreement for the su- perfluid fraction between a semi-theoretical approach and direct numerical simulations. As in 1-dimension, the superfluid density decreases exponentially with the amplitude of the particle interaction. We discuss the case when defects are present in this modulated structure. In the case of isolated defects (e.g. dislocations) the superfluid density only shows small changes. Finally, we report an increase of the superfluid fraction up to 50% in the case of extended macroscopical defects. We show also that this excess of superfluid fraction depends on the length of the complex network of grain boundaries in the system.
    [Show full text]
  • Supersolid State of Matter Nikolai Prokof 'Ev University of Massachusetts - Amherst, [email protected]
    University of Massachusetts Amherst ScholarWorks@UMass Amherst Physics Department Faculty Publication Series Physics 2005 Supersolid State of Matter Nikolai Prokof 'ev University of Massachusetts - Amherst, [email protected] Boris Svistunov University of Massachusetts - Amherst, [email protected] Follow this and additional works at: https://scholarworks.umass.edu/physics_faculty_pubs Part of the Physical Sciences and Mathematics Commons Recommended Citation Prokof'ev, Nikolai and Svistunov, Boris, "Supersolid State of Matter" (2005). Physics Review Letters. 1175. Retrieved from https://scholarworks.umass.edu/physics_faculty_pubs/1175 This Article is brought to you for free and open access by the Physics at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Physics Department Faculty Publication Series by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. On the Supersolid State of Matter Nikolay Prokof’ev and Boris Svistunov Department of Physics, University of Massachusetts, Amherst, MA 01003 and Russian Research Center “Kurchatov Institute”, 123182 Moscow We prove that the necessary condition for a solid to be also a superfluid is to have zero-point vacancies, or interstitial atoms, or both, as an integral part of the ground state. As a consequence, superfluidity is not possible in commensurate solids which break continuous translation symmetry. We discuss recent experiment by Kim and Chan [Nature, 427, 225 (2004)] in the context of this theorem, question its bulk supersolid interpretation, and offer an alternative explanation in terms of superfluid helium interfaces. PACS numbers: 67.40.-w, 67.80.-s, 05.30.-d Recent discovery by Kim and Chan [1, 2] that solid 4He theorem.
    [Show full text]
  • Does the Superfluid Part of a Supersolid, Superfluid, Or
    Annales de la Fondation Louis de Broglie, Volume 34 no 1, 2009 89 Does the superfluid part of a supersolid, superfluid, or superconducting body have, of itself, “inertia?” G. Stephens 24 Guest Road, Cambridge, CB1 2AL, United Kingdom email: g stephens @hotmail.com ABSTRACT. The contention discussed here, is that one might be able to get around the puzzle contained in the results of Kim and Chan:— That a quantity of inertial mass is effectively lost, (a so called non-classical-rotational- inertia NCRI,) but that being a “supersolid” there is no path for the normal fraction to slip past the 1 – 2 % supersolid fraction, which (it is supposed) remains stationary within the annulus. As a solution we argue that the effective loss of inertial mass might be a real loss of inertial mass– that it might be intrinsic to a supersolid or superfluid “pool,” (a portion which has gone supersolid or superfluid.) In this way the puzzle would be resolved because the normal part and the supersolid part do not need to slip past each other in order to produce the experimental results. This Essai explores some consequences of a previous writing [1]. In that writing it was argued one could not define, (either in principle or in practice,) the inertial frame of the superfluid part of a superfluid or superconductor. An inertial frame has to be based on something in the real world— i.e., matter or an experiment. Nothing exists “in-itself,” —only in rela- tion to something else [2]. The question we will ask here is; does, in the context described, an inertial frame exist? The answer will be “yes” for the normal and quasi-normal part, “no” for the superfluid part.
    [Show full text]
  • Attractive Hubbard Model As an SO(3) System of Competing Phases: Supersolid Order and Its Thermal Melting
    PHYSICAL REVIEW RESEARCH 2, 023304 (2020) Attractive Hubbard model as an SO(3) system of competing phases: Supersolid order and its thermal melting Madhuparna Karmakar 1,* and R. Ganesh 2,† 1Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India 2The Institute of Mathematical Sciences, HBNI, CIT Campus, Chennai 600113, India (Received 23 February 2020; revised manuscript received 11 April 2020; accepted 8 May 2020; published 8 June 2020) Competition between superconductivity and charge order is a recurring theme in contemporary condensed matter physics. This is quintessentially captured in the attractive Hubbard model, a simple theoretical model where the competition can be directly tuned. In previous studies by the current authors, it has been suggested that the Hubbard model maps to an SO(3) nonlinear sigma model, where the phase competition becomes manifest. In this article, we rigorously demonstrate this mapping and use it to study thermal disordering of a supersolid. Starting with the attractive Hubbard model in the presence of an orbital field, we take the limit of strong coupling where a pseudospin description emerges. The in-plane pseudospin components represent superconducting pairing while the out-of-plane component encodes charge density wave order. We obtain an effective spin-1/2 Hamiltonian with ferromagnetic in-plane couplings and antiferromagnetic z-z couplings. In addition, the orbital field gives rise to a textured Dzyaloshinskii-Moriya interaction that has the same periodicity as the magnetic unit cell. In order to examine the nature of ordering in this spin model, we consider it in the classical limit. We assume slowly varying fields, leading to the SO(3) nonlinear sigma model description.
    [Show full text]
  • Supersolids of Hardcore–Bosons on a Triangular Lattice
    Proc. Natl. Conf. Theor. Phys. 35 (2010), pp. 175-182 SUPERSOLIDS OF HARDCORE{BOSONS ON A TRIANGULAR LATTICE PHAM THI THANH NGA Water Resources University, 175 Tay Son, Hanoi NGUYEN TOAN THANG Institute of Physics, VAST, 10 Dao Tan, Hanoi Abstract. We study the boson model on a triangular lattice interacting only via on-site hardcore repulsion by mapping to a system of spins (S = 1=2). We investigate the supersolid phase of the systems which is a state matter displaying both diagonal long- range (solid) order as well as off-diagonal long-range (superfluidity) by utilizing a semionic representation for the spin-XXZ model. We show that the supersolid order is stable in the mean-field theory for a broad region of parameters. The inclusion of spin wave corrections modifies this picture, but the supersolid phase is still quite robust on the triangular lattices. I. INTRODUCTION Supersolidity where superfluid and crystalline orders coexist was firstly theoretically conjectured by Andreev and Lifshitz in 1969 [1] and then was developed by Leggett [2] and Chester [3]. A supersolids phase is a state of matter exhibiting simultaneously off - diagonal (ODLRO) and diagonal long range order (DLRO). In 2004 Kim and Chan [4,5] proved the existence of the supersolid state in solid He4 at temperatures below T = 0.2 K by measuring a tine superflow in a torsional oscillation experiment. This landmark experiment has attracted a lot of interest in the supersolid state and subsequently many new theories were proposed [6-11]. However the true nature of the supersolids state is still unclear.
    [Show full text]
  • Is There a Bose Condensate in Supersolid Helium?
    Is there a Bose condensate in Supersolid helium? Collaborators • M. A. Adams (ISIS) • O. Kirichek (ISIS) • R. B. E. Down (ISIS) “Measurement of the kinetic energy and lattice constant • in hcp solid helium at temperatures 0.07-0.4 K” M. A. Adams, J. Mayers, O. Kirichek and R.B.E. Down • Phys. Rev. Lett. 98 085301 Feb 2007 Experimental evidence E. L. Andronikashvili, (1946) E. Kim and M. H. W. Chan Science 305 2004 1 ρS 0 Liquid He4 is 100% superfluid at T=0 Solid He4 is ~2% superfluid at T=0 Bose –Einstein Condensation Momentum distribution 2 (p )n= s∫ ( d ∫ , r Ψ ) s exp(i p d r . )r r=r1 s=r2..rN Fractional weight of condensate peak = f (a)Ψ(r,s) is a non zero function of r over length scales ~ L (b) Ψ(r,s) has phase correlations over distances ~L Ground state of liquid 4He Ψ(r,s) Non-zero over length scales ~L 1 Phase correlations over distances ~L Ψ(r,s) is connected over macroscopic 2 length scales between phase coherent points e.g. 1 and 2 Single valued wave function nh v(r ). d r= ∫ m Mass flow must be quantised over macroscopic length scales Loops in Ψ(r,s) over macroscopic (cm) length scales Normal viscous processes cannot occur → zero viscosity at T=0 Ψ(r,s) in solid Can still be connected over macro length scales if enough vacancies are present Solid can “flow” if (a) Flow conserves mass density (b) wave function is connected At least ~10% vacancies →~10% condensate fraction If BEC of atoms is the origin of supersolidity, reducing T should • Decrease kinetic energy.
    [Show full text]
  • Is the Supersolid Superfluid?
    Available at: http://publications.ictp.it IC/2008/062 United Nations Educational, Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS IS THE SUPERSOLID SUPERFLUID? Dimitar I. Pushkarov1 Institute of Solid-State Physics, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria2, Fatih University, Istanbul 3400, Turkey and The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. Abstract An analysis of previous theories of superfluidity of quantum solids is presented in relation to the nonclassical rotational moment of inertia (NCRM) found first in Kim and Chan experiments. A theory of supersolidity is proposed based on the presence of an additional conservation law. It is shown that the additional entropy or mass fluxes depend on the quasiparticle dispersion relation and vanish in the effective mass approximation. This implies that at low temperatures when the parabolic part of the dispersion relation predominates the supersolid properties should be less expressed. MIRAMARE – TRIESTE August 2008 1 [email protected] 2 On leave of absence from. Introduction The experiments of Kim and Chan [1] breathed new life into the old idea of possible superflu- idity of solids. A quantum solid, possessing superfluid properties, has been called a supersolid. Originally a supersolid should be a crystalline body where a nondissipative mass current can occur. This should correspond to the superfluid state of liquid helium (helium-II) observed by Kapitsa, and explained theoretically first by Landau. The superfluidity is now well studied and a number of effects has been found, predicted and explained. Between them is the change of the rotational moment due to the fact that the superfluid fraction cannot be involved into rotation at velocities less than the critical one.
    [Show full text]
  • Arxiv:1005.2403V4 [Cond-Mat.Quant-Gas] 21 Sep 2010 Principle Numerical Simulations That Interaction Poten- Gorithm [12, 13]
    Supersolid droplet crystal in a dipole-blockaded gas F. Cinti,1 P. Jain,1 M. Boninsegni,1 A. Micheli,2 P. Zoller,2 and G. Pupillo2 1Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1 2IQOQI and Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria. (Dated: October 31, 2018) A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential \softened" at short distances. Using exact numerical techniques, we study the low temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighbouring droplets. PACS numbers: 67.80.K-, 32.80.Rm, 67.85.Hj, 67.85.Jk, 67.85.-d, 02.70.Ss The search for novel phases of matter drives much of densates (droplets) organize into a single, global conden- the current research in condensed matter physics. Of sate. Specifically, we consider the following two-body particular interest are phases simultaneously displaying potential: different types of order. A chief example, of great cur- 8 3 rent interest, is the so-called supersolid, namely a phase < D=a if r ≤ a featuring crystalline order, and also capable of sustaining v(r) = ; (1) dissipation-less flow. Attempts to observe experimentally : D=r3 if r > a a supersolid phase of matter, primarily in a crystal of solid helium, have spanned four decades since early the- D being the characteristic strength of the interaction.
    [Show full text]