簡易檢索 / 詳目顯示

研究生: 李威漢
Li, Wei Han
論文名稱: 雷德堡裝束之費米氣體的有序密度結構
Ordered Density Structure of Repulsive Rydberg-dressed Fermionic Atoms
指導教授: 王道維
Wang, Daw Wei
口試委員: 郭西川
Guo, Shih Chuan
牟中瑜
Mou, Chung Yu
學位類別: 碩士
Master
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2015
畢業學年度: 103
語文別: 英文
論文頁數: 46
中文關鍵詞: 雷德堡裝束費米子量子相轉變有序密度波
外文關鍵詞: Rydberg-dressed, Fermion, Quantum phase transition, density wave order
相關次數: 點閱:3下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 此文章研究雷德保裝束(Rydberg-dressed)費米氣體在三維自由空間中的量子相轉變現象。由隨機相位近(random phase approximation)計算得知,若原子的雷德堡阻絕長度(Rydberg blockade length)夠長,或者系統密度夠高,微弱的交互作用即可使均勻的費米液體系統中出現有序密度波。我們的平均場理論(mean-field theory)結果顯示,系統經由一級相轉變過程形成具有體心立方晶格結構的有序密度波,並且其相轉變溫度約為費米能階的十分之一。再者,此研究涉及的理論徹底不同於已知的藍道費米液體理論,意即此有序密度結構非藍道費米液體理論所能預期。


    We study quantum phase transitions of a repulsive Rydberg-dressed Fermi gas
    in 3D free space. Under random phase approximation(RPA), it is shown that a
    density wave order emerges from a Fermi liquid within week interaction and long
    blockade length (or high density) regime. Our mean-field theory results show that,
    this density wave order forms BCC structure through a first order phase transition,
    and the transition temperature is about one-tenth of the Fermi energy. Further-
    more, we argue that the theory associated with this novel phenomenon of repulsive
    Fermionic system differs completely from the well known Landau Fermi liquid
    theory.

    Abstract i 1 Introduction 1 2 The Effective Interaction 4 3 The Collective Mode 7 3.1 Random phase approximation and linear response theory 7 3.2 The density wave 10 4 The Mean-Field Theory 13 4.1 The density wave 13 4.2 Local density approximation (LDA) 18 5 Fermi Surface Distortion 22 6 Summery 28 Appendices 29 Appendix A Zero order polarization 29 Appendix B Collective mode with Hubbard approximation and in lower dimension system 31 Appendix C Fock term of the effective interaction for density wave ansatz 33 Appendix D Mean field matrixes of BCC density wave 35 Appendix E Local density approximation (LDA) for a trapped Rydberg-dressed cloud 38 Reference 43

    [1] D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Cote and M. D. Lukin Fast
    quantum gates for neutral atoms. Phys. Rev. Lett. 85, 2208-2211 (2000)
    [2] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and
    P. Zoller. Dipole blockade and quantum information processing in mesoscopic
    atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001)
    [3] E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker
    and M. Saffman, Observation of Rydberg blockade between two atoms, Nature
    Physics 5, 110 (2009)
    [4] A. Ga¨etan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P.
    Pillet, A. Browaeys and P. Grangier, Observation of collective excitation of two
    individual atoms in the Rydberg blockade regime, Nature Physics 5, 115 - 118
    (2009)
    [5] T. A. Fulton, and G. J. Dolan, Observation of single-electron charging effects in
    small tunnel junctions. Phys. Rev. Lett. 59, 190112 (1987)
    [6] D. V. Averin, and K. K. Likharev, Coulomb blockade of single-electron tunneling,
    and coherent oscillations in small tunnel-junctions. J. Low. Temp. Phys. 62,
    345373 (1986)
    [7] K. Ono, D. G. Austing, Y. Tokura, and S. Tarucha, Current rectification by Pauli
    exclusion in a weakly coupled double quantum dot system. Science 297, 1313-
    1317 (2002)
    [8] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup and H. J. Kimble,
    Photon blockade in an optical cavity with one trapped atom. Nature 436, 87-90
    (2005)
    [9] N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, Sub-poissonian loading
    of single atoms in a microscopic dipole trap. Nature 411, 1024-1027(2001)
    [10] M. Saffman, T. G. Walker, and K. MØmer, Quantum information with Rydberg
    atoms. Rev. Mod. Phys. 82, 2313-2363 (2010)
    [11] E. Brion, A. S. Mouritzen, and K. Mølmer. Conditional dynamics induced by new
    configurations for Rydberg dipole-dipole interactions. Phys. Rev. A 76, 022334
    (2007)
    [12] E. Brion, K. Mølmer, and M. Saffman. Quantum computing with collective ensembles
    of multilevel systems. Phys. Rev. Lett. 99, 260501 (2007)
    [13] D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y.P. Zhang, R. C.ot’e, E. E.
    Eyler, and P. L. Gould, Local blockade of Rydberg excitation in an ultracold gas.
    Phys. Rev. Lett. 93, 063001 (2004)
    [14] K. Singer, M. Reetz-Lamour, T. Amthor, L. G. Marcassa, and M. Weidem¨uller,
    Suppression of excitation and spectral broadening induced by interactions in a
    cold gas of Rydberg atoms. Phys. Rev. Lett. 93, 163001 (2004)
    [15] , T. C. Liebisch, A. Reinhard, P. R. Berman, and G. Raithel, Atom counting statistics
    in ensembles of interacting Rydberg atoms. Phys. Rev. Lett. 95 253002
    (2005); erratum 98, 109903 (2007)
    [16] T. Vogt, M. Viteau, J. Zhao, A. Chotia, D. Comparat, and P. Pillet, Dipole blockade
    at F¨orster resonances in high resolution laser excitation of Rydberg states of
    cesium atoms. Phys. Rev. Lett. 97, 083003 (2006)
    [17] P. Bohlouli-Zanjani, J. A. Petrus, and J. D. D. Martin, Enhancement of Rydberg
    atom interactions using ac stark shifts. Phys. Rev. Lett. 98, 203005 (2007)
    [18] R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. L¨ow, L. Santos,
    and T. Pfau, Evidence for coherent collective Rydberg excitation in the strong
    blockade regime. Phys. Rev. Lett. 99, 163601 (2007)
    [19] T. Peyronel, O. Firstenberg, Q. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M.
    D. Lukin, and V. Vuleti, Quantum nonlinear optics with single photons enabled by
    strongly interacting atoms. Nature 488, 57-60 (2012)
    [20] Y. O. Dudin and A. Kuzmich, Strongly Interacting Rydberg Excitations of a Cold
    Atomic Gas. Science 336, 887 (2012)
    [21] U. Raitzsch, V. Bendkowsky, R. Heidemann, B. Butscher, R. L¨ow, and T. Pfau,
    Echo Experiments in a Strongly Interacting Rydberg Gas. Phys. Rev. Lett. 100,
    013002 (2008)
    [22] J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, C. S.
    Adams, Cooperative Atom-Light Interaction in a Blockaded Rydberg Ensemble.
    Phys. Rev. Lett. 105, 193603 (2010)
    [23] J. Nipper, J. B. Balewski, A. T. Krupp, B. Butscher, R. Low, and T. Pfau, Highly
    Resolved Measurements of Stark-Tuned F¨orster Resonances between Rydberg
    Atoms. Phys. Rev. Lett. 108, 113001 (2012)
    [24] T. E. Lee, H. Haffner, and M. C. Cross, Antiferromagnetic phase transition in a
    nonequilibrium lattice of Rydberg atoms. Phys. Rev. A 84, 031402(R) (2011)
    [25] Jing Qian, Guangjiong Dong, Lu Zhou, and Weiping Zhang, Phase diagram of
    Rydberg atoms in a nonequilibrium optical lattice. Phys. Rev. A 85, 065401 (2012)
    [26] Xue-Feng Zhang, Qing Sun, Yu-Chuan Wen, Wu-Ming Liu, Sebastian Eggert,
    and An-Chun Ji, Rydberg Polaritons in a Cavity: A Superradiant Solid. Phys.
    Rev. Lett. 110, 090402 (2013)
    [27] K. Saha, S. Sinha, and K. Sengupta, Phases and collective modes of Rydberg
    atoms in an optical lattice. Phys. Rev. A 89, 023618 (2014)
    [28] M. Hoening, W. Abdussalam, M. Fleischhauer, and T. Pohl, Antiferromagnetic
    long-range order in dissipative Rydberg lattices. Phys. Rev. A 90, 021603(R)
    (2014)
    [29] H. Weimer, Robert L¨ow, Tilman Pfau, and Hans Peter B¨uchler, Quantum Critical
    Behavior in Strongly Interacting Rydberg Gases. Phys. Rev. Lett. 101, 250601
    (2008)
    [30] N. Henkel, R. Nath, and T. Pohl, Three-Dimensional Roton Excitations and Supersolid
    Formation in Rydberg-Excited Bose-Einstein Condensates. Phys. Rev. Lett.
    104,195302 (2010)
    [31] N. Henkel, F. Cinti, P. Jain, G. Pupillo, and T. Pohl, Supersolid Vortex Crystals
    in Rydberg-Dressed Bose-Einstein Condensates. Phys. Rev. Lett. 108, 265301
    (2012)
    [32] G. Pupillo, A. Micheli, M. Boninsegni, I. Lesanovsky, and P. Zoller, Strongly
    Correlated Gases of Rydberg-Dressed Atoms: Quantum and Classical Dynamics.
    Phys. Rev. Lett. 104, 223002 (2010)
    [33] F. Cinti, P. Jain, M. Boninsegni, A. Micheli, P. Zoller, and G. Pupillo, Supersolid
    Droplet Crystal in a Dipole-Blockaded Gas. Phys. Rev. Lett. 105, 135301 (2010)
    [34] Bo Xiong, H. H Jen and Daw-Wei Wang, Topological superfluid by blockade
    effects in a Rydberg-dressed Fermi gas. Phys. Rev. A 90, 013631 (2014)
    [35] G.Gr¨uner, The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129
    (1988)
    [36] T. G. Walker and M. Saffman, Consequences of Zeeman degeneracy for the van
    der Waals blockade between Rydberg atoms. Phys. Rev. A 77, 032723(2008)
    [37] K. Singer, J. Stanojevic, M. Weidem¨uller and R. Cˆot´e, Long-range interactions
    between alkali Rydberg atom pairs correlated to the ns-ns, np-np and nd-nd
    asymptotes. J. Phys. B: At. Mol. Opt. Phys. 38 S295(2005)
    [38] F. Maucher, N. Henkel, M. Saffman, W. Kr’Olikowski, S. Skupin and T. Pohl,
    Rydberg-Induced Solitons: Three-Dimensional Self-Trapping of Matter Waves.
    Phys. Rev. Lett. 106, 170401(2011)
    [39] J. Honer, H.Weimer, T. Pfau and H. P. B¨uchler , Collective Many-Body Interaction
    in Rydberg Dressed Atoms. Phys. Rev. Lett. 105, 160404 (2010)
    [40] L. D. Landau: On the theory of superfluidity of helium II. USSR J. Phys. 11, 91-92
    (1947)
    [41] L. D. Landau: The theory of a Fermi liquid. Sov. Phys. JETP 3, 920-925 (1957)
    [42] D. Pines, P. Nozi`eres: The Theory of Quantum Liquids (Benjamin, 1966)
    [43] A. L. Fetter and J. D. Walecka, Quantum Theory Of Many-Particle Systems, Sec
    9, 12, 13, 15, 17
    [44] D. Pines, Elementary excitations in quantum liquids. Phys. Today 34, 106V131
    (1981)
    [45] P. Nozi`eres, Is the roton in superfluid 4He the ghost of a Bragg spot? J. Low Temp.
    Phys. 137, 45V67 (2004)
    [46] L. D. Landau, Phys. Z. Sowiet 11, 26, 545 (1937)[The Collected Papers of L. D.
    Landau, edited by D. ter Haar’(Gordon and Breach-Pergamon, New York, 1965),
    p. 198].
    [47] J. Quintanilla, M. Haque, and A. J. Schofield , Symmetry-breaking Fermi surface
    deformations from central interactions in two dimensions. Phys. Rev. B 78,
    035131 (2008)
    [48] J. Quintanilla, and A. J. Schofield , Pomeranchuk and topological Fermi surface
    instabilities from central interactions. Phys. Rev. B 74, 115126 (2006)
    [49] P. W. Anderson and P. Morel, Generalized Bardeen-Cooyer-Schrieffer States and
    the Proposed Low-Temperature Phase of Liquid He III. Phys. Rev. 123, 6 (1961)
    [50] C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE