Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-17T19:11:06.473Z Has data issue: false hasContentIssue false

13 - Probing and Controlling Strongly Correlated Quantum Many-Body Systems Using Ultracold Quantum Gases

from Part III - Condensates in Atomic Physics

Published online by Cambridge University Press:  18 May 2017

By
I. Bloch
Edited by
Nick P. Proukakis ,
David W. Snoke  and
Peter B. Littlewood
I. Bloch
Affiliation:
Ludwig-Maximilians University
Nick P. Proukakis
Affiliation:
Newcastle University
David W. Snoke
Affiliation:
University of Pittsburgh
Peter B. Littlewood
Affiliation:
University of Chicago
Get access

Summary

Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems.

Introduction

Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12].

In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].

Type
Chapter
Information
Universal Themes of Bose-Einstein Condensation , pp. 253 - 273
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Jaksch, D., and Zoller, P. 2005. The cold atoms Hubbard toolbox. Ann. Phys., 315, 52.Google Scholar
[2] Bloch, I., Dalibard, J., and Zwerger, W. 2008. Many-body physics with ultracold gases. Rev. Mod. Phys., 80, 885.Google Scholar
[3] Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., De, A, Sen, and Sen, U. 2007. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys., 56, 243–379.Google Scholar
[4] Fisher, M.P.A., Weichman, P.B., Grinstein, G, and Fisher, D.S. 1989. Boson localization and the superfluid-insulator transition. Phys. Rev. B, 40, 546–570.Google Scholar
[5] Jaksch, D., Bruder, C., Cirac, J.I., Gardiner, C.W., and Zoller, P. 1998. Cold bosonic atoms in optical lattices. Phys. Rev. Lett., 81, 3108–3111.Google Scholar
[6] Greiner, M., Mandel, O., Esslinger, T., Hänsch, T.W., and Bloch, I. 2002. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature, 415, 39–44.Google Scholar
[7] Jördens, R., Strohmaier, N., Günter, K., Moritz, H., and Esslinger, T. 2008. A Mott insulator of fermionic atoms in an optical lattice. Nature, 455, 204–207.Google Scholar
[8] Schneider, U., Hackermüller, L., Will, S., Best, Th., Bloch, I., Costi, T. A, A, Helmes, R.W., Rasch, D., and Rosch, A. 2008. Metallic and insulating phases of repulsively interacting fermions in a 3D optical lattice. Science, 322, 1520–1525.Google Scholar
[9] Paredes, B., Widera, A., Murg, V., Mandel, O., Fölling, S., Cirac, J.I., Shlyapnikov, G.V., Hänsch, T.W., and Bloch, I. 2004. Tonks-Girardeau gas of ultracold atoms in an optical lattice. Nature, 429, 277–281.Google Scholar
[10] Kinoshita, T., Wenger, T., and Weiss, D.S. 2004. Observation of a one-dimensional Tonks-Girardeau gas. Science, 305, 1125–1128.Google Scholar
[11] Randeria, M., Zwerger, W., and Zwierlein, M. (eds). 2012. The BCS-BEC Crossover and the Unitary Fermi Gas. Lecture Notes in Physics, vol. 836. Springer.
[12] Chin, C., Grimm, R., Julienne, P., and Tiesinga, E. 2010. Feshbach resonances in ultracold gases. Rev. Mod. Phys., 82, 1225–1286.Google Scholar
[13] Nelson, K.D., Li, X., and Weiss, D.S. 2007. Imaging single atoms in a threedimensional array. Nat. Phys., 3, 556–560.Google Scholar
[14] Gericke, T., Würtz, P., Reitz, D., Langen, T., and Ott, H. 2008. High-resolution scanning electron microscopy of an ultracold quantum gas. Nature Phys., 4, 949–953.Google Scholar
[15] Bakr, W.S., Gillen, J.I., Peng, A., Fölling, Si., and Greiner, M. 2009. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature, 462, 74–77.Google Scholar
[16] Bakr, W.S., Peng, A., Tai, M.E., Ma, R., Simon, J., Gillen, J.I., Fölling, S., Pollet, L., and Greiner, M. 2010. Probing the superfluid-to-Mott insulator transition at the single-atom level. Science, 329, 547–550.Google Scholar
[17] Sherson, Jacob, F., Weitenberg, Christof, Endres, Manuel, Cheneau, Marc, Bloch, Immanuel, and Kuhr, Stefan. 2010. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature, 467, 68–72.Google Scholar
[18] Weitenberg, C., Endres, M., Sherson, J.F., Cheneau, M., Schauß, P., Fukuhara, T., Bloch, I., Kuhr, S., and Schauss, P. 2011. Single-spin addressing in an atomic Mott insulator. Nature, 471, 319–324.Google Scholar
[19] Trotzky, S., Cheinet, P., Fölling, S., Feld, M., Schnorrberger, U., Rey, A. M, M, Polkovnikov, A., Demler, E.A.A. Lukin, M. D, D, and Bloch, I. 2008. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science, 319, 295–299.Google Scholar
[20] Trotzky, S., Chen, Y.-A., Schnorrberger, U., Cheinet, P., and Bloch, I. 2010. Controlling and detecting spin correlations of ultracold atoms in optical lattices. Phys. Rev. Lett., 105, 265303.Google Scholar
[21] Fukuhara, T., Schauß, P., Endres, M., Hild, S., Cheneau, M., Bloch, I., and Gross, C. 2013. Microscopic observation of magnon bound states and their dynamics. Nature, 502, 76–79.Google Scholar
[22] Greif, D., Uehlinger, T., Jotzu, G., Tarruell, L., and Esslinger, T. 2013. Short-range quantum magnetism of ultracold fermions in an optical lattice. Science, 340, 1307– 10.Google Scholar
[23] Hart, R., Duarte, P., Yang, T., Liu, X., Paiva, T., Khatami, E., Scalettar, R.T., Trivedi, N., Huse, D.A., and Hulet, R. 2014. Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms. Nature, 519, 211–214.Google Scholar
[24] Lee, P.A., Nagaosa, N., and Wen, X.-G. 2006. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys., 78, 17–85.Google Scholar
[25] Le Hur, K., and Maurice Rice, T. 2009. Superconductivity close to the Mott state: from condensed-matter systems to superfluidity in optical lattices. Ann. Phys., 324, 1452–1515.Google Scholar
[26] Hofstetter, W., Cirac, J.I., Zoller, P., Demler, E., and Lukin, M.D. 2002. Hightemperature superfluidity of fermionic atoms in optical lattices. Phys. Rev. Lett., 89, 220407.Google Scholar
[27] Polkovnikov, A., Sengupta, K., Silva, A., and Vengalattore, M. 2011. Colloquium: nonequilibrium dynamics of closed interacting quantum systems. Rev. Mod. Phys., 83, 863–883.Google Scholar
[28] Trotzky, S., Chen, Y-a., Flesch, A., McCulloch, I.P., Schollwöck, U., Eisert, J., and Bloch, I. 2012. Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas. Nature Phys., 8, 325–330.Google Scholar
[29] Schneider, U., Hackermüller, L., Ronzheimer, J.-P., Will, S., Braun, S., Best, T., Bloch, I., Demler, E., Mandt, S., Rasch, D., and Rosch, A. 2012. Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms. Nature Phys., 8, 213–218.Google Scholar
[30] Ronzheimer, J.P., Schreiber, M., Braun, S., Hodgman, S.S., Langer, S., McCulloch, I.P., Heidrich-Meisner, F., Bloch, I., and Schneider, U. 2013. Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions. Phys. Rev. Lett., 110, 205301.Google Scholar
[31] Hild, S., Fukuhara, T., Schauß, P., Zeiher, J., Knap, M., Demler, E., Bloch, I., and Gross, C. 2014. Far-from-equilibrium spin transport in Heisenberg quantum magnets. Phys. Rev. Lett., 113, 147205.Google Scholar
[32] Strohmaier, N., Greif, D., Jördens, R., Tarruell, L., Moritz, H., and Esslinger, T. 2010. Observation of elastic doublon decay in the Fermi-Hubbard model. Phys. Rev. Lett., 104, 080401.Google Scholar
[33] Hung, C.-L., Zhang, X., Gemelke, N., and Chin, C. 2010. Slow mass transport and statistical evolution of an atomic gas across the superfluid-Mott-insulator transition. Phys. Rev. Lett., 104, 160403.Google Scholar
[34] Gerbier, F., Widera, A., Fölling, S., Mandel, O., Gericke, T., and Bloch, I. 2005. Phase coherence of an atomic Mott insulator. Phys. Rev. Lett., 95, 050404.Google Scholar
[35] Endres, M., Cheneau, M., Fukuhara, T., Weitenberg, C., Schauss, P., Gross, C., Mazza, L., Banuls, M.C., Pollet, L., Bloch, I., and Kuhr, S. 2011. Observation of correlated particle–hole pairs and string order in low-dimensional Mott insulators. Science, 334, 200–203.Google Scholar
[36] Endres, M., Cheneau, M., Fukuhara, T., Weitenberg, C., Schauß, P., Gross, C., Mazza, L., Bauls, M.C., Pollet, L., Bloch, I., and Kuhr, S. 2013. Single-site- and singleatom- resolved measurement of correlation functions. Appl. Phys. B, 113, 27–39.Google Scholar
[37] Greiner, M., Mandel, O., Esslinger, T., Hänsch, T.W., and Bloch, I. 2002. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature, 415, 39–44.
[38] Hubbard, J. 1963. Electron correlations in narrow energy bands. Proc. Roy. Soc. A, 276, 238–257.Google Scholar
[39] Helmes, R., Costi, T., and Rosch, A. 2008. Mott transition of fermionic atoms in a three-dimensional optical trap. Phys. Rev. Lett., 100, 056403.Google Scholar
[40] Jördens, R., Tarruell, L., Greif, D., Uehlinger, T., Strohmaier, N., Moritz, H., Esslinger, T., De Leo, L., Kollath, C., Georges, A., Scarola, V., Pollet, L., Burovski, E., Kozik, E., and Troyer, M. 2010. Quantitative determination of temperature in the approach to magnetic order of ultracold fermions in an optical lattice. Phys. Rev. Lett., 104, 180401.Google Scholar
[41] Bernier, J.-S., Kollath, C., Georges, A., De Leo, L., Gerbier, F., Salomon, C., and Köhl, M. 2009. Cooling fermionic atoms in optical lattices by shaping the confinement. Phys. Rev. A, 79, 061601(R).Google Scholar
[42] Ho, T.-L., and Zhou, Q. 2009. Universal cooling scheme for quantum simulation. arXiv:0911.5506, Nov.
[43] Auerbach, A. 1994. Interacting Electrons and Quantum Magnetism. New York: Springer-Verlag NY.
[44] Fukuhara, T., Kantian, A., Endres, M., Cheneau, M., Schauß, P., Hild, S., Bellem, D., Schollwöck, U., Giamarchi, T., Gross, C., Bloch, I., and Kuhr, S. 2013. Quantum dynamics of a mobile spin impurity. Nature Phys., 9, 235–241.Google Scholar
[45] Pauling, L. 1931. J. Am. Chem. Soc., 53, 1367.
[46] Hückel, E. 1931. Quantentheoretische Beiträge zum Benzolproblem. Z. Phys. A, 70, 204.Google Scholar
[47] Anderson, P. 1973. Resonating valence bonds: a new kind of insulator? Mat. Res. Bull., 8, 153.Google Scholar
[48] Anderson, P.W. 1987. The resonating valence bond state in La2CuO4 and superconductivity. Science, 235, 1196–1198.Google Scholar
[49] Paredes, Belén, and Bloch, I. 2008. Minimum instances of topological matter in an optical plaquette. Phys. Rev. A, 77, 23603.Google Scholar
[50] Nascimbène, S., Chen, Y.-A., Atala, M., Aidelsburger, M., Trotzky, S., Paredes, B., and Bloch, I. 2012. Experimental realization of plaquette resonating valence-bond states with ultracold atoms in optical superlattices. Phys. Rev. Lett., 108, 205301.Google Scholar
[51] Trebst, S., Schollwöck, U., Troyer, M., and Zoller, P. 2006. d-wave resonating valence bond states of fermionic atoms in optical lattices. Phys. Rev. Lett., 96, 250402.Google Scholar
[52] Rey, A.M., Sensarma, R., Fölling, S., Greiner, M., Demler, E., and Lukin, M.D. 2009. Controlled preparation and detection of d-wave superfluidity in two-dimensional optical superlattices. Europhys. Lett., 87, 60001.Google Scholar
[53] Gemelke, N., Zhang, X., Hung, Ch.-L., and Chin, Ch. 2009. In situ observation of incompressible Mott-insulating domains in ultracold atomic gases. Nature, 460, 995–998.Google Scholar
[54] Anfuso, F., and Rosch, A. 2007. String order and adiabatic continuity of Haldane chains and band insulators. Phys. Rev. B, 75, 144420.Google Scholar
[55] Berg, E., Dalla Torre, E., Giamarchi, T., and Altman, E. 2008. Rise and fall of hidden string order of lattice bosons. Phys. Rev. B, 77, 245119.Google Scholar
[56] DePue, M.T., McCormick, C., Winoto, S.L., Oliver, S., and Weiss, D.S. 1999. Unity occupation of sites in a 3D optical lattice. Phys. Rev. Lett., 82, 2262–2265.Google Scholar
[57] Weiss, D.S., Vala, J., Thapliyal, A.V., Myrgren, S., Vazirani, U., and Whaley, K.B. 2004. Another way to approach zero entropy for a finite system of atoms. Phys. Rev. A, 70, 40302.Google Scholar
[58] Braun, S., Ronzheimer, J.P., Schreiber, M., Hodgman, S.S., Rom, T., Bloch, I., and Schneide, U. 2013. Negative absolute temperature for motional degrees of freedom. Science, 339, 52–55.Google Scholar
[59] Podolsky, D., Auerbach, A., and Arovas, D. 2011. Visibility of the amplitude (Higgs) mode in condensed matter. Phys. Rev. B, 84, 174522.Google Scholar
[60] Endres, M., Fukuhara, T., Pekker, D., Cheneau, M., Schauss, P., Gross, C., Demler, E., Kuhr, S., and Bloch, I. 2012. The “Higgs” amplitude mode at the two-dimensional superfluid/Mott insulator transition. Nature, 487, 454–8.Google Scholar
[61] Wen, X.G. 2004. Quantum Field Theory of Many-Body Systems. Oxford Graduate Texts. Oxford: Oxford University Press.
[62] Rath, S.P., Simeth, W., Endres, M., and Zwerger, W. 2013. Non-local order in Mott insulators, duality and Wilson loops. Annals of Physics, 334, 256–271.Google Scholar
[63] Alves, C., and Jaksch, D. 2004. Multipartite entanglement detection in bosons. Phys. Rev. Lett., 93, 1–4.Google Scholar
[64] Daley, A.J., Pichler, H., Schachenmayer, J., and Zoller, P. 2012. Measuring entanglement growth in quench dynamics of bosons in an optical lattice. Phys. Rev. Lett., 109, 020505.Google Scholar
[65] Pichler, H., Bonnes, L., Daley, A.J., Läuchli, A.M., and Zoller, P. 2013. Thermal versus entanglement entropy: a measurement protocol for fermionic atoms with a quantum gas microscope. New J. Phys., 15, 063003.Google Scholar
[66] Ni, K.-K., Ospelkaus, S., de Miranda, M. H, G., Pe'er, A., Neyenhuis, B., Zirbel, J.J., Kotochigova, S., Julienne, P. S., Jin, D. S., and Ye, J. 2008. A high phase-spacedensity gas of polar molecules. Science, 322, 231–235.Google Scholar
[67] Schauß, P., Cheneau, M., Endres, M., Fukuhara, T., Hild, S., Omran, A., Pohl, T., Gross, C., Kuhr, S., and Bloch, I. 2012. Observation of spatially ordered structures in a two-dimensional Rydberg gas. Nature, 490, 87–91.Google Scholar
[68] Schauß, P., Zeiher, J., Fukuhara, F., Hild, S., Cheneau, M., Macri, T., Pohl, T., Bloch, I., and Gross, C. 2015. Crystallization in Ising quantum magnets. Science, 347, 1455–1458.Google Scholar
[69] Atala, M., Aidelsburger, M., Barreiro, J. T., Abanin, D. A., Kitagawa, T., Demler, E., and Bloch, I. 2013. Direct measurement of the Zak phase in topological Bloch bands. Nature Phys., 9, 795–800.Google Scholar
[70] Aidelsburger, M., Atala, M., Lohse, M., Barreiro, J. T., Paredes, B., and Bloch, I. 2013. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett., 111, 185301.Google Scholar
[71] Miyake, H., Siviloglou, G., Kennedy, C. J., Burton, W. C., and Ketterle, W. 2013. Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices. Phys. Rev. Lett., 111, 185302.Google Scholar
[72] Atala, M., Aidelsburge, M., Lohse, M., Barreiro, J. T., Paredes, B., and Bloch, I. 2014. Observation of chiral currents with ultracold atoms in bosonic ladders. Nature Phys., 10, 13–15.Google Scholar
[73] Jotzu, G., Messer, M., Desbuquois, R., Lebrat, M., Uehlinger, T., Greif, D., and Esslinger, T. 2014. Experimental realisation of the topological Haldane model. Nature, 515, 237–240.Google Scholar
[74] Aidelsburger, M., Lohse, M., Schweizer, C., Atala, M., Barreiro, J. T., Nascimbène, S., Cooper, N. R., Bloch, I., and Goldman, N. 2015. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nature Phys., 11, 162–166.Google Scholar
[75] Basko, D. M., Aleiner, I. L., and Altshuler, B. L. 2006. Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states. Annals of Physics, 321, 1126–1205.Google Scholar
[76] Gornyi, I. V., Mirlin, A. D., and Polyakov, D. G. 2005. Dephasing and weak localization in disordered Luttinger liquid. Phys. Rev. Lett., 95(4).Google Scholar
[77] Nandkishore, R., and Huse, D., A. 2015. Many-body localization and thermalization in quantum statistical mechanics. Ann. Rev. Cond. Mat. Phys., 6, 15–38.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×