Abstract
At nanokelvin temperatures, ultracold quantum gases can be stored in optical lattices, which are arrays of microscopic trapping potentials formed by laser light. Such large arrays of atoms provide opportunities for investigating quantum coherence and generating large-scale entanglement, ultimately leading to quantum information processing in these artificial crystal structures. These arrays can also function as versatile model systems for the study of strongly interacting many-body systems on a lattice.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Pitaevskii, L. & Stringari, S. Bose–Einstein Condensation (Oxford Univ. Press, Oxford, 2003).
Grimm, R., Weidemü ller, M. & Ovchinnikov, Y. B. Optical dipole traps for neutral atoms. Adv. At. Mol. Opt. Phys. 42, 95–170 (2000).
Jessen, P. S. & Deutsch, I. H. Optical lattices. Adv. At. Mol. Opt. Phys. 37, 95–139 (1996).
Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Preprint at <http://arxiv.org/abs/0704.3011> (2007).
Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose–Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995).
Davis, K. B. et al. Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).
Bradley, C. C., Sackett, C. A., Tollett, J. J. & Hulet, R. G. Evidence of Bose–Einstein condensation in an atomic gas with attractive interactions. Phys. Rev. Lett. 75, 1687–1690 (1995).
DeMarco, B. & Jin, D. D. Onset of Fermi degeneracy in a trapped atomic gas. Science 285, 1703–1706 (1999).
Schreck, F. et al. Quasipure Bose–Einstein condensate immersed in a Fermi Sea. Phys. Rev. Lett. 87, 080403 (2001).
Truscott, A. G., Strecker, K. E., McAlexander, W. I., Partridge, G. P. & Hulet, R.G. Observation of Fermi pressure in a gas of trapped atoms. Science 291, 2570–2572 (2001).
Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989).
Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998).
Greiner, M., Mandel, M. O., Esslinger, T., Hänsch, T. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).
Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004).
Spielman, I. B., Phillips, W. D. & Porto, J. V. The Mott insulator transition in two dimensions. Phys. Rev. Lett. 98, 080404 (2007).
Köhl, M., Moritz, H., Stöferle, T., Günter, K. & Esslinger, T. Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions. Phys. Rev. Lett. 94, 080403 (2005).
Jaksch, D. & Zoller, P. The cold atoms Hubbard toolbox. Ann. Phys. (NY) 315, 52–79 (2005).
Bloch, I. Ultracold quantum gases in optical lattices. Nature Phys. 1, 23–30 (2005).
Lewenstein, M. et al. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007).
Jaksch, D., Briegel, H. J., Cirac, J. I., Gardiner, C. W. & Zoller, P. Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975–1978 (1999).
Mandel, O. et al. Controlled collisions for multiparticle entanglement of optically trapped atoms. Nature 425, 937–940 (2003).
Sebby-Strabley, J., Anderlini, M., Jessen, P. S. & Porto, J. V. Lattice of double wells for manipulating pairs of cold atoms. Phys. Rev. A 73, 033605 (2006).
Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature 448, 452–456 (2007).
Fölling, S. et al. Direct observation of second-order atom tunnelling. Nature 448, 1029–1032 (2007).
Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).
Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).
Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).
Beugnon, J. et al. Two-dimensional transport and transfer of a single atomic qubit in optical tweezers. Nature Phys. 3, 696–699 (2007).
Schrader, D. et al. A neutral atom quantum register. Phys. Rev. Lett. 93, 150501 (2004).
Miroshnychenko, Y. et al. Precision preparation of strings of trapped neutral atoms. New J. Phys. 8, 191 (2006).
Miroshnychenko, Y. et al. An atom-sorting machine. Nature 442, 151 (2006).
Nelson, K. D., Li, X. & Weiss, D. S. Imaging single atoms in a three-dimensional array. Nature Phys. 3, 556–560 (2007).
Cho, J. Addressing individual atoms in optical lattices with standing-wave driving fields. Phys. Rev. Lett. 99, 020502 (2007).
Joo, J., Lim, Y. L., Beige, A. & Knight, P. L. Single-qubit rotations in two-dimensional optical lattices with multiqubit addressing. Phys. Rev. A 74, 042344 (2006).
Gorshkov, A. V., Jiang, L., Greiner, M., Zoller, P. & Lukin, M. D. Coherent quantum optical control with subwavelength resolution. Preprint at <http://arxiv.org/abs/0706.3879> (2007).
Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001).
Griessner, A., Daley, A. J., Clark, S. R., Jaksch, D. & Zoller, P. Dark-state cooling of atoms by superfluid immersion. Phys. Rev. Lett. 97, 220403 (2006).
Griessner, A., Daley, A. J., Clark, S. R., Jaksch, D. & Zoller, P. Dissipative dynamics of atomic Hubbard models coupled to a phonon bath: dark state cooling of atoms within a Bloch band of an optical lattice. New J. Phys. 9, 44 (2007).
Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).
Inouye, S. et al. Observation of Feshbach resonances in a Bose–Einstein condensate. Nature 392, 151–154 (1998).
Courteille, P., Freeland, R. S., Heinzen, D. J., van Abeelen, F. A. & Verhaar, B. J. Observation of a Feshbach resonance in cold atom scattering. Phys. Rev. Lett. 81, 69–72 (1998).
Micheli, A., Brennen, G. K. & Zoller, P. A toolbox for lattice-spin models with polar molecules. Nature Phys. 2, 341–347 (2006).
Jaksch, D. et al. Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85, 2208–2211 (2000).
Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001).
Tong, D. et al. Local blockade of Rydberg excitation in an ultracold gas. Phys. Rev. Lett. 93, 063001 (2004).
Singer, K., Reetz-Lamour, M., Amthor, T., Marcassa, L. G. & Weidemü ller, M. Suppression of excitation and spectral broadening induced by interactions in a cold gas of Rydberg atoms. Phys. Rev. Lett. 93, 163001 (2004).
Liebisch, T. C., Reinhard, A., Berman, P. R. & Raithel, G. Atom counting statistics in ensembles of interacting Rydberg atoms. Phys. Rev. Lett. 95, 253002 (2005).
Heidemann, R. et al. Evidence for coherent collective Rydberg excitation in the strong blockade regime. Phys. Rev. Lett. 99, 163601 (2007).
Hayes, D., Julienne, P. S. & Deutsch, I. H. Quantum logic via the exchange blockade in ultracold collisions. Phys. Rev. Lett. 98, 070501 (2007).
Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, New York, 2006).
Duan, L.-M., Demler, E. & Lukin, M. D. Controlling spin exchange interactions of ultracold atoms in an optical lattice. Phys. Rev. Lett. 91, 090402 (2003).
Kuklov, A. B. & Svistunov, B. V. Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice. Phys. Rev. Lett. 90, 100401 (2003).
Widera, A. et al. Coherent collisional spin dynamics in optical lattices. Phys. Rev. Lett. 95, 190405 (2005).
Vaucher, B., Nunnenkamp, A. & Jaksch, D. Creation of resilient entangled states and a resource for measurement-based quantum computation with optical superlattices. Preprint at 〈http://arxiv.org/abs/0710.5099〉 (2007).
Deutsch, D. Quantum computational networks. Proc. R. Soc. Lond. A 425, 73–90 (1989).
Yao, A. in Proc. 34th Annu. Symp. Found. Comput. Sci. 352–361 (IEEE Computer Soc., Los Alamitos, 1993).
Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995).
Farhi, E. et al. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–476 (2001).
Deutsch, D. Quantum-theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985).
Bernstein, E. & Vazirani, U. in Proc. 25th Annu. ACM Symp. Theor. Comput. 11–20 (ACM Press, New York, 1993).
Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999).
Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).
Nielsen, M. A. Quantum computation by measurement and quantum memory. Phys. Lett. A 308, 96–100 (2003).
Raussendorf, R. & Briegel, H. J. A One-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001).
Raussendorf, R. & Briegel, H. J. Computational model underlying the one-way quantum computer. Quant. Info. Comput. 2, 443–486 (2002).
Walther, P. et al. Experimental one-way quantum computing. Nature 434, 169–176 (2005).
Kiesel, N. et al. Experimental analysis of a four-qubit photon cluster state. Phys. Rev. Lett. 95, 210502 (2005).
Gross, D., Eisert, J., Schuch, N. & Perez-Garcia, D. Measurement-based quantum computation beyond the one-way model. Phys. Rev. A 76, 052315 (2007).
Van den Nest, M., Miyake, A., Dür, W. & Briegel, H. J. Universal resources for measurement-based quantum computation. Phys. Rev. Lett. 97, 150504 (2006).
Van den Nest, M., Dü r, W., Miyake, A. & Briegel, H. J. Fundamentals of universality in one-way quantum computation. New J. Phys. 9, 204 (2007).
Gross, D. & Eisert, J. Novel schemes for measurement-based quantum computation. Phys. Rev. Lett. 98, 220503 (2007).
Browne, D. E. et al. Phase transition of computational power in the resource states for one-way quantum computation. Preprint at 〈http://arxiv.org/abs/0709.1729〉 (2007).
Verstraete, F. & Cirac, J. I. Valence-bond states for quantum computation. Phys. Rev. A 70, 060302 (2004).
Aliferis, P. & Leung, D. W. Computation by measurements: a unifying picture. Phys. Rev. A 70, 062314 (2004).
Childs, A. M., Leung, D. W. & Nielsen, M. A. Unified derivations of measurement-based schemes for quantum computation. Phys. Rev. A 71, 032318 (2005).
Jorrand, P. & Perdrix, S. Unifying quantum computation with projective measurements only and one-way quantum computation. Preprint at 〈http://arxiv.org/abs/quant-ph/0404125〉 (2004).
Shor, P. W. in Proc. 37th Annu. Symp. Found. Comput. Sci. 56–65 (IEEE Computer Soc., Los Alamitos, 1996).
Aharonov, D. & Ben-Or, M. in Proc. 29th Annu. ACM Symp. Theor. Comput. 176–188 (ACM Press, New York, 1997).
Gottesman, D. Stabilizer Codes and Quantum Error Correction. PhD thesis, California Inst.Technol. (1997).
Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation: error models and thresholds. Proc. R. Soc. Lond. A 454, 365–384 (1998).
Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. (NY) 303, 2–30 (2003).
Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007).
Hofstetter, W., Cirac, J. I., Zoller, P., Demler, E. & Lukin, M. D. High-temperature superfluidity of fermionic atoms in optical lattices. Phys. Rev. Lett. 89, 220407 (2002).
Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).
Werner, F., Parcollet, O., Georges, A. & Hassan, S. R. Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices. Phys. Rev. Lett. 95, 056401 (2005).
Acknowledgements
I thank H. Briegel for discussions, and the German Research Foundation (DFG), the European Union (through the OLAQUI and SCALA projects) and the Air Force Office of Scientific Research (AFOSR) for support.
Author information
Authors and Affiliations
Ethics declarations
Competing interests
The author declares no competing financial interests.
Additional information
Correspondence should be addressed to the author (bloch@uni-mainz.de).
Rights and permissions
About this article
Cite this article
Bloch, I. Quantum coherence and entanglement with ultracold atoms in optical lattices. Nature 453, 1016–1022 (2008). https://doi.org/10.1038/nature07126
Published:
Issue Date:
DOI: https://doi.org/10.1038/nature07126
This article is cited by
-
Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape
Nature Communications (2023)
-
Photonic integrated beam delivery for a rubidium 3D magneto-optical trap
Nature Communications (2023)
-
Wide and fast-frequency tuning for a stabilized diode laser
Frontiers of Physics (2022)
-
Thermal correction to entanglement spectrum for conformal field theories
Journal of High Energy Physics (2022)
-
Ultracold chemical reactions reveal the quantum mechanism of product formation
Nature (2021)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.