Quantum simulation with cold atoms in optical lattices is an attractive avenue for explorations of quantum many-body physics. A principal challenge in the field is to increase the energy and length scales in current set-ups, thereby reducing temperature and coherence-time requirements. Here, we present a new paradigm for high-density, two-dimensional optical lattices in photonic crystal waveguides. Specially engineered two-dimensional photonic crystals provide a practical platform to trap atoms and engineer their interactions in ways that surpass the limitations of current technologies and enable investigations of novel quantum many-body matter. Our schemes remove the constraint on the lattice constant set by the free-space optical wavelength in favour of deeply sub-wavelength atomic arrays. We further describe possibilities for atom–atom interactions mediated by photons in two-dimensional photonic crystal waveguides with energy scales several orders of magnitude larger than for exchange interactions in free-space lattices and with the capability to engineer strongly long-range interactions.
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Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nature Phys. 8, 267–276 (2012).
Cirac, J. I. & Zoller, P. Goals and opportunities in quantum simulation. Nature Phys. 8, 264–266 (2012).
Micheli, A., Brennen, G. & 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. & Ĭmamoglu, A. Controlling photons using electromagnetically induced transparency. Nature 413, 273–276 (2001).
Bouchet, F., Gupta, S. & Mukamel, D. Thermodynamics and dynamics of systems with long-range interactions. Physica A 389, 4389–4405 (2010).
Gullans, M. et al. Nanoplasmonic lattices for ultracold atoms. Phys. Rev. Lett. 109, 235309 (2012).
Romero-Isart, O., Navau, C., Sanchez, A., Zoller, P. & Cirac, J. I. Superconducting vortex lattices for ultracold atoms. Phys. Rev. Lett. 111, 145304 (2013).
Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2011).
Buhmann, S. Y. & Welsch, D.-G. Dispersion forces in macroscopic quantum electrodynamics. Prog. Quant. Electron. 31, 51–130 (2007).
John, S. & Wang, J. Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms. Phys. Rev. Lett. 64, 2418–2421 (1990).
Kurizki, G. Two-atom resonant radiative coupling in photonic band structures. Phys. Rev. A 42, 2915–2924 (1990).
Lambropoulos, P., Nikolopoulos, G. M., Nielsen, T. R. & Bay, S. Fundamental quantum optics in structured reservoirs. Rep. Prog. Phys. 63, 455–503 (2000).
Shahmoon, E. & Kurizki, G. Nonradiative interaction and entanglement between distant atoms. Phys. Rev. A 87, 033831 (2013).
Vetsch, E. et al. Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber. Phys. Rev. Lett. 104, 203603 (2010).
Goban, A. et al. Demonstration of a state-insensitive, compensated nanofiber trap. Phys. Rev. Lett. 109, 033603 (2012).
Thompson, J. D. et al. Coupling a single trapped atom to a nanoscale optical cavity. Science 340, 1202–1205 (2013).
Goban, A. et al. Atom–light interactions in photonic crystals. Nature Commun. 5, 3808 (2014).
Yu, S.-P. et al. Nanowire photonic crystal waveguides for single-atom trapping and strong light–matter interactions. Appl. Phys. Lett. 104, 111103 (2014).
Tiecke, T. et al. Nanophotonic quantum phase switch with a single atom. Nature 508, 241–244 (2014).
Chang, D. E., Cirac, J. I. & Kimble, H. J. Self-organization of atoms along a nanophotonic waveguide. Phys. Rev. Lett. 110, 113606 (2013).
Douglas, J. S. et al. Quantum many-body models with cold atoms coupled to photonic crystals. Nature Photon. http://dx.doi.org/10.1038/nphoton.2015.57 (2015).
Cho, J., Angelakis, D. G. & Bose, S. Fractional quantum Hall state in coupled cavities. Phys. Rev. Lett. 101, 246809 (2008).
Diehl, S., Rico, E., Baranov, M. A. & Zoller, P. Topology by dissipation in atomic quantum wires. Nature Phys. 7, 971–977 (2011).
Bardyn, C. et al. Topology by dissipation. New J. Phys. 15, 085001 (2013).
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).
Yannopapas, V. Optical forces near a plasmonic nanostructure. Phys. Rev. B 78, 045412 (2008).
Contreras-Reyes, A. M. et al. Casimir–Polder interaction between an atom and a dielectric grating. Phys. Rev. A 82, 052517 (2010).
Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).
Büchler, H. P. et al. Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential. Phys. Rev. Lett. 98, 060404 (2007).
Hauke, P. et al. Complete devil's staircase and crystal–superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation. New J. Phys. 12, 113037 (2010).
Maik, M., Hauke, P., Dutta, O., Zakrzewski, J. & Lewenstein, M. Quantum spin models with long-range interactions and tunnelings: a quantum Monte Carlo study. New J. Phys. 14, 113006 (2012).
Trefzger, C., Menotti, C. & Lewenstein, M. Ultracold dipolar gas in an optical lattice: the fate of metastable states. Phys. Rev. A 78, 043604 (2008).
Hauke, P. & Tagliacozzo, L. Spread of correlations in long-range interacting quantum systems. Phys. Rev. Lett. 111, 207202 (2013).
Verstraete, F., Wolf, M. M. & Cirac, J. I. Quantum computation and quantum-state engineering driven by dissipation. Nature Phys. 5, 633–636 (2009).
González-Tudela, A. & Porras, D. Mesoscopic entanglement induced by spontaneous emission in solid-state quantum optics. Phys. Rev. Lett. 110, 080502 (2013).
Rodriguez, A. W., McCauley, A. P., Joannopoulos, J. D. & Johnson, S. G. Casimir forces in the time domain: theory. Phys. Rev. A 80, 012115 (2009).
Hung, C.-L., Meenehan, S. M., Chang, D. E., Painter, O. & Kimble, H. J. Trapped atoms in one-dimensional photonic crystals. New J. Phys. 15, 083026 (2013).
Greiner, M. Ultracold Quantum Gases in Three-Dimensional Optical Lattice Potentials PhD thesis, Ludwig-Maximilians-Universität München (2003).
Shen, J.-T. & Fan, S. Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits. Phys. Rev. Lett. 95, 213001 (2005).
Johnson, S. G. & Joannopoulos, J. D. Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. Opt. Express 8, 173–190 (2001).
Breuer, H.-P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford Univ. Press, 2002).
Srinivasan, K. & Painter, O. Momentum space design of high-Q photonic crystal optical cavities. Opt. Express 10, 670–684 (2002).
Taguchi, Y., Takahashi, Y., Sato, Y., Asano, T. & Noda, S. Statistical studies of photonic heterostructure nanocavities with an average Q factor of three million. Opt. Express 19, 11916–11921 (2011).
Sekoguchi, H., Takahashi, Y., Asano, T. & Noda, S. Photonic crystal nanocavity with a Q-factor of˜ 9 million. Opt. Express 22, 916–924 (2014).
The authors thank O. Painter, J. Muñiz and S. Meenehan for discussions. The work of A.G.-T. and J.I.C. was funded by European Union integrated project ‘Simulators and Interfaces with Quantum Systems’ (SIQS). A.G.-T. also acknowledges support from the Alexander Von Humboldt Foundation and Intra-European Fellowship NanoQuIS (625955). J.I.C. acknowledges support as a Moore Distinguished Scholar. D.E.C. acknowledges support from Fundacio Privada Cellex Barcelona. H.J.K. and C.-L.H. acknowledge funding by the Institute for Quantum Information and Matter, a National Science Foundation (NSF) Physics Frontier Center, with support of the Moore Foundation, by the Air Force Office of Scientific Research, Quantum Memories in Photon-Atomic-Solid State Systems (QuMPASS) Multidisciplinary University Research Initiatives (MURI), by the Department of Defense National Security Science and Engineering Faculty Fellows (DoD NSSEFF) programme, and by NSF PHY1205729. H.J.K. acknowledges support as a Max Planck Institute for Quantum Optics Distinguished Scholar.
The authors declare no competing financial interests.
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González-Tudela, A., Hung, CL., Chang, D. et al. Subwavelength vacuum lattices and atom–atom interactions in two-dimensional photonic crystals. Nature Photon 9, 320–325 (2015). https://doi.org/10.1038/nphoton.2015.54
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