- Letter
- Open Access
Synthetic Landau levels and robust chiral edge states for dark-state polaritons in a static and scalable continuum media
Phys. Rev. Research 5, L042029 – Published 27 November, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L042029
Abstract
We demonstrate the generation and dynamical control of synthetic Landau levels and robust chiral edge states for neutral dark-state polaritons using electromagnetically induced transparency in our theoretical studies. We adopt an optical approach to produce synthetic magnetic fields for dark-state polaritons in the static laboratory frame. In our scalable system, an Aharonov-Bohm phase is obtained along a closed loop in a continuous material rather than a sophisticated lattice structure. Our scheme paves the way toward versatile quantum simulators, dynamically controllable photonic circuits, and generators for exotic states of light carrying topological winding numbers.
Physics Subject Headings (PhySH)
Article Text
References (88)
- K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45, 494 (1980).
- R. B. Laughlin, Quantized Hall conductivity in two dimensions, Phys. Rev. B 23, 5632 (1981).
- D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
- K. von Klitzing, Quantum Hall effect: Discovery and application, Annu. Rev. Condens. Matter Phys. 8, 13 (2017).
- T. H. Hansson, M. Hermanns, S. H. Simon, and S. F. Viefers, Quantum Hall physics: Hierarchies and conformal field theory techniques, Rev. Mod. Phys. 89, 025005 (2017).
- K. von Klitzing, T. Chakraborty, P. Kim, V. Madhavan, X. Dai, J. McIver, Y. Tokura, L. Savary, D. Smirnova, A. M. Rey, C. Felser, J. Gooth, and X. Qi, 40 years of the quantum Hall effect, Nat. Rev. Phys. 2, 397 (2020).
- J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Colloquium: Artificial gauge potentials for neutral atoms, Rev. Mod. Phys. 83, 1523 (2011).
- M. Lewenstein, S. Anna, and A. Verònica, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems (Oxford University Press, Oxford, 2012).
- N. Goldman, G. Juzeliūnas, P. Öhberg, and I. B. Spielman, Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys. 77, 126401 (2014).
- N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices, Nat. Phys. 12, 639 (2016).
- Y.-J. Lin and I. B. Spielman, Synthetic gauge potentials for ultracold neutral atoms, J. Phys. B: At. Mol. Opt. Phys. 49, 183001 (2016).
- N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019).
- V. Galitski, I. B. Spielman, and G. Juzeliūnas, Artificial gauge fields with ultracold atoms, Phys. Today 72(1), 38 (2019).
- M. Hafezi, A. S. Sørensen, E. Demler, and M. D. Lukin, Fractional quantum Hall effect in optical lattices, Phys. Rev. A 76, 023613 (2007).
- F. D. M. Haldane and S. Raghu, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett. 100, 013904 (2008).
- M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, Imaging topological edge states in silicon photonics, Nat. Photon. 7, 1001 (2013).
- M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Photonic Floquet topological insulators, Nature (London) 496, 196 (2013).
- D.-W. Wang, H. Cai, L. Yuan, S.-Y. Zhu, and R.-B. Liu, Topological phase transitions in superradiance lattices, Optica 2, 712 (2015).
- M. Schmidt, S. Kessler, V. Peano, O. Painter, and F. Marquardt, Optomechanical creation of magnetic fields for photons on a lattice, Optica 2, 635 (2015).
- N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Synthetic Landau levels for photons, Nature (London) 534, 671 (2016).
- M. Minkov and V. Savona, Haldane quantum Hall effect for light in a dynamically modulated array of resonators, Optica 3, 200 (2016).
- P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Lasing in topological edge states of a one-dimensional lattice, Nat. Photon. 11, 651 (2017).
- M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science 359, eaar4005 (2018).
- S. Mukherjee, H. K. Chandrasekharan, P. Öhberg, N. Goldman, and R. R. Thomson, State-recycling and time-resolved imaging in topological photonic lattices, Nat. Commun. 9, 4209 (2018).
- T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
- L. W. Clark, N. Schine, C. Baum, N. Jia, and J. Simon, Observation of Laughlin states made of light, Nature (London) 582, 41 (2020).
- A. D'Errico, F. Cardano, M. Maffei, A. Dauphin, R. Barboza, C. Esposito, B. Piccirillo, M. Lewenstein, P. Massignan, and L. Marrucci, Two-dimensional topological quantum walks in the momentum space of structured light, Optica 7, 108 (2020).
- I. Carusotto, A. A. Houck, A. J. Kollár, P. Roushan, D. I. Schuster, and J. Simon, Photonic materials in circuit quantum electrodynamics, Nat. Phys. 16, 268 (2020).
- O. Jamadi, E. Rozas, G. Salerno, M. Milićević, T. Ozawa, I. Sagnes, A. Lemaître, L. Le Gratiet, A. Harouri, I. Carusotto, J. Bloch, and A. Amo, Direct observation of photonic Landau levels and helical edge states in strained honeycomb lattices, Light Sci. Appl. 9, 144 (2020).
- O. Kocharovskaya and Y. I. Khanin, Population trapping and coherent bleaching of a three-level medium by a periodic train of ultrashort pulses, Zh. Eksp. Teor. Fiz. 90, 1610 (1986).
- E. Arimondo, Coherent population trapping in laser spectroscopy, Prog. Opt. 35, 257 (1996).
- S. E. Harris, Electromagnetically induced transparency, Phys. Today 50(7), 36 (1997).
- M. D. Lukin, Colloquium: Trapping and manipulating photon states in atomic ensembles, Rev. Mod. Phys. 75, 457 (2003).
- M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Electromagnetically induced transparency: Optics in coherent media, Rev. Mod. Phys. 77, 633 (2005).
- N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, Stimulated Raman adiabatic passage in physics, chemistry, and beyond, Rev. Mod. Phys. 89, 015006 (2017).
- K.-J. Boller, A. Imamoğlu, and S. E. Harris, Observation of electromagnetically induced transparency, Phys. Rev. Lett. 66, 2593 (1991).
- L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Light speed reduction to 17 metres per second in an ultracold atomic gas, Nature (London) 397, 594 (1999).
- M. Fleischhauer and M. D. Lukin, Dark-state polaritons in electromagnetically induced transparency, Phys. Rev. Lett. 84, 5094 (2000).
- G. Juzeliūnas and H. J. Carmichael, Systematic formulation of slow polaritons in atomic gases, Phys. Rev. A 65, 021601(R) (2002).
- A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, Transporting and time reversing light via atomic coherence, Phys. Rev. Lett. 88, 103601 (2002).
- M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Stationary pulses of light in an atomic medium, Nature (London) 426, 638 (2003).
- S. A. Moiseev and B. S. Ham, Quantum manipulation of two-color stationary light: Quantum wavelength conversion, Phys. Rev. A 73, 033812 (2006).
- F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M. Fleischhauer, Dark-state polaritons for multicomponent and stationary light fields, Phys. Rev. A 77, 063823 (2008).
- Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Stationary light pulses in cold atomic media and without Bragg gratings, Phys. Rev. Lett. 102, 213601 (2009).
- A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, Photon-photon interactions via Rydberg blockade, Phys. Rev. Lett. 107, 133602 (2011).
- D. Petrosyan, J. Otterbach, and M. Fleischhauer, Electromagnetically induced transparency with Rydberg atoms, Phys. Rev. Lett. 107, 213601 (2011).
- T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, Quantum nonlinear optics with single photons enabled by strongly interacting atoms, Nature (London) 488, 57 (2012).
- J. D. Pritchard, K. J. Weatherill, and C. S. Adams, Nonlinear optics using cold Rydberg atoms, in Annual Review of Cold Atoms and Molecules Vol. 1 (World Scientific, Singapore, 2012), pp. 301–350.
- M. Gärttner, S. Whitlock, D. W. Schönleber, and J. Evers, Collective excitation of Rydberg-atom ensembles beyond the superatom model, Phys. Rev. Lett. 113, 233002 (2014).
- C. R. Murray and T. Pohl, Coherent photon manipulation in interacting atomic ensembles, Phys. Rev. X 7, 031007 (2017).
- D. Roy, C. M. Wilson, and O. Firstenberg, Colloquium: Strongly interacting photons in one-dimensional continuum, Rev. Mod. Phys. 89, 021001 (2017).
- K.-T. Chen, B. Kim, C.-C. Su, S.-S. Hsiao, S.-J. Huang, W.-T. Liao, and I. A. Yu, Increasing the decoherence rate of Rydberg polaritons due to accumulating dark Rydberg atoms, Phys. Rev. Res. 4, 023024 (2022).
- D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48, 1559 (1982).
- J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliūnas, and M. Fleischhauer, Effective magnetic fields for stationary light, Phys. Rev. Lett. 104, 033903 (2010).
- N. R. Cooper, Rapidly rotating atomic gases, Adv. Phys. 57, 539 (2008).
- P. C. Haljan, I. Coddington, P. Engels, and E. A. Cornell, Driving Bose-Einstein-condensate vorticity with a rotating normal cloud, Phys. Rev. Lett. 87, 210403 (2001).
- A. Di Piazza, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys. 84, 1177 (2012).
- M. A. Khamehchi, K. Hossain, M. E. Mossman, Y. Zhang, T. Busch, M. M. Forbes, and P. Engels, Negative-mass hydrodynamics in a spin-orbit–coupled Bose-Einstein condensate, Phys. Rev. Lett. 118, 155301 (2017).
- C. M. Bender and S. Boettcher, Real spectra in non-Hermitian Hamiltonians having symmetry, Phys. Rev. Lett. 80, 5243 (1998).
- C. E. Rüter, K. G Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Observation of parity–time symmetry in optics, Nat. Phys. 6, 192 (2010).
- G. T. Campbell, Y.-W. Cho, J. Su, J. Everett, N. Robins, P. K. Lam, and B. Buchler, Direct imaging of slow, stored and stationary EIT polaritons, Quantum Sci. Technol. 2, 034010 (2017).
- S.-W. Su, Z.-K. Lu, S.-C. Gou, and W.-T. Liao, Controllable vacuum-induced diffraction of matter-wave superradiance using an all-optical dispersive cavity, Sci. Rep. 6, 35402 (2016).
- Y.-H. Kuan and W.-T. Liao, Transition between amplified spontaneous emission and superfluorescence in a longitudinally pumped medium by an x-ray free-electron-laser pulse, Phys. Rev. A 101, 023836 (2020).
- M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
- D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
- Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, and I. B. Spielman, Synthetic magnetic fields for ultracold neutral atoms, Nature (London) 462, 628 (2009).
- Y.-J. Lin, R. L. Compton, K. Jimenez-Garcia, W. D. Phillips, J. V. Porto, and I. B. Spielman, A synthetic electric force acting on neutral atoms, Nat. Phys. 7, 531 (2011).
- Y.-F. Hsiao, H.-S. Chen, P.-J. Tsai, and Y.-C. Chen, Cold atomic media with ultrahigh optical depths, Phys. Rev. A 90, 055401 (2014).
- F. Blatt, T. Halfmann, and T. Peters, One-dimensional ultracold medium of extreme optical depth, Opt. Lett. 39, 446 (2014).
- Y.-F. Hsiao, P.-J. Tsai, H.-S. Chen, S.-X. Lin, C.-C. Hung, C.-H. Lee, Y.-H. Chen, Y.-F. Chen, I. A. Yu, and Y.-C. Chen, Highly efficient coherent optical memory based on electromagnetically induced transparency, Phys. Rev. Lett. 120, 183602 (2018).
- A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, Bose-Einstein condensation of atoms in a uniform potential, Phys. Rev. Lett. 110, 200406 (2013).
- N. Navon, R. P. Smith, and Z. Hadzibabic, Quantum gases in optical boxes, Nat. Phys. 17, 1334 (2021).
- Here we provide the calculations for the 2D atomic gas with up to , which are based on experimental data from Ref. [88]. Evaporative cooling reduces the atom number and increases the density, and we obtain the scaling law in Ref. [88]: temperature and . For example, the numbers for Fig. 3 with , or 4 mm, and mm are as follows: We start with a nonuniform 3D cloud with atoms and and then increase to with a reduced number . The volume is about , where we make mm. To make mm with a fixed , we use a smaller density and a larger number with mm.
- V. Gavryusev, A. Signoles, M. Ferreira-Cao, G. Zürn, C. S. Hofmann, G. Günter, H. Schempp, M. Robert-de Saint-Vincent, S. Whitlock, and M. Weidemüller, Density matrix reconstruction of three-level atoms via Rydberg electromagnetically induced transparency, J. Phys. B: At. Mol. Opt. Phys. 49, 164002 (2016).
- O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, Stopping light via hot atoms, Phys. Rev. Lett. 86, 628 (2001).
- D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Storage of light in atomic vapor, Phys. Rev. Lett. 86, 783 (2001).
- Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Coherent optical memory with high storage efficiency and large fractional delay, Phys. Rev. Lett. 110, 083601 (2013).
- J. Radić, T. A. Sedrakyan, I. B. Spielman, and V. Galitski, Vortices in spin-orbit-coupled Bose-Einstein condensates, Phys. Rev. A 84, 063604 (2011).
- Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, Low-light-level cross-phase-modulation based on stored light pulses, Phys. Rev. Lett. 96, 043603 (2006).
- W.-T. Liao, C. H. Keitel, and A. Pálffy, All-electromagnetic control of broadband quantum excitations using gradient photon echoes, Phys. Rev. Lett. 113, 123602 (2014).
- S.-W. Su, S.-C. Gou, L. Y. Chew, Y.-Y. Chang, I. A. Yu, A. Kalachev, and W.-T. Liao, Setting a disordered password on a photonic memory, Phys. Rev. A 95, 061805(R) (2017).
- N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Generation of optical phase singularities by computer-generated holograms, Opt. Lett. 17, 221 (1992).
- L. Marrucci, C. Manzo, and D. Paparo, Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media, Phys. Rev. Lett. 96, 163905 (2006).
- P. Vaity, J. Banerji, and R. P. Singh, Measuring the topological charge of an optical vortex by using a tilted convex lens, Phys. Lett. A 377, 1154 (2013).
- D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, Controlled generation of higher-order Poincaré sphere beams from a laser, Nat. Photon. 10, 327 (2016).
- I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
- Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
- Y.-J. Lin, A. R. Perry, R. L. Compton, I. B. Spielman, and J. V. Porto, Rapid production of Bose-Einstein condensates in a combined magnetic and optical potential, Phys. Rev. A 79, 063631 (2009).