Photonic molecule

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Photonic molecules are a form of matter in which photons bind together to form "molecules". [1] [2] [3] They were first predicted in 2007. Photonic molecules are formed when individual (massless) photons "interact with each other so strongly that they act as though they have mass". [4] In an alternative definition (which is not equivalent), photons confined to two or more coupled optical cavities also reproduce the physics of interacting atomic energy levels, and have been termed as photonic molecules.

Contents

Researchers drew analogies between the phenomenon and the fictional "lightsaber" from Star Wars . [4] [5]

Construction

Gaseous rubidium atoms were pumped into a vacuum chamber. The cloud was cooled using lasers to just a few degrees above absolute zero. Using weak laser pulses, small numbers of photons were fired into the cloud. [4]

As the photons entered the cloud, their energy excited atoms along their path, causing them to lose speed. Inside the cloud medium, the photons dispersively coupled to strongly interacting atoms in highly excited Rydberg states. This caused the photons to behave as massive particles with strong mutual attraction (photon molecules). Eventually the photons exited the cloud together as normal photons (often entangled in pairs). [4]

The effect is caused by a so-called Rydberg blockade, which, in the presence of one excited atom, prevents nearby atoms from being excited to the same degree. In this case, as two photons enter the atomic cloud, the first excites an atom, annihilating itself in the interaction, but the transmitted energy must move forward inside the excited atom before the second photon can excite nearby atoms. In effect the two photons push and pull each other through the cloud as their energy is passed from one atom to the next, forcing them to interact. This photonic interaction is mediated by the electromagnetic interaction between photons and atoms. [4]

Possible applications

The interaction of the photons suggests that the effect could be employed to build a system that can preserve quantum information, and process it using quantum logic operations. [4]

The system could also be useful in classical computing, given the much-lower power required to manipulate photons than electrons. [4]

It may be possible to arrange the photonic molecules in such a way within the medium that they form larger two-dimensional structures (similar to drawings). [4]

Interacting optical cavities as photonic molecules

The term photonic molecule has been also used since 1998 for an unrelated phenomenon involving electromagnetically interacting optical microcavities. The properties of quantized confined photon states in optical micro- and nanocavities are very similar to those of confined electron states in atoms. [6] Owing to this similarity, optical microcavities can be termed 'photonic atoms'. Taking this analogy even further, a cluster of several mutually-coupled photonic atoms forms a photonic molecule. [7] When individual photonic atoms are brought into close proximity, their optical modes interact and give rise to a spectrum of hybridized super-modes of photonic molecules. [8] This is very similar to what happens when two isolated systems are coupled, like two hydrogen atomic orbitals coming together to form the bonding and antibonding orbitals of the hydrogen molecule, which are hybridized super-modes of the total coupled system.

"A micrometer-sized piece of semiconductor can trap photons inside it in such a way that they act like electrons in an atom. Now the 21 September PRL describes a way to link two of these "photonic atoms" together. The result of such a close relationship is a "photonic molecule," whose optical modes bear a strong resemblance to the electronic states of a diatomic molecule like hydrogen." [9] "Photonic molecules, named by analogy with chemical molecules, are clusters of closely located electromagnetically interacting microcavities or "photonic atoms"." [10] "Optically coupled microcavities have emerged as photonic structures with promising properties for investigation of fundamental science as well as for applications." [11]

The first photonic realization of the two-level system of a photonic molecule was by Spreew et al., [12] who used optical fibers to realize a ring resonator, although they did not use the term "photonic molecule". The two modes forming the molecule could then be the polarization modes of the ring or the clockwise and counterclockwise modes of the ring. This was followed by the demonstration of a lithographically fabricated photonic molecule, inspired by an analogy with a simple diatomic molecule. [13] However, other nature-inspired PM structures (such as ‘photonic benzene’) have been proposed and shown to support confined optical modes closely analogous to the ground-state molecular orbitals of their chemical counterparts. [14]

Photonic molecules offer advantages over isolated photonic atoms in a variety of applications, including bio(chemical) sensing, [15] [16] cavity optomechanics, [17] [18] and microlasers, [19] [20] [21] [22] Photonic molecules can also be used as quantum simulators of many-body physics and as building blocks of future optical quantum information processing networks. [23]

In complete analogy, clusters of metal nanoparticles – which support confined surface plasmon states – have been termed ‘plasmonic molecules.” [24] [25] [26] [27] [28]

Finally, hybrid photonic-plasmonic (or opto-plasmonic) [29] [30] [31] [32] and elastic molecules [33] have also been proposed and demonstrated.

See also

Related Research Articles

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References

  1. Shen, Jung-Tsung; Fan, Shanhui (2007-04-13). "Strongly Correlated Two-Photon Transport in a One-Dimensional Waveguide Coupled to a Two-Level System". Physical Review Letters. 98 (15): 153003. arXiv: quant-ph/0701170 . Bibcode:2007PhRvL..98o3003S. doi:10.1103/PhysRevLett.98.153003. PMID   17501344. S2CID   37715281.
  2. Shen, Jung-Tsung; Fan, Shanhui (2007-12-27). "Strongly correlated multiparticle transport in one dimension through a quantum impurity". Physical Review A. 76 (6): 062709. arXiv: 0707.4335 . Bibcode:2007PhRvA..76f2709S. doi:10.1103/PhysRevA.76.062709. S2CID   119608892.
  3. Deutsch, Ivan H.; Chiao, Raymond Y.; Garrison, John C. (1992-12-21). "Diphotons in a nonlinear Fabry-Pérot resonator: Bound states of interacting photons in an optical quantum wire". Physical Review Letters. 69 (25): 3627–3630. Bibcode:1992PhRvL..69.3627D. doi:10.1103/PhysRevLett.69.3627. PMID   10046872.
  4. 1 2 3 4 5 6 7 8 "Seeing light in a new light: Scientists create never before seen form of matter". Science-daily.com. September 2013.
  5. Firstenberg, O.; Peyronel, T.; Liang, Q. Y.; Gorshkov, A. V.; Lukin, M. D.; Vuletić, V. (2013). "Attractive photons in a quantum nonlinear medium" (PDF). Nature (Submitted manuscript). 502 (7469): 71–75. Bibcode:2013Natur.502...71F. doi:10.1038/nature12512. hdl: 1721.1/91605 . PMID   24067613. S2CID   1699899.
  6. Benson, T. M.; Boriskina, S. V.; Sewell, P.; Vukovic, A.; Greedy, S. C.; Nosich, A. I. (2006). "Micro-Optical Resonators for Microlasers and Integrated Optoelectronics". Frontiers in Planar Lightwave Circuit Technology. NATO Science Series II: Mathematics, Physics and Chemistry. Vol. 216. p. 39. CiteSeerX   10.1.1.518.8691 . doi:10.1007/1-4020-4167-5_02. ISBN   978-1-4020-4164-8. S2CID   8299535.
  7. Boriskina, S. V. (2010). "Photonic Molecules and Spectral Engineering". Photonic Microresonator Research and Applications. Springer Series in Optical Sciences. Vol. 156. pp. 393–421. arXiv: 1207.1274 . doi:10.1007/978-1-4419-1744-7_16. ISBN   978-1-4419-1743-0. S2CID   13276928.
  8. Rakovich, Y.; Donegan, J.; Gerlach, M.; Bradley, A.; Connolly, T.; Boland, J.; Gaponik, N.; Rogach, A. (2004). "Fine structure of coupled optical modes in photonic molecules". Physical Review A. 70 (5): 051801. Bibcode:2004PhRvA..70e1801R. doi:10.1103/PhysRevA.70.051801. hdl: 2262/29166 .
  9. Antia, Meher (1998). "A Molecule of Light". Physical Review Focus. Vol. 2. doi:10.1103/PhysRevFocus.2.14.
  10. Boriskina, Svetlana V.; Benson, Trevor M.; Sewell, Phillip (2007). "Photonic molecules made of matched and mismatched microcavities: New functionalities of microlasers and optoelectronic components". In Kudryashov, Alexis V; Paxton, Alan H; Ilchenko, Vladimir S (eds.). Laser Resonators and Beam Control IX. Vol. 6452. pp. 64520X. arXiv: 0704.2154 . doi:10.1117/12.714344. S2CID   55006344.
  11. Grossmann, Tobias; Wienhold, Tobias; Bog, Uwe; Beck, Torsten; Friedmann, Christian; Kalt, Heinz; Mappes, Timo (2013). "Polymeric photonic molecule super-mode lasers on silicon". Light: Science & Applications. 2 (5): e82. Bibcode:2013LSA.....2E..82G. doi: 10.1038/lsa.2013.38 .
  12. Spreeuw, R. J. C.; van Druten, N. J.; Beijersbergen, M. W.; Eliel, E. R.; Woerdman, J. P. (1990-11-19). "Classical realization of a strongly driven two-level system" (PDF). Physical Review Letters. 65 (21): 2642–2645. Bibcode:1990PhRvL..65.2642S. doi:10.1103/PhysRevLett.65.2642. PMID   10042655.
  13. Bayer, M.; Gutbrod, T.; Reithmaier, J.; Forchel, A.; Reinecke, T.; Knipp, P.; Dremin, A.; Kulakovskii, V. (1998). "Optical Modes in Photonic Molecules". Physical Review Letters. 81 (12): 2582–2585. Bibcode:1998PhRvL..81.2582B. doi:10.1103/PhysRevLett.81.2582.
  14. Lin, B. (2003). "Variational analysis for photonic molecules: Application to photonic benzene waveguides". Physical Review E. 68 (3): 036611. Bibcode:2003PhRvE..68c6611L. doi:10.1103/PhysRevE.68.036611. PMID   14524916.
  15. Boriskina, S. V. (2006). "Spectrally engineered photonic molecules as optical sensors with enhanced sensitivity: A proposal and numerical analysis". Journal of the Optical Society of America B. 23 (8): 1565. arXiv: physics/0603228 . Bibcode:2006JOSAB..23.1565B. doi:10.1364/JOSAB.23.001565. S2CID   59580074.
  16. Boriskina, S. V.; Dal Negro, L. (2010). "Self-referenced photonic molecule bio(chemical)sensor". Optics Letters. 35 (14): 2496–8. Bibcode:2010OptL...35.2496B. CiteSeerX   10.1.1.470.1926 . doi:10.1364/OL.35.002496. PMID   20634875.
  17. Jiang, X.; Lin, Q.; Rosenberg, J.; Vahala, K.; Painter, O. (2009). "High-Q double-disk microcavities for cavity optomechanics". Optics Express. 17 (23): 20911–9. Bibcode:2009OExpr..1720911J. doi: 10.1364/OE.17.020911 . PMID   19997328.
  18. Hu, Y. W.; Xiao, Y. F.; Liu, Y. C.; Gong, Q. (2013). "Optomechanical sensing with on-chip microcavities". Frontiers of Physics. 8 (5): 475–490. Bibcode:2013FrPhy...8..475H. doi:10.1007/s11467-013-0384-y. S2CID   122299018.
  19. Hara, Y.; Mukaiyama, T.; Takeda, K.; Kuwata-Gonokami, M. (2003). "Photonic molecule lasing". Optics Letters. 28 (24): 2437–9. Bibcode:2003OptL...28.2437H. doi:10.1364/OL.28.002437. PMID   14690107.
  20. Nakagawa, A.; Ishii, S.; Baba, T. (2005). "Photonic molecule laser composed of GaInAsP microdisks". Applied Physics Letters. 86 (4): 041112. Bibcode:2005ApPhL..86d1112N. doi:10.1063/1.1855388.
  21. Boriskina, S. V. (2006). "Theoretical prediction of a dramatic Q-factor enhancement and degeneracy removal of whispering gallery modes in symmetrical photonic molecules". Optics Letters. 31 (3): 338–40. Bibcode:2006OptL...31..338B. doi:10.1364/OL.31.000338. PMID   16480201. S2CID   22088884.
  22. Smotrova, E. I.; Nosich, A. I.; Benson, T. M.; Sewell, P. (2006). "Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes". Optics Letters. 31 (7): 921–3. Bibcode:2006OptL...31..921S. doi:10.1364/OL.31.000921. PMID   16599212.
  23. Hartmann, M.; Brandão, F.; Plenio, M. (2007). "Effective Spin Systems in Coupled Microcavities". Physical Review Letters. 99 (16): 160501. arXiv: 0704.3056 . Bibcode:2007PhRvL..99p0501H. doi:10.1103/PhysRevLett.99.160501. PMID   17995228. S2CID   592659.
  24. Nordlander, P.; Oubre, C.; Prodan, E.; Li, K.; Stockman, M. I. (2004). "Plasmon Hybridization in Nanoparticle Dimers". Nano Letters. 4 (5): 899–903. Bibcode:2004NanoL...4..899N. doi:10.1021/nl049681c.
  25. Fan, J. A.; Bao, K.; Wu, C.; Bao, J.; Bardhan, R.; Halas, N. J.; Manoharan, V. N.; Shvets, G.; Nordlander, P.; Capasso, F. (2010). "Fano-like Interference in Self-Assembled Plasmonic Quadrumer Clusters". Nano Letters. 10 (11): 4680–5. Bibcode:2010NanoL..10.4680F. doi:10.1021/nl1029732. PMID   20923179.
  26. Liu, N.; Mukherjee, S.; Bao, K.; Brown, L. V.; Dorfmüller, J.; Nordlander, P.; Halas, N. J. (2012). "Magnetic Plasmon Formation and Propagation in Artificial Aromatic Molecules". Nano Letters. 12 (1): 364–9. Bibcode:2012NanoL..12..364L. doi:10.1021/nl203641z. PMID   22122612.
  27. Yan, B.; Boriskina, S. V.; Reinhard, B. R. M. (2011). "Optimizing Gold Nanoparticle Cluster Configurations (n≤ 7) for Array Applications". The Journal of Physical Chemistry C. 115 (11): 4578–4583. doi:10.1021/jp112146d. PMC   3095971 . PMID   21603065.
  28. Yan, B.; Boriskina, S. V.; Reinhard, B. R. M. (2011). "Design and Implementation of Noble Metal Nanoparticle Cluster Arrays for Plasmon Enhanced Biosensing". The Journal of Physical Chemistry C. 115 (50): 24437–24453. doi:10.1021/jp207821t. PMC   3268044 . PMID   22299057.
  29. Boriskina, S. V.; Reinhard, B. M. (2011). "Spectrally and spatially configurable superlenses for optoplasmonic nanocircuits". Proceedings of the National Academy of Sciences. 108 (8): 3147–3151. arXiv: 1110.6822 . Bibcode:2011PNAS..108.3147B. doi: 10.1073/pnas.1016181108 . PMC   3044402 . PMID   21300898.
  30. Boriskina, S. V.; Reinhard, B. R. M. (2011). "Adaptive on-chip control of nano-optical fields with optoplasmonic vortex nanogates". Optics Express. 19 (22): 22305–15. arXiv: 1111.0022 . Bibcode:2011OExpr..1922305B. doi:10.1364/OE.19.022305. PMC   3298770 . PMID   22109072.
  31. Hong, Y.; Pourmand, M.; Boriskina, S. V.; Reinhard, B. R. M. (2013). "Enhanced Light Focusing in Self-Assembled Optoplasmonic Clusters with Subwavelength Dimensions". Advanced Materials. 25 (1): 115–119. Bibcode:2013AdM....25..115H. doi:10.1002/adma.201202830. PMID   23055393. S2CID   205247073.
  32. Ahn, W.; Boriskina, S. V.; Hong, Y.; Reinhard, B. R. M. (2012). "Photonic–Plasmonic Mode Coupling in On-Chip Integrated Optoplasmonic Molecules". ACS Nano. 6 (1): 951–60. doi:10.1021/nn204577v. PMID   22148502.
  33. Martínez-Argüello, A. M.; Toledano-Marino, M. P.; Terán-Juárez, A. E.; Flores-Olmedo, E.; Báez, G.; Sadurní, E.; Méndez-Sánchez, R. A. (2022-02-21). "Molecular orbitals of an elastic artificial benzene". Physical Review A. 105 (2): 022826. arXiv: 2108.12027 . Bibcode:2022PhRvA.105b2826M. doi:10.1103/PhysRevA.105.022826. S2CID   237347078.