Mage's Rhizome

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====== Polaritons ======

===== Selected Literature =====

  * Polaritonic Chemistry
    -  Pioneers of the field, good review (from experimentalis perspective):\\ Ebbesen, T. W. Hybrid light–matter states in a molecular and material science perspective. Acc. Chem. Res. 49, 2403–2412 (2016)
    - Theoretical Minimal model for polaritonic chemistry: \\ Galego, J., Garcia-Vidal, F. J. & Feist, J. Cavity-induced modifications of molecular structure in the strong-coupling regime. Phys. Rev. X 5, 041022 (2015)
   

===== General Properties =====

  * what are the conditions for high Rabi-frequencies/strong coupling? 
    * large oscillator strength -> much bigger in organic materials (because?) 
    * small excitation linewidth (so small inhomogeneous broading for instance)
    * molecule assemblies/liquids/? with particle density $N/\nu$, in a cavity have enhanced coupling $\omega_{Rabi}\propto \sqrt{N/\nu}$ (**REFERENCE?**)
  * properties of (molecular) polaritons
    * N molecules generate N+1 collective states: 
      * 2 polariton states P+,P-, and 
      * N-1 "dark states" (excitation from groundstate forbidden)
    * collective wave functions are strongly delocalized, P- emission is spatially coherent: "molecules that are micrometers apart emit in-phase!"
    * dispersion: dependent on angle/direction (because light-matter coupling is!  $\rightarrow d\cdot E$)
      * k=0 (normal incidence): matter and light contribute equally
      * large k: P+ more photonic, while P- more matter-like
    * Life times: can vary a lot, especially there are a lot of cases, where the lifetime of the Polariton is much longer than the lifetimes of the constituents (matter, photon)! (some sources can be found in [1])


===== Effects =====

  * "Organic materials present a particularly favorable case, as the Frenkel excitons in these materials possess large binding energies, large dipole moments, and can reach high densities." [1] 
    * First experiment with such organic semiconductors: \\ D. G. Lidzey, D. D. C. Bradley, M. S. Skolnick, T. Virgili, S. Walker, and D. M. Whittaker, Strong Exciton-Photon Coupling in an Organic Semiconductor Microcavity, Nature (London) 395, 53 \\ use tetra-(2,6-t-butyl)phenol-porphyrin zinc (4TBPPZn) as the organic semiconductor, which has high oscillator strength and sufficiently small linewidth
    * organic materials have much more complicated electronic structure than conventional non-organic semiconductors (few level approximations are bad!)
  * investigating polaritons in complex electronic systems (and even taking chemical reactions into account)
    * BOA can break down because polariton introduces intermediate energy level in the large gap between electron and nucleus energies
    * strong coupling due to collective coupling of many molecules to one mode ($w_{Rabi}$ enhanced by $\sqrt(N)$): only small fraction of the modes are coupled, rest is "dark", but still affected by the strong coupling [1]
    * Ultra strong coupling (USC): also ground state acquires photonic contribution: 
      * (like super fluid to mott state?): I. Carusotto and C. Ciuti, Quantum Fluids of Light, RevModPhys 85, 299 (2013)
      *  Rabi frequency due to (strong) coupling to vacuum: \\ J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, Modifying Chemical Landscapes by Coupling to Vacuum Fields, Angew. Chem. 124, 1624 (2012)
    * minimal model [1]: 1d valence electron coupled to 1 mode of rest atoms (nuclei plus frozen core electrons), which could be a "stretching" of a phonon mode or of a bond, inter-rest-atom potential modeled by Morse potential (with fitting parameters)
  * polariton lasing (typically exciton polaritons in semiconductors)
    * First experiment: Kéna-Cohen, S.; Forrest, S. R. Room-temperature Polariton Lasing in an Organic Single-crystal Microcavity. Nat. Photonics 2010, 4, 371−375
  *  (Exciton-)Polariton condensates: Byrnes, T., Kim, N. Y. & Yamamoto, Y. Exciton–polariton condensates. Nat. Phys. 10, 803–813 (2014).
    * "photon and exciton dispersions anticross under strong coupling, resulting in two new dispersion relations for the lower polariton (LP, lower energy branch) and upper polariton (UP, higher energy branch)"
    * mass (~10^-4 m_e) and lifetime (dependent on Q-factor of cavity, 10-100 ps possible so far) dominated by photon, interactions instead by excitons (mainly coulomb exchange), but this varies with momentum/dispersion
    * non-equilibrium due to finite lifetime of excitons (induced by scattering) and photons (by mirror quality)
    * condensation is highly non-linear, governed by two mechanisms: 1) dissipation via phonons, 2) dissipation via polariton-polariton scattering
    * measurement easy, as polaritons decay through the mirror as photons that have the same energy and momentum!! (why that?)
    * ongoing discussion on separation/validity: Bose-Einstein-Condensate - Polariton Laser - Photon Laser, main problem lies in the definition of concept either in or out of equilibrium
    * has Berezinskii–Kosterlitz– Thouless (BKT) and BCS pahse
    * first experimental relaization (in orgaanic semiconductor cavity):\\ Plumhof, J. D.; Stöferle, T.; Mai, L.; Scherf, U.; Mahrt, R. F. Room-temperature Bose−Einstein Condensation of Cavity Exciton−Polaritons in a Polymer. Nat. Mater. 2014, 13, 247−252
  * Formation of Polaritons can change chemical reactions significantly
    * Slow down of reaction in e.g. vibrational SC (light coupled to vibration mode) as the splitting changes the vibration frequency and thus the bond strength [2]
    * change of character of reaction: from an associative to a dissociative transition state [2]
  * Ultra-Strong Coupling (USC): also other eigenstates of the matter system are significantly perturbed
    * delocalized nature of polaritons give them good transport properties, also dark-states play a role [2]\\ $\rightarrow$ Förster-type nonradiative transfer rate can be increased by a factor of 7 with an efficiency approaching unity
  * Plasmon-Polaritons
    * Theory (not read yet):\\ Y. Todorov and C. Sirtori, Intersubband polaritons in the electrical dipole gauge, Phys.Rev.B 85, 045304 (2012)
    * Another USC situation: 2d QW of electrons (2 bands) coupled to a 0d-mode (plasmon polaritons)\\ Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato,C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, Ultrastrong Light-Matter Coupling Regime with Polariton Dots Phys. Rev. Lett. 105, 196402 (2010)
  * Application to light-harvesting complexes:\\ Coles, D. M. et al. Strong coupling between chlorosomes of photosynthetic bacteria and a confined optical cavity mode. Nat. Commun. 5, 5561 (2014)
    * proof strong coupling between a "large biological system" (conglomerate of photoactive molecule BChl c that form a chlorosome in a very complicated way) to a cavity: despite a large scattering, polaritons form
    * could be used to make photosynthetic process more efficient
    * They imagine: "since the density of chlorosomes within the green sulfur bacteria is high, it may be possible to strongly couple a living bacteria to a cavity mode resulting in a ‘living polariton’"