Polariton

In physics, a polariton is a quasiparticle that arises when there is a strong interaction (coupling) of an electromagnetic field with an excited state (for example a phonon or exciton in a solid body that has a dipole moment ).

A typical example is the coupling of a collective mechanical lattice oscillation (phonon with frequencies in the optical range and transverse polarization) of a solid to an electromagnetic wave (photon). Typically they form polaritons in interaction with photons in ionic crystals. Excitons are particle-hole excitations in semiconductors or insulators, which also form polaritons in interaction with photons. In metals, surface plasmons with photons also form polaritons, which has led to important applications, since in this way light can be manipulated in the nanoscale, far below its diffraction limit. If you catch excitons in a trap (quantum well) and place them in a microresonator for the coupled photons, you can create a coherent Bose-Einstein condensate of the polaritons. In simple terms, polaritons can be imagined as light, to which properties (mass, repulsive interaction) otherwise only known from solid particles are assigned. For example, they can be exposed to a constant force field in which they show a movement similar to a trajectory parabola (slow reflection).

The polaritons should not be confused with the polarons . With the latter one has to do with fermionic quasiparticles, e.g. B. with an electron plus a "dragged polarization cloud", while the polaritons represent bosonic quasiparticles.

history

The first theoretical considerations come from Kirill Borissowitsch Tolpygo , who in 1950 predicted a bound state of optical phonons and photons. Solomon Isaakowitsch Pekar called them light excitons, but the name polariton introduced by John Hopfield prevailed. Independently from Tolpygo, Huang Kun introduced polaritons in 1951.

The case of plasmons does not concern ion crystals or semiconductors, but for example the electron gas in metals with theoretical and experimental pioneering work in the 1950s. About surface plasmon polaritons (Surface Plasmon Polariton, SPP) was first reported by Andreas Otto in 1968 .

Polaritons in a solid

In a solid body , a polariton is created when an elementary excitation (e.g. phonon, exciton or plasmon ) interacts with photons . The underlying physical phenomena are absorption , reflection or dispersion of electromagnetic radiation by the solid.

In the case of strong coupling of the photons in the solid to other elementary excitations, the effect can no longer be described in terms of perturbation theory. Instead, the photon and the elementary excitation form a new quasiparticle - the polariton . Strong coupling is found if the dispersion curves of the photon and the excitation intersect, that is, if the energy and momentum of the interaction partners practically coincide.

With regard to the quasiparticles involved, a detailed distinction is made between phonon polaritons, exciton polaritons and plasmon polaritons.

The phonon polariton

The phonon polariton can be found in crystals with an ionic bond (e.g. NaCl). Figuratively speaking, an electromagnetic wave calls a polarization

${\displaystyle {\vec {P}}=\varepsilon _{0}\chi {\vec {E}}}$

and thus a lattice distortion. Conversely, a transverse optical grating wave is accompanied by an electromagnetic grating wave. Two different types of polarization play an important role here:

• The ion polarization is based on the displacement of the lattice ions of an ion crystal in the electric field.
• The electronic polarization can be understood as a shift of the electron cloud with respect to the nuclei.

Both can be described by the oscillator model. If one looks at an ion pair, one obtains for each individual ion the differential equation of the damped harmonic oscillator on which an external disturbance, the electric field, acts. For the dielectric constant, the Lyddane-Sachs-Teller relation results in the following important relationship:

${\displaystyle \varepsilon (\omega )=\varepsilon _{\infty }+{\frac {\omega _{0}^{2}\cdot (\varepsilon _{\mathrm {st} }-\varepsilon _{\infty })}{\omega _{0}^{2}-\omega ^{2}-i\gamma \omega }}}$

Description of the introduced variables:

• ${\displaystyle \omega _{0}}$:  Resonance frequency of the vibratory system, i.e. the ion
• ${\displaystyle \varepsilon _{\mathrm {st} }}$: Dielectric constant of the material under consideration at frequencies far below the resonance frequency    ( "static") ${\displaystyle \omega _{0}}$ ${\displaystyle \mathrm {st} {\widehat {=}}}$
• ${\displaystyle \varepsilon _{\infty }}$: Dielectric constant of the material under consideration at frequencies well above the resonance frequency ${\displaystyle \omega _{0}}$
• ${\displaystyle \gamma }$: Attenuation constant of the harmonic oscillator

Assuming a plane wave, one obtains the general dispersion relation of electromagnetic waves in the medium with the help of Maxwell's equations (with the wave number k):

${\displaystyle \omega ^{2}={\frac {c^{2}k^{2}}{\varepsilon (\omega )}}}$

If you insert the derived equation into this, you get (with ) the dispersion relation of the polaritons : ${\displaystyle \gamma =0}$

${\displaystyle \omega ^{2}\cdot \left(\varepsilon _{\infty }+{\frac {\omega _{0}^{2}\cdot (\varepsilon _{\mathrm {st} }-\varepsilon _{\infty })}{\omega _{0}^{2}-\omega ^{2}}}\right)=c^{2}k^{2}}$

The exciton polariton

Exciton-polariton dispersion with longitudinal (upper polariton branch, UPB) and transversal (lower polariton branch, LPB) splitting, as well as the dispersion relation for light in vacuum. Note: corresponds ${\displaystyle k}$ ${\displaystyle q}$

The exciton polariton arises like the phonon polariton from the interaction between electromagnetic waves and matter , e.g. B. when excited in photoluminescence spectroscopy . Electromagnetic radiation creates a polarization in the solid (see above):

${\displaystyle {\vec {P}}=\varepsilon _{0}\chi {\vec {E}}}$

This means that matter is partially polarized. Electromagnetic waves are transversely polarized in a vacuum . However, a longitudinal polarization also forms in matter .

During recombination, excitons emit electromagnetic radiation. This radiation interacts with the solid or its polarization . The exciton polariton "arises". Electromagnetic waves as well as excitons have a dispersion. The interaction of these two particles creates the polariton, which is described by the exciton-polariton dispersion (see picture: exciton-polariton dispersion).

Longitudinal and transversal polarization, or correspondingly the longitudinal and transversal polariton, split energetically. The figure shows the course of the uncoupled exciton dispersion (dashed lines), but already in the longitudinal and transversal splitting, as it contributes to the exciton-polariton dispersion. The dispersion of photons in vacuum (uncoupled / without interaction) is shown in red.

Polariton-LT splitting between longitudinal and transversal mode, shown on a fictitious measurement result; green: two exciton peaks with constant background, blue: resulting measurement curve; What is striking is the shift in the peak maxima due to the superposition, which shows that fitting should always be used for accurate results

With the interaction, the longitudinal exciton polariton ( ) kinks from the origin ( ) and approaches asymptotically the uncoupled dispersion of the photons (UPB and its course in blue). In the transverse branch, the exciton polariton kinks from the course of the photons with the coupling (interaction) and asymptotically approaches the dispersion of the transverse exciton ( ) (LPB and its course in blue). The split can be seen in the origin between UPB and LPB as the difference in the dashed lines, which corresponds to an energy, da ${\displaystyle \omega _{L}}$ ${\displaystyle k=0}$ ${\displaystyle \omega _{T}}$

${\displaystyle E=\hbar \cdot \omega }$.

This difference can be seen in the experiment. Excitons are formed from an electron from the conduction band and a hole from the valence band , whereby there are three valence bands, which are called A, B and C in descending order of energy. These are e.g. B. can be seen in the schematic diagram of photoluminescence spectroscopy . All excitons split LT. Thus each exciton splits. This splitting of the excitons can be measured in photoluminescence spectroscopy with very good resolution . All radiant events appear as peaks, as do the excitonic events. In the measurement, two peaks can be seen instead of one, whereby the distance on the energy scale corresponds to the splitting (see picture: Polariton LT splitting).

The split can e.g. B. in zinc oxide (ZnO) barely measurable (approx. 0.2 meV: with one of the A-valence band exciton polaritons) or measurable (approx. 10 meV: with one of the B-valence band exciton polaritons).

Bose-Einstein condensates of polaritons and polariton lasers

Atac Imamoglu and colleagues were the first to propose in 1996 that polaritons form Bose-Einstein condensates (BEC). This made possible the concept of the polariton laser , a laser without inversion . Evidence was provided by H. Deng and colleagues in 2002 and by Benoit Devaud and colleagues. Polariton-BEC in a trap (i.e. under controlled conditions) was successful in 2007 by David W. Snoke and in 2009 by Jacqueline Bloch . In 2013, signs of superfluidity were found in polaritone BEC, which was also observed at room temperature. Typically excitons are used, which are trapped in quantum wells and interact with light in a microresonator in the micrometer range that is tuned to the wavelength of the light. The strong correlation in the Bose-Einstein condensate generates coherence, which is also transferred to the light (laser).

While until then the observations were made in non-equilibrium systems, David W. Snoke, Keith Nelson and co-workers observed BEC in thermal equilibrium. In addition, the experimental results were provided by optical pumping, but excitation by electrical injection was proven in 2013, which brought technical applications in semiconductor technology closer.

literature

• Charles Kittel: Introduction to Solid State Physics . Oldenbourg Wissenschaftsverlag, 2005, ISBN 3-486-57723-9 , p. 449 ff . ( limited preview in Google Book search).
• Gerd Czycholl: Theoretical solid state physics . Springer, 2007, ISBN 978-3-540-74789-5 , pp. 340 ff . ( limited preview in Google Book search).

Polariton BEC:

• David Snoke, Peter Littlewood: Polariton condensates Physics Today, Vol. 63, Aug 2010, p. 42
• H. Deng, H. Haug, Y. Yamamoto: Exciton-polariton Bose-Einstein condensation, Reviews of Modern Physics, Volume 82, 2010, p. 1489
• T. Byrnes, Na Young Kim, Y. Yamamoto: Exciton – polariton condensates, Nature Physics, Volume 10, 2014, p. 803
• Benoit Devaud: Exciton-Polariton Bose-Einstein Condensates, Annual Review of Condensed Matter Physics, Volume 6, 2015, pp. 155-175
• D. Sanvitto, S. Kéna-Cohen: The road towards polaritonic devices, Nature Materials, Volume 15, 2016, p. 1061
• DW Snoke, J. Keeling: The new era of polariton condensates, Physics Today, 70, 2017, No. 10, p. 54
• Nick P. Proukakis, David W. Snoke, Peter B. Littlewood (Eds.): Universal themes of Bose-Einstein-condensation, Cambridge UP 2017

Web links

• Video explaining a polariton, University of Sheffield (youtube)

Individual evidence

1. ↑ Mark Steger, Chitra Gautham, David W. Snoke, Loren Pfeiffer, Ken West: Slow reflection and two-photon generation of microcavity exciton – polaritons , Optica, Volume 2, 2015, No. 1, p. 1
2. ↑ Tolpygo, Journal for Experimental and Theoretical Physics , Volume 20, No. 6, 1950, pp. 497-509. Reprinted in English: Physical properties of a rock salt lattice made up of deformable ions. In: Ukrainian Journal of Physics. 53, special edition, 2008, pp. 497-509.
3. ↑ Kun, Lattice vibrations and optical waves in ionic crystals, Nature, Volume 167, 1951, pp. 779-780
4. ^ Kun, On the interaction between the radiation field and ionic crystals, Proc. Roy. Soc. London, Volume 208, 1951, pp. 352-356
5. ^ A. Otto, Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection, Zeitschrift für Physik A, Volume 216, 1968, pp. 398-410
6. ↑ H. Deng et al. a., Condensation of semiconductor microcavity exciton polaritons, Science, Vol. 298, 2002, p. 199
7. ↑ J. Kasprzak, B. Devaud et al. a .: Bose-Einstein condensation of exciton polaritons, Nature, Volume 443, 2006, p. 409
8. ^ R. Balili, V. Hartwell, DW Snoke, L. Pfeiffer, K. West: Bose-Einstein Condensation of Microcavity Polaritons in a Trap, Science, Volume 316, 2017, pp. 1007-1010
9. ↑ E. Wertz, J. Bloch et al. a .: Spontaneous formation of a polariton condensate in a planar GaAs microcavity, Applied Physics Letters, Volume 95, 2009 p. 051108
10. ↑ A. Arno et al. a., Superfluidity of polaritons in semiconductor microcavities, Nature Physics, Volume 5, 2009, p. 805
11. ↑ Giovanni Lerario et al. a., Room-temperature superfluidity in a polariton condensate, Nature Physics, Volume 13, 2017, p. 837, Arxiv
12. ↑ YN Sun et al. a., Bose-Einstein Condensation of long-lifetime polaritons in thermal equilibrium, Physical Review Letters, Volume 118, 2017, p. 016602
13. ↑ P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, J. Heo: Solid State Electrically Injected Exciton-Polariton Laser, Physical Review Letters, Volume 110, 2013, p. 206403, PMID 25167434
14. ↑ Christian Schneider, Arash Rahimi-Iman, Na Young Kim, Julian Fischer, Ivan G. Savenko, Matthias Amthor, Matthias Lermer, Adriana Wolf, Lukas Worschech, Vladimir D. Kulakovskii, Ivan A. Shelykh, Martin Kamp, Stephan Reitzenstein, Alfred Forchel, Yoshihisa Yamamoto, Sven Höfling: An electrically pumped polariton laser, Nature, Volume 497, 2013, pp. 348-352, PMID 23676752