Abstract
The study of the fundamental properties of phonons is crucial to understand their role in applications in quantum information science, where the active use of phonons is currently highly debated. A genuine quantum phenomenon associated with the fluctuation properties of phonons is squeezing, which is achieved when the fluctuations of a certain variable drop below their respective vacuum values. We consider a semiconductor quantum dot (QD) in which the exciton is coupled to phonons. We review the fluctuation properties of the phonons, which are generated by optical manipulation of the QD, in the limiting case of ultra-short pulses. Then, we discuss the phonon properties for an excitation with finite pulses. Within a generating function formalism, we calculate the corresponding fluctuation properties of the phonons and show that phonon squeezing can be achieved by the optical manipulation of the QD exciton for certain conditions even for a single-pulse excitation where neither for short nor for long pulses squeezing occurs. To explain the occurrence of squeezing, we employ a Wigner function picture providing a detailed understanding of the induced quantum dynamics.
Similar content being viewed by others
References
Volz, S., Ordonez-Miranda, J., Shchepetov, A., Prunnila, M., Ahopelto, J., Pezeril, T., Vaudel, G., Gusev, V., Ruello, P., Weig, E.M., Schubert, M., Hettich, M., Grossman, M., Dekorsy, T., Alzina, F., Graczykowski, E., Chavez-Angel, E., Reparaz, J.S., Wagner, M.R., Sotomayor-Torres, C.M., Xiong, S., Neogi, S., Donadio, D.: Nanophononics: state of the art and perspectives. Eur. Phys. J. B 89, 1–20 (2016)
Brüggemann, C., Akimov, A.V., Scherbakov, A.V., Bombeck, M., Schneider, C., Höfling, S., Forchel, A., Yakovlev, D.R., Yakovlev, D.R., Bayer, M.: Laser mode feeding by shaking quantum dots in a planar microcavity. Nat. Photon. 6, 30–34 (2011)
Czerniuk, T., Brüggemann, C., Tepper, J., Brodbeck, S., Schneider, C., Kamp, M., Höfling, B.A., Glavin, S., Yakovlev, D.R., Akimov, A.V., Bayer, M.: Lasing from active optomechanical resonators. Nat. Commun. 5, 4038 (2014)
Stotz, J.A.H., Hey, R., Santos, P.V., Ploog, K.H.: Coherent spin transport through dynamic quantum dots. Nat. Mater. 4, 585–588 (2005)
Völk, S., Schulein, F.J.R., Knall, F., Reuter, D., Wieck, A.D., Truong, T.A., Kim, H., Petroff, P.M., Wixforth, A., Krenner, H.J.: Enhanced sequential carrier capture into individual quantum dots and quantum posts controlled by surface acoustic waves. Nano Lett. 10, 3399–3407 (2010)
Fuhrmann, D.A., Thon, S.M., Kim, H., Bouwmeester, D., Petroff, P.M., Wixforth, A., Krenner, H.J.: Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons. Nat. Photon. 5, 605–609 (2011)
Weiß, M., Kinzel, J.B., Schülein, F.J.R., Heigl, M., Rudolph, D., Morkötter, S., Döblinger, M., Bichler, M., Abstreiter, G., Finley, J.J., Koblmüller, G., Wixforth, A., Krenner, H.J.: Dynamic acoustic control of individual optically active quantum dot-like emission centers in heterostructure nanowires. Nano Lett. 14, 2256–2264 (2014)
Gustafsson, M.V., Aref, T., Kockum, A.F., Ekström, M.K., Johansson, G., Delsing, P.: Propagating phonons coupled to an artificial atom. Science 346, 207–211 (2014)
Kerfoot, M.L., Govorov, A.O., Scheibner, M.: Optophononics with coupled quantum dots. Nat. Commun. 5, 3299 (2014)
Nakamura, K.G., Shikano, Y., Kayanuma, Y.: Influence of pulse width and detuning on coherent phonon generation. Phys. Rev. B 92, 144304 (2015)
Kabuss, J., Carmele, A., Brandes, T., Knorr, A.: Optically driven quantum dots as source of coherent cavity phonons: a proposal for a phonon laser scheme. Phys. Rev. Lett. 109, 054301 (2012)
Dodonov, V.V.: ‘Nonclassical’ states in quantum optics: a ‘squeezed’ review of the first 75 years. J. Opt. B 4, R1 (2002)
Polzik, E.S.: Quantum physics: the squeeze goes on. Nature 453, 45–46 (2008)
Drummond, P.D., Ficek, Z.: Quantum Squeezing, vol. 27. Springer-Verlag Berlin Heidelberg, New York (2013)
Goda, K., Miyakawa, O., Mikhailov, E.E., Saraf, S., Adhikari, R., McKenzie, K., Ward, R., Vass, S., Weinstein, A.J., Mavalvala, N.: A quantum-enhanced prototype gravitational-wave detector. Nat. Phys. 4, 472–476 (2008)
Janszky, J., Vinogradov, A.V.: Squeezing via one-dimensional distribution of coherent states. Phys. Rev. Lett. 64, 2771 (1990)
Hu, X., Nori, F.: Squeezed phonon states: modulating quantum fluctuations of atomic displacements. Phys. Rev. Lett. 76, 2294 (1996)
Sauer, S., Daniels, J.M., Reiter, D.E., Kuhn, T., Vagov, A., Axt, V.M.: Lattice fluctuations at a double phonon frequency with and without squeezing: an exactly solvable model of an optically excited quantum dot. Phys. Rev. Lett. 105, 157401 (2010)
Papenkort, T., Axt, V.M., Kuhn, T.: Optical excitation of squeezed longitudinal optical phonon states in an electrically biased quantum well. Phys. Rev. B 85, 235317 (2012)
Zijlstra, E.S., Kalitsov, A., Zier, T., Garcia, M.E.: Squeezed thermal phonons precurse nonthermal melting of silicon as a function of fluence. Phys. Rev. X 3, 011005 (2013)
Garrett, G.A., Rojo, A.G., Sood, A.K., Whitaker, J.F., Merlin, R.: Vacuum squeezing of solids: macroscopic quantum states driven by light pulses. Science 275, 1638–1640 (1997)
Misochko, O.V.: Implication of phase-dependent noise of coherent phonons in \(\text{ YBa }_2\text{ Cu }_3\text{ O }_7- \delta \). Phys. Lett. A 269, 97–102 (2000)
Johnson, S.L., Beaud, P., Vorobeva, E., Milne, C.J., Murray, É.D., Fahy, S., Ingold, G.: Directly observing squeezed phonon states with femtosecond X-ray diffraction. Phys. Rev. Lett. 102, 175503 (2009)
Esposito, M., Titimbo, K., Zimmermann, K., Giusti, F., Randi, F., Boschetto, D., Parmigiani, F., Floreanini, R., Benatti, F., Fausti, D.: Photon number statistics uncover the fluctuations in non-equilibrium lattice dynamics. Nat. Commun. 6, 10249 (2015)
Vagov, A., Axt, V.M., Kuhn, T.: Electron–phonon dynamics in optically excited quantum dots: exact solution for multiple ultrashort laser pulses. Phys. Rev. B 66, 165312 (2002)
Axt, V.M., Kuhn, T., Vagov, A., Peeters, F.M.: Phonon-induced pure dephasing in exciton–biexciton quantum dot systems driven by ultrafast laser pulse sequences. Phys. Rev. B 72, 125309 (2005)
Wigger, D., Reiter, D.E., Axt, V.M., Kuhn, T.: Fluctuation properties of acoustic phonons generated by ultrafast optical excitation of a quantum dot. Phys. Rev. B 87, 085301 (2013)
Wigger, D., Lüker, S., Reiter, D.E., Axt, V.M., Machnikowski, P., Kuhn, T.: Energy transport and coherence properties of acoustic phonons generated by optical excitation of a quantum dot. J. Phys. Condens. Matter 26, 355802 (2014)
Wigger, D., Lüker, S., Axt, V.M., Reiter, D.E., Kuhn, T.: Squeezed phonon wave packet generation by optical manipulation of a quantum dot. Photonics 2, 214–227 (2015)
Stauber, T., Zimmermann, R., Castella, H.: Electron–phonon interaction in quantum dots: a solvable model. Phys. Rev. B 62, 7336 (2000)
Reiter, D.E., Wigger, D., Axt, V.M., Kuhn, T.: Generation and dynamics of phononic cat states after optical excitation of a quantum dot. Phys. Rev. B 84, 195327 (2011)
Axt, V.M., Herbst, M., Kuhn, T.: Coherent control of phonon quantum beats. Superlattices Microstruct. 26, 117–128 (1999)
Schleich, W.P.: Quantum Optics in Phase Space. Wiley-VCH, Berlin (2011)
Janszky, J., Adam, P., Vinogradov, A.V., Kobayashi, T.: Influence of phonon squeezing on the transient spectrum. Spectrochim. Acta 48, 31–39 (1992)
Gerry, C., Knight, P.: Introductory Quantum Optics. Cambridge University Press, Cambridge (2005)
Haroche, S., Raimond, J.M.: Exploring the Quantum. Oxford Univ. Press, Oxford (2006)
Schulte, C.H.H., Hansom, J., Jones, A.E., Matthiesen, C., Le Gall, C., Atatüre, M.: Quadrature squeezed photons from a two-level system. Nature 525, 222–225 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wigger, D., Gehring, H., Axt, V.M. et al. Quantum dynamics of optical phonons generated by optical excitation of a quantum dot. J Comput Electron 15, 1158–1169 (2016). https://doi.org/10.1007/s10825-016-0856-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10825-016-0856-8