Query: –Einstein condensation of excitons in potential traps

Candidate papers:

abstract: An exciton is an electron hole bound pair in a semiconductor. In the low density limit, it is a composite Bose quasi particle, akin to the hydrogen atom. Just as in dilute atomic gases, reducing the temperature or increasing the exciton density increases the occupation numbers of the low energy states leading to quantum degeneracy and eventually to Bose Einstein condensation (BEC) Because the exciton mass is small even smaller than the free electron mass exciton BEC should occur at temperatures of about 1 K, many orders of magnitude higher than for atoms. However, it is in practice difficult to reach BEC conditions, as the temperature of excitons can considerably exceed that of the semiconductor lattice. The search for exciton BEC has concentrated on long lived excitons: the exciton lifetime against electron hole recombination therefore should exceed the characteristic timescale for the cooling of initially hot photo generated excitons. Until now, all experiments on atom condensation were performed on atomic gases confined in the potential traps. Inspired by these experiments, and using specially designed semiconductor nanostructures, we have collected quasi two dimensional excitons in an in plane potential trap. Our photoluminescence measurements show that the quasi two dimensional excitons indeed condense at the bottom of the traps, giving rise to a statistically degenerate Bose gas.
author_names: L V Butov

Chih-wei Lai

Arkadii L Ivanov

Arthur C Gossard

Daniel S Chemla
title: Towards Bose Einstein condensation of excitons in potential traps
venue: Nature
year: 2002

abstract: An asymmetric multi quantum state magnetic lattice is proposed to host excitons formed in a quantum degenerate gas of ultracold fermionic atoms to simulate Bose Einstein condensation (BEC) of excitons. A Quasi two dimensional degenerate gas of excitons can be collected in the in plane asymmetric magnetic bands created at the surface of the proposed magnetic lattice, where the ultracold fermions simulate separately direct and indirect confined electronhole pairs (spin up fermions spin down fermions) rising to the statistically degenerate Bose gas and eventually through controlled tunnelling to BEC of excitons. The confinement of the coupled magnetic quantum well (CMQWs) system may significantly improve the condition for long lived exciton BEC. The exciton BEC, formed in CMQWs can be regarded as a suitable host for the multi qubits (multipartite) systems to be used in quantum information processors.
author_names: Ahmed M Abdelrahman

Mikhail A Vasiliev

Karmal Alameh

Peter Hannaford

Byoung Seung Ham

Yong-Tak Lee
title: Towards Bose Einstein condensation of excitons in an asymmetric multi quantum state magnetic lattice
year: 2009

abstract: We calculate the spatially resolved optical emission spectrum of a weakly interacting Bose gas of excitons confined in a three dimensional potential trap due to interband transitions involving weak direct and phonon mediated exciton photon interactions. Applying the local density approximation, we show that for a noncondensed system the spatiospectral lineshape of the direct process reflects directly the shape of the potential. The existence of a Bose Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Typical examples are given for parameters of the lowest yellow excitons in \text{Cu}}_{2}\text{O}
author_names: Heinrich Stolz

Dirk Semkat
title: Unique signatures for Bose Einstein condensation in the decay luminescence lineshape of weakly interacting excitons in a potential trap
year: 2010

abstract: Coupled states of semiconductor quantum well (QW) excitons and photons in a two dimensional (2D) periodic lattice of microcavities are analyzed theoretically, revealing allowed bands and forbidden gaps in the energy spectrum of exciton polaritons. Photonic crystal exciton polaritons have spatially uniform excitonic constituent set by at QWs, but exhibit periodic Bloch oscillations in the plane of QWs due to their photonic component. The envelope functions of photonic crystal exciton polaritons can be tailored via efiective potential of a photonic crystal heterostructure, by using quasi periodic lattices of microcavities. Conflned envelope function states of lower and upper polaritons and the Bose Einstein condensation of lower polaritons are analyzed here in a photonic crystal heterostructure trap with harmonic oscillator potential. This concept is numerically illustrated on example of CdTe/CdMgTe microcavities.
author_names: Dmitri L Boiko
title: Towards R space Bose Einstein Condensation of Photonic Crystal Exciton Polaritons
year: 2008

abstract: Exciton polaritons, with extremely low effective mass 1 are regarded as promising candidates to realize Bose Einstein condensation in lattices for quantum simulations 2 towards room temperature operations 3 8 Along with the condensation, an efficient exciton polariton quantum simulator 9 would require a strong lattice with robust polariton trapping as well as strong intersite coupling to allow coherent quantum motion of polaritons within the lattice. A strong lattice can be characterized with a larger forbidden bandgap opening and a larger lattice bandwidth compared with the linewidth. However, exciton polaritons in such strong lattices have only been shown to condense at cryogenic temperatures 3 8 Here, we report the observation of non equilibrium exciton polariton condensation in a one dimensional strong lead halide perovskite lattice at room temperature. Modulated by deep periodic potentials, the strong lead halide perovskite lattice exhibits a large forbidden bandgap opening up to 13.3 meV and a lattice band up to 8.5 meV wide, which are at least 10 times larger than previous systems. Above a critical density, we observe polariton condensation into p y orbital states with long range spatial coherence at room temperature. Our result opens the route to the implementation of polariton condensates in quantum simulators at room temperature. Non equilibrium Bose Einstein condensation of exciton polaritons in chains of lead halide perovskite pillars can occur at room temperature. These condensates have long spatial coherence.
author_names: Rui Su

Sanjib Ghosh

Jian Wang

Songting Liu

Carole Diederichs

Timothy C H Liew

Qihua Xiong
title: Observation of exciton polariton condensation in a perovskite lattice at room temperature
year: 2019

abstract: Spatially indirect excitons, being composite bosons, are attractive candidates to explore correlated many body systems. They possess an inherent large electric dipole, a four fold spin manifold, and can be studied via the emitted photoluminescence after electrons and holes have recombined. Due to their extremely low mass compared to atoms, a sufficiently dense gas of indirect excitons is expected to form a Bose Einstein condensate below a critical temperature of a few Kelvins. Recent theoretical results show that this condensation must take place in optically dark states of the spin manifold. However, under a density increase the condensate is expected to coherently couple to a small population of bright excitons. It is then possible to study the condensate through its weak photoluminescence. In this thesis we report on experiments with a cold gas of indirect excitons in coupled quantum wells embedded in a field effect device. Indirect excitons are photo generated through pulsed laser excitation, in a fashion that minimizes photo induced perturbations in the field effect device. Confinement is provided by exploiting the high field seeking dipolar nature of spatially indirect excitons through independently biased surface gate electrodes. Time and spectrally resolved analysis of the photoluminescence allow us to extract the decay time of the bright exciton population while at the same time monitoring the decay of the overall exciton population through the energy of the photoluminescence. Maintaining a fixed density while varying the bath temperature, we are able to observe a depletion of the bright state population, by even three fold when the bath temperature is lowered from 3.5 K to 0.33 K. This stands in stark contrast to the expected classical behavior of a cold gas of excitons obeying Maxwell Boltzmann statistics. The experimental results are confirmed by a phenomenological model which shows that Bose stimulation from bright to dark excitons is compatible with the observed anomalous darkening. Lowering the exciton gas temperature should reinforce these signatures. However, in GaAs exciton phonon interaction is the main mechanism to cooling an exciton gas to quantum degeneracy. The efficiency of this process is strongly reduced for temperatures below 330 mK. We have thus developed a technique to control the exciton confinement in situ, on a time scale of nanoseconds by pulsing the gate electrode. Our approach relies on a complete characterization of the transfer function linking the response of the indirect excitons to a voltage pulse, i.e. the strength of the confining potential. Our method shows no increase of the bath temperature thus paves the way towards exploration of evaporative cooling methods for a gas of cold indirect excitons.
author_names: Mussie Beian
title: Spectral evidence for a condensate of dark excitons in a trap
year: 2016

abstract: Mixed light matter nature of exciton polaritons brings the rich physics of correlated systems, e.g. Bose Einstein like condensation, to an all semiconductor platform with potential applications for generation of correlated and entangled photons. One strategy towards this goal is to engineer the polariton density of states by spatial confinement. In this way, one can create a discrete spectrum of polariton energies to control the scattering pathways in an optical parametric oscillator (OPO) configuration. We fabricated 3D traps with quasi equidistant energy levels and positioned them at the anti nodes of a standing surface acoustic wave (SAW) The SAW modulates the energies of the trap as a whole up to one meV and allows to realize perfect energy and momentum matching. When we resonantly excited polaritons in the confined middle level of the trap with a CW laser under an applied SAW, we observed two emission peaks on both energy sides of the pump, spaced equidistantly with respect to the excitation energy a typical OPO signature. The observation of an OPO for the confined polaritons is an important step towards novel sources of entangled photons. Another significant aspect of this work is the dynamic control of the generation of correlated photons by the SAW amplitude, frequency and phase.
author_names: Alexander S Kuznetsov

Klaus Biermann

Paulo Ventura Santos
title: Parametric photons from confined polariton condensates driven by acoustic fields
venue: 2019 Compound Semiconductor Week (CSW)
year: 2019

abstract: We theoretically investigate coupling interaction between molecule excitons and whispering gallery modes (WGMs) that approaches the limit of single exciton strong coupling in hyperbolic metamaterial (HMM) cavity, composed of a dielectric core wrapped by several stacks of alternative layers of metal and dielectric. We demonstrate that associated with the excitation of the whispering gallery mode, the electric fields with resonance wavelengths that are much larger than the cavity size can be highly localized within a dielectric layer, leading to extremely small mode volumes. By using temporal coupled mode theory to model the interaction in the proposed WGMs exciton system, we are able to demonstrate that the coupling between molecular excitons and hyperbolic cavity WGMs can reach the strong coupling regime. Furthermore, we also prove that changing both the thickness of inner core and outermost layer can lead to invariant resonance frequency while the threshold number of coupled excitons to fulfill the criteria for strong coupling remains 4 in various sets of tunable HMM cavities. References and links 1. R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, "Single molecule strong coupling at room temperature in plasmonic nanocavities," Nature 535, 127 130 (2016) 2. D. M. Coles, Y. Yang, Y. Wang, R. T. Grant, R. A. Taylor, S. K. Saikin, A. Aspuru Guzik, D. G. Lidzey, J. K. Tang, and J. M. Smith, "Strong coupling between chlorosomes of photosynthetic bacteria and a confined optical cavity mode," Nat Commun 5, 5561 (2014) 3. J. D. Plumhof, T. Stoferle, L. Mai, U. Scherf, and R. F. Mahrt, "Room temperature Bose Einstein condensation of cavity exciton polaritons in a polymer," Nat Mater 13, 247 252 (2014) 4. D. Yelin, D. Oron, S. Thiberge, E. Moses, and Y. Silberberg, "Multiphoton plasmon resonance microscopy," Opt. Express 11(12) 1385 1391 (2003) 5. J. Z. Bernad, and G. Alber, "Photon assisted entanglement creation by minimum error generalized quantum measurements in the strong coupling regime," Physical Review A 87, 012311 (2013) 6. C. Coulson, G. Christmann, P. Cristofolini, C. Grossmann, J. J. Baumberg, S. I. Tsintzos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, "Electrically controlled strong coupling and polariton bistability in double quantum wells," Physical Review B 87, 045311 (2013) 7. R. Konoike, H. Nakagawa, M. Nakadai, T. Asano, Y. Tanaka, and S. Noda, "On demand transfer of trapped photons on a chip," Science Advances 2 (2016) 8. Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, "Strong coupling between distant photonic nanocavities and its dynamic control," Nature Photonics 6, 56 61 (2011) 9. F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. Garcia Etxarri, and J. Aizpurua, "Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection," Phys Rev Lett 101, 157403 (2008) 10. L. V. Brown, K. Zhao, N. King, H. Sobhani, P. Nordlander, and N. J. Halas, "Surface enhanced infrared absorption using individual cross antennas tailored to chemical moieties," J Am Chem Soc 135, 3688 3695 (2013) 11. D. Nau, A. Seidel, R. B. Orzekowsky, S. H. Lee, S. Deb, and H. Giessen, "Hydrogen sensor based on metallic photonic crystal slabs," Opt. Lett. 35, 3150 3152 (2010) 12. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Letters 8, 4391 (2008) 13. A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, "Near field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers," Nano Lett 13, 3281 3286 (2013) 14. W. Wu, M. Wan, P. Gu, Z. Chen, and Z. Wang, "Strong coupling between few molecular excitons and Fanolike cavity plasmon in two layered dielectric metal core shell resonators," Opt Express 25, 1495 1504 (2017) 15. P. Torma, and W. L. Barnes, "Strong coupling between surface plasmon polaritons and emitters: a review," Rep Prog Phys 78, 013901 (2015) 16. G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, "Vacuum Rabi splitting in semiconductors," Nat Phys 2, 81 90 (2006) 17. K. J. Vahala, "Optical microcavities," Nature 424, 839 846 (2003) 18. S. Anand, M. Eryurek, Y. Karadag, A. Erten, A. Serpenguzel, A. Jonas, and A. Kiraz, "Observation of whispering gallery modes in elastic light scattering from microdroplets optically trapped in a microfluidic channel," J. Opt. Soc. Am. B 33, 1349 1354 (2016) 19. B. Gayral, J. M. Gerard, A. Lemaitre, C. Dupuis, L. Manin, and J. L. Pelouard, "High Q wet etched gaas microdisks containing inas quantum boxes," Appl. Phys. Lett. 75(13) 1908 (1999) 20. E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton Photon StrongCoupling Regime for a Single Quantum Dot Embedded in a Microcavity," Physical Review Letters 95, 067401 (2005) 21. D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vuckovic, "Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity," Phys Rev Lett 104, 073904 (2010) 22. P. Androvitsaneas, A. B. Young, C. Schneider, S. Maier, M. Kamp, S. Hofling, S. Knauer, E. Harbord, C. Y. Hu, J. G. Rarity, and R. Oulton, "Charged quantum dot micropillar system for deterministic light matter interactions," Physical Review B 93, 241409 (2016) 23. Y. Yang, O. D. Miller, T. Christensen, J. D. Joannopoulos, and M. Soljacic, "Low Loss Plasmonic Dielectric Nanoresonators," Nano Letters 17, 3238 3245 (2017) 24. X. Chen, Y. H. Chen, J. Qin, D. Zhao, B. Ding, R. J. Blaikie, and M. Qiu, "Mode Modification of Plasmonic Gap Resonances Induced by Strong Coupling with Molecular Excitons," Nano Letters 17, 3246 3251 (2017) 25. P. Oskar, S. Kartik, D. O. B. John, S. Axel, and P. D. Dapkus, "Tailoring of the resonant mode properties of optical nanocavities in two dimensional photonic crystal slab waveguides," Journal of Optics A: Pure and Applied Optics 3, S161 (2001) 26. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, "Photonic bandgap microcavities in optical waveguides," Nature 390, 143 145 (1997) 27. R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proceedings Optoelectronics 145, 391 397 (1998) 28. A. Faraon, P. E. Barclay, C. Santori, K. M. C. Fu, and R. G. Beausoleil, "Resonant enhancement of the zerophonon emission from a colour centre in a diamond cavity," Nat Photon 5, 301 305 (2011) 29. J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot semiconductor microcavity system," Nature 432, 197 200 (2004) 30. D. Wang, H. Kelkar, D. Martin Cano, T. Utikal, S. Gotzinger, and V. Sandoghdar, "Coherent Coupling of a Single Molecule to a Scanning Fabry Perot Microcavity," Physical Review X 7, 021014 (2017) 31. P. B. Johnson, and R. W. Christy, "Optical Constants of the Noble Metals," Physical Review B 6, 4370 4379 (1972) 32. P. Gu, M. Wan, Q. Shen, X. He, Z. Chen, P. Zhan, and Z. Wang, "Experimental observation of sharp cavity plasmon resonances in dielectric metal core shell resonators," Applied Physics Letters 107, 141908 (2015) 33. C. F. Bohren, and D. R. Huffman, "Absorption and Scattering of Light by Small Particles," Journal of Colloid Interface Science 98, 290 291 (1998) 34. C. Wu, A. Salandrino, X. Ni, and X. Zhang, "Electrodynamical Light Trapping Using Whispering Gallery Resonances in Hyperbolic Cavities," Physical Review X 4 (2014) 35. S. T. Smiley, M. Reers, C. Mottolahartshorn, M. Lin, A. Chen, T. W. Smith, G. D. Steele, and L. B. Chen, "Intracellular heterogeneity in mitochondrial membrane potentials revealed by a J aggregate forming lipophilic cation JC 1," Proceedings of the National Academy of Sciences of the United States of America 88, 3671 (1991) 36. E. T. Jaynes, and F. W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser," Proceedings of the IEEE 51, 89 109 (2005) 37. S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569 572 (2003) 38. F. Vaianella, and B. Maes, "Fano resonance engineering in slanted cavities with hyperbolic metamaterials," Physical Review B 94, 125442 (2016)
title: Tunable hyperbolic metamaterial cavity towards few exciton strong coupling
year: 2017

abstract: Polaritons are half matter half light quasiparticles, arising, in a two dimensional semiconductor microcavity, from the strong coupling between an exciton (an elementary electronic excitation of a crystal) and a photon. This thesis presents the fabrication of polariton confining structures, their characterization and the study of the linear and non linear optical properties of the confined polaritons. Thanks to their bosonic character, to their extremely light effective mass and to the peculiar shape of their dispersion curve, polaritons were proven to accumulate in their ground state to form a Bose Einstein condensate in a CdTe based sample, at a high temperature of the order of 20 Kelvin. No such effect was observed in GaAs materials, who offer a less disordered environment, where we developed a method to fabricate traps of any shape and size. The latter should facilitate the condensation of polaritons by lowering the density thresholds, and allow us to manipulate the condensate. Thanks to the strong coupling regime, it is possible to confine polaritons either through their photon or through their exciton part. We thus fabricated two dimensional microcavities with local thickness variations, confining the cavity photon along its two free dimensions. We were able to perform this through high quality molecular beam epitaxy (MBE) growth, accompanied by a controlled processing of the sample. We measured the anticrossing behaviors characteristic of the strong coupling regime in zero and two dimensions. As the confining structures have sizes of the order of the micron, we could image the confined polaritons' wave functions in the real and reciprocal (momentum) spaces, and tried to understand how the transition between confined (0D) and extended (2D) polariton modes occurs. We also gave first evidences of the interaction between the two and zero dimensional structures, and of the polariton trapping from one to the other. We then studied the nonlinear optical properties of this new object, performing two different kinds of experiments: a study of the response of the system to a non resonant excitation, in order to probe the formation of a condensed phase. Collective electronic excitations were created, at energies far higher than the modes which are of interest for us. We observed the effect of high densities in the system and evidenced Coulomb interaction. We then observed the cross over from strong to weak coupling regime, and the onset of lasing in the weakly coupled system. a study of the response of the system to a resonant excitation in order to probe parametric effects between the discrete states. In this configuration a number of polaritons are intentionally created in a given state. We observed various nonlinear behaviors as a function of the created population, which may be interpreted as effects of Coulomb interaction, or indications of bistable behaviors in the system. We were nevertheless not able to discriminate. We give some potential applications in the field of single or correlated photon emission. Although industrial applications may not be in the short term agenda, it should be possible to take advantages of this original type of structures for research and development applications. We finally give some experimental perspectives, which may help deepen the observations shown and the interpretations proposed here, and should allow to work towards the fabrication of new samples, where BEC of polaritons is observed and controlled, as well as parametric oscillations between various confined states.
author_names: O El Daif
title: 0D microcavity polaritons
year: 2007

abstract: This dissertation consists of a theoretical investigation into the transport and coherence properties of indirect excitons in coupled quantum wells (QWs) at helium temperatures. The motion of excitons along the quantum well plane is described through a quantum diffusion equation and the possibility of excitonic cloud formation is studied both due to the natural potential fluctuations and externally applied confining potentials. The photoluminescence (PL) of decaying excitons is used as a probe for their properties such as concentration, effective temperature and optical lifetime. The exciton thermalisation from an initial high energy to the lattice temperature is achieved within their lifetime due to a very effective coupling between the exciton states and a continuum of phonon states, a direct consequence of the relaxation of momentum conservation along the growth direction of a QW. Moreover, the natural spatial separation between electrons and holes prevents their recombination, resulting in long lifetimes. The dynamics of the system of excitons in optically induced traps is also studied and the numerical solution of the quantum diffusion equation provides an insight into the extremely fast loading times of the trap with a highly degenerate exciton gas. The hierarchy of timescales in such a trap allows for the creation of a cold and dense gas confined within the trap, opening a new route towards the long sought Bose Einstein Condensation (BEC) in solid state. Finally the issue of exciton spatial coherence is studied and an analytic expression for the coherence function, i.e. the measure of the coherence in a system, is derived. A direct comparison with large coherence lengths recently observed in systems of quantum well excitons and microcavity polaritons is attempted and interesting conclusions are drawn regarding the build up of spontaneous coherence in these systems.
author_names: Leonidas Mouchliadis
title: Transport and coherence properties of indirect excitions in coupled quantum wells
year: 2008