Abstract
The complementarity principle1 demands that a particle reveals wave-like properties only when the different paths that it can take are indistinguishable2,3. The complementarity has been demonstrated in optics with pairs of correlated photons4,5 and in two-path solid-state interferometers with phase-coherent electrons6. In the latter experiment, a charge detector embedded near one path of a two-path electron interferometer provided which-path information3. Here, we report on electron dephasing in an Aharonov–Bohm ring interferometer7 via a charge detector adjacent to the ring. In contrast to the two-path interferometer, charge detection in the ring does not always provide path information. The interference was suppressed only when path information could be acquired, even if only in principle. This confirms that dephasing is not always induced by ‘disturbing’ the interfering particle through the interferometer–environment interactions: path information of the particle must be available too. Our experiment suggests that acquisition of which-path information is more fundamental than the back-action in understanding quantum mechanical complementarity.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
USD 39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Bohr, N. in Quantum Theory and Measurement (eds Wheeler, J. A. & Zurek, W. H.) 9–49 (Princeton Univ. Press, Princeton, 1983).
Feynman, R., Leighton, R. & Sands, M. The Feynman Lectures on Physics Vol. III, Ch. 1 (Addison Wesley, Reading, 1965).
Stern, A., Aharonov, Y. & Imry, Y. Phase uncertainty and loss of interference: A general picture. Phys. Rev. A 41, 3436–3448 (1990).
Zou, X. Y., Wang, L. J. & Mandel, L. Induced coherence and indistinguishability in optical interference. Phys. Rev. Lett. 67, 318–321 (1991).
Dürr, S., Nonn, T. & Rempe, G. Origin of quantum-mechanical complementarity probed by a ‘which-way’ experiment in an atom interferometer. Nature 395, 33–37 (1998).
Buks, E., Schuster, R., Heiblum, M., Mahalu, D. & Umansky, V. Dephasing in electron interference by a ‘which-path’ detector. Nature 391, 871–874 (1998).
Yacoby, A., Heiblum, M., Mahalu, D. & Shtrikman, H. Coherence and phase sensitive measurements in a quantum dot. Phys. Rev. Lett. 74, 4047–4050 (1995).
Schuster, R. et al. Phase measurement in a quantum dot via a double-slit interference experiment. Nature 385, 417–420 (1997).
Field, M. et al. Measurements of Coulomb blockade with a noninvasive voltage probe. Phys. Rev. Lett. 70, 1311–1314 (1993).
Sprinzak, D., Ji, Y., Heiblum, M., Mahalu, D. & Shtrikman, H. Charge distribution in a Kondo-correlated quantum dot. Phys. Rev. Lett. 88, 176805 (2002).
Avinun-Kalish, M., Heiblum, M., Zarchin, O., Mahalu, D. & Umansky, V. Crossover from ‘mesoscopic’ to ‘universal’ phase for electron transmission in quantum dots. Nature 436, 529–533 (2005).
Khym, G. L. & Kang, K. Charge detection in a closed-loop Aharonov–Bohm interferometer. Phys. Rev. B 74, 153309 (2006).
Aharonov, Y. & Bohm, D Significance of electromagnetic potentials in the quantum theory. Phy. Rev. 115, 485–491 (1959).
Aronov, A. G. & Sharvin, Yu. V. Magnetic flux effects in disordered conductors. Rev. Mod. Phys. 59, 755–779 (1987).
Avinun-Kalish, M., Heiblum, M., Silva, A., Mahalu, D. & Umansky, V. Controlled dephasing of a quantum dot in the Kondo regime. Phys. Rev. Lett. 92, 156801 (2004).
Aleiner, I. L., Wingreen, N. S. & Meir, Y. Dephasing and the orthogonality catastrophe in tunneling through a quantum dot: “The which path?” interferometer. Phys. Rev. Lett. 79, 3740–3743 (1997).
Gurvitz, S. A. Measurements with a noninvasive detector and dephasing mechanism. Phys. Rev. B 56, 15215–15223 (1997).
Levinson, Y. Dephasing in a quantum dot due to coupling with a quantum point contact. Europhys. Lett. 39, 299–304 (1997).
Stodolsky, L. Measurement process in a variable-barrier system. Phys. Lett. B 459, 193–200 (1999).
Sprinzak, D., Buks, E., Heiblum, M. & Shtrikman, H. Controlled dephasing of electrons via a phase sensitive detector. Phys. Rev. Lett. 84, 5820–5823 (2000).
Kang, K. Decoherence of the Kondo singlet via a quantum point contact detector. Phys. Rev. Lett. 95, 206808 (2005).
Buttiker, M. & Martin, A. M. Charge relaxation and dephasing in Coulomb-coupled conductors. Phys. Rev. B 61, 2737–2741 (2000).
Levinson, Y. Quantum dot dephasing by edge states. Phys. Rev. B 61, 4748–4753 (2000).
Hackenbroich, G. Phase coherent transmission through interacting mesoscopic systems. Phys. Rep. 343, 463–538 (2001).
Acknowledgements
H.-J.L. was supported by the Electron Spin Science Center in POSTECH and the Pure Basic Research Program (Grant No. R01-2006-000-11248-0) administered by the Korea Science and Engineering Foundation (KOSEF), by the Korea Research Foundation (Grant No. KRF-2005-070-C00055) and by the POSTECH Core Research Program. Y.C. was supported by the Korea Foundation for International Cooperation of Science and Technology (KICOS; Grant No. 2006-04969), Nanoscopia Center of Excellence (NCoE; Grant No. M60504000249-06A0400-24910) at Hanyang University through a grant provided by the Korean Ministry of Science & Technology, and the Priority Research Centers Program (Grant No. KRF-2006-005-J02801) funded by KRF. K.K. was also supported by KRF (Grant No. KRF-2006-331-C00016). M.H. wishes to acknowledge the partial support of the MINERVA foundation, the German Israeli foundation (GIF), the German Israeli project cooperation (DIP), the Israeli Science foundation (ISF) and the Korea Ministry of Science and Technology program.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Chang, DI., Khym, G., Kang, K. et al. Quantum mechanical complementarity probed in a closed-loop Aharonov–Bohm interferometer. Nature Phys 4, 205–209 (2008). https://doi.org/10.1038/nphys854
Received:
Accepted:
Published:
Issue date:
DOI: https://doi.org/10.1038/nphys854
This article is cited by
-
Electric-field-induced interferometric resonance of a one-dimensional spin-orbit-coupled electron
Scientific Reports (2016)
-
Observation of interaction-induced modulations of a quantum Hall liquid’s area
Nature Communications (2016)
-
Critique of Quantum Optical Experimental Refutations of Bohr’s Principle of Complementarity, of the Wootters–Zurek Principle of Complementarity, and of the Particle–Wave Duality Relation
Foundations of Physics (2016)
