A New View on Quantum Complementarity
According to laws of quantum mechanics a physical entity may possess either particle-like or wave-like properties. A particle exhibits wave properties when one cannot tell the path the particle may take among different paths available. Once the path information is obtained, however, the wave-like properties of a particle are supposed to disappear. In any case, it is not possible to observe both the wave and particle properties simultaneously, which is known as complementarity of a physical entity. In early days around the advent of quantum mechanics the concept of complementarity was considered only in hypothetical thought experiments. More recently, however, the progress in the nano-scale artificial fabrication technique enables one to examine the validity of complementarity through the direct experimental realization. To that purpose, one can resort to the double-slit-type interference involving photons, atoms, or electrons in solids.
Traditionally the reduction of the wave properties to the particle ones was thought to result from a momentum transfer to a physical entity while getting its path information. If one attempts to find the path that a physical entity (i.e., an electron) takes in a double-path interferometer, for instance, a momentum transfer causes uncertainty in the phase of the affected wave packet in one path, which results in the suppression of the interference between the partial waves along the two paths. Although this point of view was physically easy to accept, it began to face a challenge since the late twentieth century. It was debated that, in a certain circumstance, only the quantum correlation or the entanglement may lead to the path information even without a momentum transfer, which in turn suppresses the quantum interference.
In this study, we adopt a “closed-loop-type” Aharonov-Bohm electron interferometer [Fig. (a)] to find a clue to the fundamental cause of complementarity. The electron interferometer was fabricated on a two-dimensional electron gas existing at the interface of a GaAs-AlGaAs heterojunction semiconducting wafer. Electrons in the twodimensional gas are laterally confined to be transferred along the two arms of the Aharonov-Bohm interferometer by the electron-confining gates patterned on the surface of a heterojunction wafer and negative voltages applied on them. In the interferometer, a quantum dot is embedded in one arm of the interferometer. The detection of the electrons through this quantum dot is made by monitoring the conductance of the quantum point contact (QPC), which is placed in proximity to the quantum dot and thus electrostatically coupled to the quantum dot. Once the electron path information is obtained by the QPC detector in this double-path interferometer the quantum interference is supposed to be suppressed in proportion to the electron detectability. Complementarity of electrons in this kind of solid-state double-path interferometer was already observed in 1998 by Moty Heiblum’s group in Weizmann Institute of Science, Israel.
Different from the multi-terminal open-loop-type double-path interferometer used by the Weizmann group, our closed-loop-type electron interferometer has only two terminals (the source and the drain). Thus, in our interferometer, multiple turns of electron passage around the interferometer loop is possible in principle. In the case of the double-path interferometer with only a single turn of electron passage, the charge detection always provides the path information. In this case, one cannot tell whether the suppression of the interference due to the charge detection is caused by a momentum transfer or simply by the quantum entanglement. In our closed-loop interferometer, however, the charge detection does not necessarily provide the path information. In Figure (b) the detector responds to the electrons passing the red path only; thus, the path detection is equivalent to the path information. But for the multiple-turn path shown in Fig. (c) both the red and blue paths are through the quantum dot once so that the charge detection does not provide the path information. If only the path information, irrespective of the momentum transfer, suppresses the wave nature of electrons the charge detection will suppress the firstharmonic interference for the path in Fig. (b) but will not affect the second-harmonic interference for the path in Fig. (c). In case the momentum transfer is the cause of the suppression of the interference both the first and second harmonics of the interference will be affected by the charge detection. In our measurements the amplitudes of the first and second harmonic interferences were monitored as a function of the voltage bias of the charge detector. Measurements show that the first harmonics decrease linearly with the voltage bias of the detector while the second harmonics remain unaffected. The results of this study decisively demonstrate that the path information itself rather than the momentum transfer is the essential element of determining the particle-wave nature of an electron or quantum complementarity.
Professor Hu-Jong Lee
Department of Physics