Quantum energy teleportation (QET) is a proposed protocol related to quantum vacuum. The edge channels in a quantum Hall system are well suited for the experimental verification of QET. For this purpose, we examine a charge-density wave packet excited and detected by capacitively coupled front gate electrodes. We observe the waveform of the charge packet, which is proportional to the time derivative of the applied square voltage wave. Further, we study the transmission and reflection behaviors of the charge-density wave packet by applying a voltage to another front gate electrode to control the path of the edge state. We show that the threshold voltages where the dominant direction is switched in either transmission or reflection for dense and sparse wave packets are different from the threshold voltage where the current stops flowing in an equilibrium state.
It should be noted that there are two different important length scales. The quantum correlation length discussed in QET theory is the decay length of quantum correlations, i.e., quantum entanglement in the zero-point fluctuation.4 The order of this length scale is theoretically estimated to be on the order of 10 μm. In contrast, the length scale we discuss in this paper is the length that the charge density wave packet propagates along the edge channel without dissipation. This decay length has been confirmed to be on the order of mm in previous research.
Although we only discuss the average velocity of charge-density wave packets in this paper, one should note that the change of the velocity of the edge channel along the center gate, , appears to be much bigger than reported earlier.