Quantum Coherence Engineering in the Integer Quantum Hall Regime

P-A. Huynh, F. Portier, H. le Sueur, G. Faini, U. Gennser, D. Mailly, F. Pierre, W. Wegscheider, and P. Roche

Phys. Rev. Lett. 108, 256802 – Published 18 June 2012

Abstract

We present an experiment where the quantum coherence in the edge states of the integer quantum Hall regime is tuned with a decoupling gate. The coherence length is determined by measuring the visibility of quantum interferences in a Mach-Zehnder interferometer as a function of temperature, in the quantum Hall regime at a filling factor 2. The temperature dependence of the coherence length can be varied by a factor of 2. The strengthening of the phase coherence at finite temperature is shown to arise from a reduction of the coupling between copropagating edge states. This opens the way for a strong improvement of the phase coherence of quantum Hall systems. The decoupling gate also allows us to investigate how interedge state coupling influences the quantum interferences’ dependence on the injection bias. We find that the finite bias visibility can be decomposed into two contributions: a Gaussian envelope which is surprisingly insensitive to the coupling, and a beating component which, on the contrary, is strongly affected by the coupling.

Received 16 February 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.256802

Authors & Affiliations

P-A. Huynh¹, F. Portier¹, H. le Sueur², G. Faini², U. Gennser², D. Mailly², F. Pierre², W. Wegscheider³, and P. Roche^1,*

¹CEA, SPEC, Nanoelectronics Group, URA 2464, F-91191 Gif-sur-Yvette, France
²CNRS, LPN, Phynano Team, route de Nozay, 91460 Marcoussis, France
³Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland

^*patrice.roche@cea.fr

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 108, Iss. 25 — 22 June 2012

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Scanning electronic microscope view of the sample: the quantum point contacts $G 1$ and $G 2$ are the beam splitters of the MZI. Additional gates $D G 1$ and $D G 2$ are placed on the upper and lower arms to force the inner edge state into small closed loops. The interferences are realized on the outer edge state. The two edge states are fed with different bias voltage with the aid of $G 0$ : $V 1$ for the outer one, and $V 2$ for the inner one. The variation of the phase with respect to $V 2$ allows us to determine the coupling between the two edge states. The picture was taken before the final fabrication step, where bridges are realized to connect both sides of the quantum point contacts and the small Ohmic contact in the center of the figure.Reuse & Permissions
Figure 2
Solid (red) dot: Visibility of quantum interferences for different values of $V_{D G_{1}}$ as a function of the bias voltage at 25 mK. Open (black) dot: Transmission probability through the upper arm of the interferometer. Open (blue) square: Mean transmission through the MZI when revealing interference, the IES being fully reflected by $G 0$ . The departure from the 0.25 value below $V_{D G_{1}} \sim 0.1 V$ indicates a detuning of the MZI due to $D G_{1}$ . The trajectories of both edge states are shown schematically for different values of $V_{D G_{1}}$ in the inserted scanning electronic microscope pictures.Reuse & Permissions
Figure 3
Open circles: Coupling $V_{0}^{- 1}$ between the IES and the OES (left axis). Filled squares (right axis): Measured dephasing $T_{φ}^{- 1} = - \partial \ln (V) / \partial T$ . Solid line (right axis): Measured $T_{φ}^{- 1}$ after subtracting the thermal averaging (see Supplemental Material 20). Open squares (right axis): $T_{T}^{- 1}$ , calculated from the phase variation of the bias (see text). The solid black square at $V_{D G 1} = 0.3 V$ represents the dephasing $T_{φ, up}^{- 1}$ in the upper arm, deduced from a which-path experiment. The scale of the left axis has been adjusted so that the dephasing $T_{φ, up}^{- 1}$ of the upper arm corresponding to $V_{0}^{- 1}$ can be read on the right axis. The lower panel is a sketch of the edge state coupling for different values of $V_{D G 1}$ .Reuse & Permissions
Figure 4
(a) Visibility as a function of the bias voltage for different polarizations of $D G 1$ . Inset: Transmission of the IES through the upper arm of the MZI as a function of $V_{D G 1}$ . (b) Two-dimensional color plot of the visibility normalized to the zero bias visibility as a function of $V_{D G 1}$ and $V_{1}$ .Reuse & Permissions
Figure 5
$V_{C}$ (open dots) and $V_{l}$ (black squares) as a function of the coupling between the two edge states characterized by $V_{0}$ . The dashed line is a guide for the eye. The solid line is the theoretical prediction [18] assuming the same interedge state coupling in both arms of the interferometer.Reuse & Permissions

Physical Review Letters