Decoherence and single electron charging in an electronic Mach-Zehnder interferometer

Abstract

We investigate the temperature and voltage dependence of the quantum interference in an electronic MachZehnder interferometer using edge channels in the integer quantum-Hall regime. The amplitude of the interference fringes is significantly smaller than expected from theory; nevertheless the functional dependence of the visibility on temperature and bias voltage agrees very well with theoretical predictions. Superimposed on the Aharonov-Bohm ͑AB͒ oscillations, a conductance oscillation with a six times smaller period is observed. The latter depends only on gate voltage and not on the AB phase, and may be related to single electron charging.Electron interferences in mesoscopic conductors manifest themselves in conductance oscillations which are h / e periodic in the magnetic field B. 1 In conventional metals the visibility I of these Aharonov-Bohm ͑AB͒ oscillations typically amounts to I = G 0 / G Ӎ 10 −3 , where G is the conductance of the sample and G 0 =2e 2 / h the conductance quantum. The visibility can be enhanced to I Ӎ 0.1 by reducing the number of conductance channels, e.g., in nanostructures based on two-dimensional electron systems 2,3 containing only a small number of conductance channels. Recently an electronic analog 4 of the well-known optical Mach-Zehnder interferometer ͑MZI͒ was realized, which employs the onedimensional edge channels in the integer quantum Hall regime. 5 In these devices single channel interference can be realized, while backscattering processes are suppressed. This results in measured visibilities up to I Ӎ 0.6. Such devices open a path for the realization of fundamental two-particle interference experiments in the spirit of Hanbury-Brown and Twiss, 6 as recently proposed. 7 We have realized MZIs similar to those in Ref. 5. A quantum point contact ͑QPC͒ is used to partition an edge channel leaving contact S in two paths. After propagation of the edge channel along the inner and outer edge of a ring-shaped mesa, the two paths are brought to interference at a second QPC, resulting in two output channels D1 and D2 of the interferometer ͑see Fig. 1͒. The phase of the two partial waves can be changed both by magnetic field and by an electrostatic gate G. The measured visibility is much smaller than expected from theory 8 and reported in Ref. 5. Despite this quantitative disagreement, the functional dependence of I on T and V bias fits very well the simple model of Ref. 8. In addition to the AB oscillations we found another type of conductance oscillations, which have a significantly smaller period in gate voltage when compared to the AB period.The mesa was prepared through wet etching of a modulation doped GaAs/ Ga x Al 1−x As heterostructure containing a two-dimensional electron system ͑2DES͒ 90 nm below the surface. At 4 K, the unpatterned 2DES density and mobility were n = 2.0ϫ 10 15 m −2 and = 206 m 2 / ͑V s͒, respectively. Using standard electron beam lithography techniques, we prepared split gates connected by air bridges, defining QPCs of 500 nm length and 220 nm gap width. Th...

Direct Measurement of the Coherence Length of Edge States in the Integer Quantum Hall Regime

“…Quantum dot systems also implicate the possible interplay of Coulomb Blockade effects [13]. The Mach-Zender interferometers (MZI) [2,4,6] used in the present study do not suffer from the same limitations. First, we will show that the observed oscillations result from the interference of two paths of equal length, making thermal smearing negligible.…”

“…Finally, the results of ref. [4], again interpreted by the authors as resulting from thermal smearing, lead to l ϕ ∼ 80 µm at 20 mK.…”

“…Yz, 73.43.Fj, 73.23.Ad The understanding of the decoherence process is a major issue in solid state physics, especially in view of controlling entangled states for quantum information purposes. The edge states of the quantum Hall effect are known to present an extremely long coherence length l ϕ at low temperature [1], providing a useful tool for quantum interference experiments [2,3,4,5,6]. Surprisingly, very little is known on the exact value of this length and the mechanisms which reduce the coherence of edge states.…”

Suppression of Interference in Quantum Hall Mach-Zehnder Geometry by Upstream Neutral Modes

“…From a broader perspective, here we explore how these two experimental facts, namely the undetectability of anyonic AB fringes in MZI (unlike the high visibility of interference in the integer QH regime [8][9][10][11][12][13][14]), and the ubiquity of upstream neutral modes in FQH systems, are related. We show that the latter leads to an exponential suppression of the former.…”

“…A natural probe of statistics is through its effect on the AharonovBohm (AB) interferometry of anyons moving along the gapless edges of a FQH system. Mach-Zehnder interferometers [8][9][10][11][12][13][14] would have been efficient tools to observe anionic interferometry as they avoid interference-masking Coulomb effects [15,16] and are robust against further quasiparticle fluctuations in the bulk [17][18][19].…”