Only one edge channel is biased
They suppose first, that only one edge channel is biased (experimentally occurs when
T0 =1, namely the inner edge state is reflected) and that T1 is much smaller than 1/2 corresponding to the weak tunneling regime (they obtain same results in the weak backscattering
regime if ∆L = 0).
They first calculate the variation of the Aharonov Bohm phase with the potential
(∆µ = eV )
∂∆φAB
u+ν
=
∆L
∂∆µ
2uν
Therefore, for the symmetric interferometer, ∆L=0, the phase shift is independent of
the bias. This may explain the phenomenon of phase rigidity observed [56][69][44], if one
assumes that the interferometer is symmetric. However, this conclusion is exactly the same
that we obtain when considering non-interacting quasi particle. Regarding the visibility,
this model gives :
|ν| = | cos(∆µL/(2v))|
(5.16)
where L is the length of one arm of the interferometer. It simply describes the beating
between the two interferences leading to periodic zeros of the visibility with the bias.
This approach seems to contradict some experimental results. First, the period of the
calculated visibility is ∼ to v/L, and should thus depend on the size of the interferometer
in contradiction with our data since we have shown that for the middle and large MZI,
we obtained the same lobe width. 20 This model is unfortunately only valid in the weak
backscattering (tunneling) regime. However, it is known that far from the perturbative
limit, the theory does not apply. If one tries to extend their theory to higher (smaller)
value of T1 , we can show that the visibility will be ∼ to v/((1 − 2T1 ) × L) in contradiction
with experiments where it has been shown that the lobe pattern did not depend on T1 [68]
[57].

### Language ###
English

### Assessment ###
The text discusses visibility period's independence from interferometer size, which could spark a natural query about this relationship.

### Query ###
The visibility period of a quantum interferometer depends on its physical size, right or wrong?

Note: This query is naturally worded, avoids interrogative pronouns, and seeks a specific piece of information that the text can directly answer, while being formulated independently of the text's existence.
The visibility period of a quantum interferometer depends on its physical size, right or wrong?

Note: This query is naturally worded, avoids interrogative pronouns, and seeks a specific piece of information that the text can directly answer, while being formulated independently of the text's existence.