In contrast with usual MZI implementations
( 17 – 21 ), one of the paths can controllably be
diverted toward a small floating metallic island
(Fig. 1). In that case, any two-path quantum
interferences involve both the initial electrons
(direct left path) and the reemitted ones (in-
terrupted right path, assuming a perfect con-
tact with the island). Therefore high-visibility
interferences directly ascertain a high fidelity
of the electron state replication. The Coulomb
interaction was previously invoked to account
for various observations in electron interfer-
ometers,suchasthemultiplesidelobesversus
voltage bias in ( 22 ) or the phase rigidity versus
magnetic field in ( 23 ).
A colorized e-beam micrograph of the mea-
sured device is shown in Fig. 1. The sample
was nanofabricated from a high-mobility
Ga(Al)As two-dimensional electron gas (2DEG)
and immersed in a perpendicular magnetic
fieldB≃5 T corresponding to the integer quan-
tum Hall filling factorn¼2, where the elec-
tron quantum coherence length is the largest
( 18 , 19 , 21 ). In this regime, two quantum Hall
channels copropagate along the edges (the
electron gas was etched away in the brighter
areas), and the MZI is formed using only the
outer edge channel. The followed paths are
represented by thick lines with arrows for
the configuration where one MZI arm goes
through the floating metallic island (corre-
sponding schematic shown in Fig. 2B). The
two MZI beam splitters, each tuned to half
transmission, are realized with quantum
point contacts formed by field effect using
split gates (colored green; the inner quantum
Hall channel, not shown, is fully reflected).
One of the two MZI outputs is the small
central metallic electrode (light brown, in
left half of Fig. 1), which is grounded through a
suspended bridge. The quantum interferences
are characterized by the oscillations of the
current transmitted to the second MZI output
formed by a much larger electrode 60mm
away (represented in Fig. 1 by the top white
circle), while sweeping either the magnetic
fieldBor the voltageVplapplied to a lateral
plunger gate (purple). The floating metallic
island (sand yellow, in right half of Fig. 1)
consists of 2mm^3 of a gold-germanium-nickel
alloy diffused into the Ga(Al)As heterojunction
by thermal annealing. The typical metallic den-
sity of states of such metals isnF≈ 1047 J^1 m^3
(1.14 × 10^47 for gold, the main constituent),
corresponding to a very small average elec-
tronic level spacing in the island ofd≈30 peV.
The dwell (wandering) time of individual
electrons within this island is given by the
expressiontD¼Nhd≈^130 Nms, wherehis the Planck
constant andNis the number of connected
edge channels ( 1 ). As pointed out in the intro-
duction, this is much longer than the quantum
coherence time of electrons in similar metals,
whichisatmostinthe20-nsrange( 3 , 24 ). The
gates barring the broad way on each side of
the floating island (blue) are normally tuned
to either fully reflect or fully transmit the outer
edge channel, in order to implement the MZI
configurations schematically represented in
Fig. 2, A to C. The second (inner) quantum
Hall edge channel is always completely ref-
lected at the barring gate (fig. S1) and can
therefore be ignored ( 5 ). The island charging
energyEC≃kB 0 :3 K was obtained from
standard Coulomb diamond measurements [in
a specifically tuned tunnel regime; see Fig. 3B
and ( 25 )]. At the experimental electronic tem-
peratureT≃10 mK [measured on-chip from
shot noise ( 26 )], the criterionkBT≪ECfor
fully developed Coulomb-induced correlations
is therefore well verified. The previous experi-
ments were performed in the opposite“high-
temperature”regimekBT≫ECof negligible
Coulomb correlations, in which case, unsur-
prisingly, a complete quantum decoherence
( 27 ) and energy relaxation ( 28 ) of electrons
were observed with a single connected chan-
nel. Finally, the transparency of the contact
between the floating island and the outer
quantum Hall edge channel plays an essential
role: If the transparency is poor, many elec-
trons would simply be reflected at the inter-
face. Here,≳ 97 %of the incoming current
penetrates into the floating island ( 25 ), which
is also reflected by the marked changes of
behavior detailed later.In Fig. 2D, we show typical MZI oscillations
versusBoftMZI, the fraction of outer edge
channel current transmitted across the device.
The measurements were performed in the
three configurations depicted in Fig. 2, A to C.
The red continuous line in Fig. 2D corre-
sponds to a standard electronic MZI, with the
floating metallic island bypassed (schematic in
Fig. 2A). In that case, the oscillations are of
high visibilityV≡ðtmaxMZItminMZIÞ=ðtmaxMZIþtminMZIÞ≈
90% and, as expected for the Aharonov-Bohm
phase, the magnetic field period of 241T 3 mT
(red symbols in Fig. 2E show consecutive extrema
positions) closely corresponds to one flux quan-
tum (241mTS≃ 0 : 98 h=eusing the nomi-
nal areaS≃ 16 : 8 mm^2 ). A small asymmetry in
thetMZIdata (the average is slightly above 0:5)
results from a small reflection of the outer
edge channel on the grounded central ohmic
contact [of≈5% ; see ( 25 )]. The black con-
tinuous line in Fig. 2D was measured with
the right MZI arm deviated to go through the
floating ohmic island (edge channel paths dis-
played in Fig. 1, and schematic in Fig. 2B). We
observe first that the visibility of quantum
interference remains of the same high ampli-
tude, which corresponds to a perfect fidelity
(at experimental accuracy) of the replicated
quantum states imprinted on the electrons
reemitted from the island, in agreement with
low-temperature predictions ( 4 , 5 ). Second, the
magnetic field period of 305T 4 mT is foundDuprezet al.,Science 366 , 1243–1247 (2019) 6 December 2019 2of4
Fig. 2. Quantum
oscillations versus
magnetic field.(Ato
C) Schematics of imple-
mented MZI configura-
tions. (D) FractiontMZI
of the outer edge
channel current
transmitted across
the MZI as a function
ofB. Continuous lines
are measurements
performed in the
configuration framed
by a box of the same
colorin(A),(B),and
(C). The horizontal black
dashed lines represent
thetMZIextrema for the
standard and floating
island MZI configurations
[schematics in (A) and
(B), respectively],
corresponding to a high
quantum oscillations
visibility ofVe90%. With a second channel connected to the floating island (configuration shown Fig. 2C), the
quantum oscillations are strongly reduced to a visibilityVe20%, consistent with the separately characterized
small residual reflection ofe3% [see text and ( 25 )], and the averagetMZIis diminished as part of the current is
transmitted across the island towardaremoteelectricalground.(E) Symbols display the magnetic field position
of consecutive extrema (both peaks and dips increment the index number).RESEARCH | REPORT
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