MESOSCOPIC PHYSICS
Transmitting the quantum state of electrons across a
metallic island with Coulomb interaction
H. Duprez^1 , E. Sivre^1 , A. Anthore1,2, A. Aassime^1 , A. Cavanna^1 , U. Gennser^1 , F. Pierre^1 †
The Coulomb interaction generally limits the quantum propagation of electrons. However, it can also
provide a mechanism to transfer their quantum state over larger distances. Here, we demonstrate such
a form of electron teleportation across a metallic island. This effect originates from the low-temperature
freezing of the island’s chargeQwhich, in the presence of a single connected electronic channel,
enforces a one-to-one correspondence between incoming and outgoing electrons. Such faithful quantum
state imprinting is established between well-separated injection and emission locations and evidenced
through two-path interferences in the integer quantum Hall regime. The additional quantum phase of
2 pQ/e, whereeis the electron charge, may allow for decoherence-free entanglement of propagating
electrons, and notably of flying qubits.
A
disordered environment, with a large
number of interacting degrees of free-
dom, is generally considered unfavorable
for quantum technologies. Such an en-
vironment is exemplified by a metallic
island with a large energy density of states and
a small number of connected electronic chan-
nels, through which there is no quantum co-
herent propagation of individual electrons.
Indeed, the time that an individual electron
spends inside the island ( 1 ) is typically much
longer than the interval between inelastic
collisions destroying its quantum coherence
( 2 , 3 ). In contrast to this conventional wisdom,
we show experimentally that the Coulomb
interaction in such an island can, under the
right circumstances, lead to a near perfect
transmission of the quantum state of elec-
trons across it, mediated by the collective
surface plasmon modes of the island ( 4 , 5 ).
In the quantum Hall regime implementa-
tion, where injection and emission points
are physically separated by chirality, this con-
stitutes a form of teleportation of the electrons’
state. This phenomenon is different from the
standard“quantum teleportation”protocol
( 6 ) and similar to the“electron teleportation”
proposed in ( 7 ).
Thevoltageprobemodelofametallicisland
( 8 ) is widely used to mimic the electrons’quan-
tum decoherence and energy relaxation toward
equilibrium [see, e.g., ( 9 )]. However, independ-
ent absorption and emission of electrons result
in fluctuations of the total island chargeQ,with
a characteristic charging energyEC¼e^2 = 2 C(C
is the geometrical capacitance of the island
andeis the elementary electron charge). At
low temperaturesT≪EC=kB(wherekBis the
Boltzmann constant), this energy is not avail-
able, and the macroscopic quantum charge
stateQis effectively frozen ( 5 , 10 ) [although
not quantized in units ofeas long as one
channel is perfectly connected ( 11 – 13 )]. Conse-
quently, correlations develop between absorbed
and emitted electrons. Such correlations are
strongest if only one transport channel is con-
nected to the island, in which case theory
predicts that the electrons entering it and
those concomitantly exiting it are in identi-
cal quantum states ( 4 , 5 ) [see also ( 14 ) for a
related prediction in the presence of strong
nonlocal interactions along quantum Hall
edges]. Effectively, the electronic states within
the connected quantum channel are decoupled
from the many quasiparticles within the island,
even though the incoming (outgoing) physical
electron particles penetrate into (originatefrom) the island. Another consequence is that
heat evacuation from the island’s internal
states along the channel is fully suppressed
( 10 ). By contrast, in the presence of two or
more open channels, the coherence is lost
( 5 ), and heat evacuation is restored, in agree-
ment with the recently observed systematic
heat Coulomb blockade of one ballistic chan-
nel ( 15 ). The comparable“electron telepo-
rtation”proposed in ( 7 )alsoreliesonthe
“all-important”Coulomb charging energy
of a small island, which has to prevail over
temperature and voltage bias. In this pro-
posal ( 7 ), the island is superconducting,
without subgap states except for Majorana
bound states at the injection and emission
locations. Such a teleportation process was
recently invoked as one possible mechanism
for the observed coherent single-electron
transport across a hybrid superconductor-
semiconductor island in the Coulomb blockade
regime ( 16 ). We additionally point out some
similarities with quasiparticle correlations in-
duced by Andreev reflections that take place at
the interface between a normal metal and a
superconductor ( 2 ). These correlations can be
created nonlocally, through the so-called crossed
Andreev reflection involving an electron and a
hole separated by at most the superconducting
coherence length.
We demonstrate the high-fidelity replica-
tion of the quantum state of electrons across
a metallic island through quantum interfer-
ences. For this purpose, an injected current is
first split along two separate paths that are
subsequently recombined, thereby realizing an
electronic Mach-Zehnder interferometer (MZI).RESEARCH
Duprezet al.,Science 366 , 1243–1247 (2019) 6 December 2019 1of4
(^1) Université Paris-Saclay, CNRS, Centre de Nanosciences et de
Nanotechnologies (C2N), 91120 Palaiseau, France^2 Université de
Paris, C2N, 91120 Palaiseau, France
*These authors contributed equally to this work.
†Corresponding author. Email: [email protected]
Fig. 1. Device e-beam
micrograph.Areas with a
Ga(Al)As 2DEG underneath
the surface appear darker.
The applied perpendicular
magnetic fieldB’5T
corresponds to the integer
quantum Hall regime at
a filling factor of 2. Capaci-
tively coupled gates colored
green and blue control,
respectively, the MZI beam
splitters for the outer quan-
tum Hall edge channel
(lines with arrow, here
corresponding to the sche-
matic in Fig. 2B) and the
connection to the floating
metallic island (sand yellow,
in right half) in good ohmic
contact with the buried 2D electron gas. One of the two MZI outputs is the central small ohmic contact (light
brown, in left half) connected to ground through a suspended bridge. The secondone,largerandlocatedfarther
away, is schematically represented by the top white circle. The MZI phase difference is controlled throughB
or the plunger gate voltageVpl. The red dashed line visually represents the nonlocal quantum state transfer across
the island, between electrons’injection (starting point) and emission (arrow).
on December 12, 2019^
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