Counting statistics and dephasing transition in an electronic Mach-Zehnder interferometer

Abstract

It was recently suggested that a novel type of phase transition may occur in the visibility of electronic Mach-Zehnder interferometers. Here, we present experimental evidence for the existence of this transition. The transition is induced by strongly non-Gaussian noise that originates from the strong coupling of a quantum point contact to the interferometer. We provide a transparent physical picture of the effect by exploiting a close analogy to the neutrino oscillations of particle physics. In addition, our experiment constitutes a probe of the singularity of the elusive full counting statistics of a quantum point contact. The recent discovery of a lobe-type behavior in the visibility of Aharonov-Bohm oscillations in electronic Mach-Zehnder interferometers (MZI) has triggered extensive theoretical studies in this field. These interferometers were implemented in the edge channels in the integer quantum Hall effect (QHE), mostly for filling factor ff = 2 [see Figs. 1(a) and 1(b)] [1-3]. Many sophisticated theories have been proposed to explain the lobes in the differential visibility of Aharonov-Bohm oscillations as a function of the voltage bias [4][5][6][7][8][9][10][11]. While the central lobe and next side lobe are easy to explain, observation of additional side lobes in a number of experiments is considered to be a puzzling phenomenon. Here, we show that this effect can be explained in a rather simple way, if two interacting edge channels are present. The underlying phenomenon turns out to be very similar to that of neutrino oscillations in high-energy physics: neutrinos oscillate between different flavor states because they are created in a flavor eigenstate, which is not an eigenstate of the Hamiltonian. Similarly, when an electron wave packet is partitioned by a beam splitter, it excites a collective charge mode, which is not an eigenstate of our model Hamiltonian [6]. At the second beam splitter of the interferometer, this leads to a secondary interference between the collective modes as a function of the applied voltage bias. This model can explain many of the experimental observations [12][13][14][15][16], most importantly the visibility lobes [17] and the phase rigidity of the visibility [1,2].Dephasing of the Aharanov-Bohm interference results from random fluctuations of the phase that are averaged out by the detector. In our devices, fluctuations are generated by an additional quantum point contact (QPC-0) in front of the interferometer input, which can be controlled by its transmission probability T 0 . The noisy input current leads to charge fluctuations in the interferometer. The accumulated charge shifts the edge, which leads to the Aharonov-Bohm phase shift. Hence, the strong Coulomb interaction between the edge channels guarantees a strong coupling of the electrons in the interferometer to the noise. The visibility will thus be suppressed by the charge fluctuations induced by partitioning of electrons at QPC-0. Most interestingly, the lobe pattern was predicted to undergo a sudden change at T ...

Coulomb and exchange interaction effects on the exact two-electron dynamics in the Hong-Ou-Mandel interferometer based on Hall edge states

“…Regarding the electronic HOM effect, recent experiments highlight the presence of charge fractionalization [29,33,34] in the propagation of single excitations in edge channels, so that the coherence of the traveling qubit is not preserved [35,36]. This effect originates at bulk filling factor 2 due to interchannel interactions that destroy the coherence of the injected Landau quasiparticles [37][38][39]. As recently proposed, strategies can be implemented to quench this source of decoherence, e.g., the introduction of top gates to loop the second channel [40] or to increase the distance between the two copropagating states [15].…”

Optimal Quantum Interference Thermoelectric Heat Engine with Edge States

“…Dephasing and path-length difference.-A key question is how robust the obtained results are to possible deviations from optimal conditions, most importantly due to dephasing effects and unequal path lengths. Dephasing, the loss of phase coherence for electrons traversing the interferometers, has been investigated in depth for Mach-Zehnder interferometers [60][61][62][63][64][65][66]. Adapting here a qualitative model [67,68], treating dephasing as phase averaging or equivalently, via coupling of the interferometer to a dephasing probe, we can write the total phase as φ 0 =φ 0 + δφ, a sum of a constant, controllable partφ 0 and a randomly fluctuating part δφ.…”

Relaxation of an electron wave packet at the quantum Hall edge at filling factorν=2

“…New interesting mesoscopic phenomena that arise from this correlations have recently been the subject of experimental studies and intensive theoretical discussions. In the context of the present paper we would like to mention the observation of the lobes [4][5][6][7][8][9][10] and of the shot noise-induced phase transition 11 in the visibility of Aharonov-Bohm (AB) oscillations in electronic MZ interferometers, and the experimental studies of relaxation of non-equilibrium electron distribution functions.…”