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

Abstract

Mach-Zehnder interferometry has been proposed as a probe for detecting the statistics of anyonic quasiparticles in fractional quantum Hall (FQH) states. Here we focus on interferometers made of multimode edge states with upstream modes. We find that the interference visibility is suppressed due to downstream-upstream mode entanglement; the latter serves as a "which path" detector to the downstream interfering trajectories. Our analysis tackles a concrete realization of filling factor ν = 2/3, but its applicability goes beyond that specific case, and encompasses the recent observation of ubiquitous emergence of upstream neutral modes in FQH states. The latter, according to our analysis, goes hand in hand with the failure to observe Mach-Zehnder anyonic interference in fractional states. We point out how charge-neutral mode disentanglement will resuscitate the interference signal. Introduction.-One of the most striking implications of the theory of the fractional quantum Hall (FQH) effect is the nature of the elementary excitations ("anyons"), featuring fractional charge and fractional statistics. The latter concerns the change in the state of the system upon braiding the anyons: it is multiplied by a phase in the abelian case, and by a unitary operator in the nonabelian case, thus raising the prospect of topologicallyprotected quantum computation [1]. Experimental evidence for fractional charge dates back almost two decades ago [2][3][4]. Notwithstanding intriguing results [5][6][7], fractional statistics has remained elusive to date. 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].The interfering paths of a Mach-Zehnder interferometer (MZI) rely on the chiral edge modes of the FQH geometries. Multimode edges [20][21][22] present one with an interesting twist: the possibility of upstream moving modes (i.e., modes moving against the "downstream" direction set by the magnetic field). These may be neutral [23][24][25]. Such modes have been experimentally detected through the generation of upstream charge noise [26][27][28][29] and thermometry [30]. Recent measurements [31] have surprisingly found that, unlike earlier predictions, upstream neutral modes are not restricted to "hole-like" states (e.g., 1/2 < ν < 1), but rather show up in virtually all FQH states, including simple "electron-like" Laughlin states (such as ν = 1/3) [32]. How do these upstream moving modes affect the expected anyonic interference?Here we show that their effect on the anyonic interference visibility is detrimental. The present analysis, employing the example of a ν = 2/3 FQH system [23,24], entails a single upstream-propagating neutral mode along the edge of a MZI. We note that our...

Creating topological interfaces and detecting chiral edge modes in a two-dimensional optical lattice

“…A striking demonstration of the outline trajectory performed by QH edge states was provided by a doubleslit-electron-interferometer experiment, which realized a QHbased Mach-Zehnder interferometer [28]. Interestingly, such geometries have been considered to probe the fractional (anyonic) statistics of FQH excitations [33]. More recent experiments also revealed signatures of exotic counter-propagating ("neutral upstream") modes in FQH liquids [29][30][31][32], in agreement with early theoretical works [23][24][25][26].…”

“…Even more recently, it was suggested in Ref. [33] that the presence of such counter-propagating edge modes could have important consequences on the detection of fractional (anyonic) statistics, based on QH Mach-Zehnder interferometers [28]. The unique possibility of creating topological interfaces in a cold-atom experiment offers a promising platform for the analysis of these topological edge structures, where Bragg spectroscopy [101,128] and high-resolution imaging techniques could be exploited in view of revealing their exotic dispersion relations and dynamical properties in the presence of controllable interactions and disorder.…”

“…Detecting and analyzing the properties of topological edge excitations constitutes an intense field of research since the early days of the QH effect [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The chiral nature of QH edge modes was first revealed through edge-magnetoplasma experiments [21] (see also the pioneer measurements reported in Refs.…”

Aharonov–Bohm interference of fractional quantum Hall edge modes

“…[40]. We mention that a sharp confining potential may also be beneficial for measuring interference at the ν = 1/3 state by preventing edge reconstruction and the proliferation of neutral edge modes [20,47,48] which may cause dephasing [49,50]; neutral modes have been detected at ν = 1/3 and numerous other fractional quantum Hall states in standard GaAs structures without screening wells [51].…”

Conductance plateaus and shot noise in fractional quantum Hall point contacts

“…46. attributed the loss of interference to proliferation of neutral modes [48,49] induced by edge reconstruction due to a soft edge confinement potential [17,18,47].…”