Nonequilibrium Dephasing in an Electronic Mach-Zehnder Interferometer

Abstract

We study nonequilibrium dephasing in an electronic Mach-Zehnder interferometer. We demonstrate that the shot noise at the beam splitter of the interferometer generates an ensemble of nonequilibrium electron density configurations and that electron interactions induce configuration-specific phase shifts of an interfering electron. The resulting dephasing exhibits two characteristic features, a lobe pattern in the visibility and phase jumps of π, in good agreement with experimental data.PACS numbers: 85.35. Ds, 72.70.+m, 03.65.Yz, Introduction. -An electronic analog of optical MachZehnder interferometry (E-MZI) has been recently realized [1,2,3,4] by utilizing edge channels of integer quantum Hall (IQH) liquids. As it is one of elementary types of interferometry, it can serve as an important probe of electronic coherence [5] and entanglement [6,7,8].The E-MZI has a simple setup consisting of two arms and two beam splitters. Recent experiments [2, 4] on it, nevertheless, revealed puzzling behavior that is hard to understand within a noninteracting-electron description [9]; the interference visibility of the differential conductance shows bias-dependent lobe patterns, accompanied by phase jumps of π at the minima of the lobes. There may exist some unnoticed fundamental physics behind it.Electron-electron interactions may be important for the puzzling nonequilibrium behavior. Interaction effects were studied [10,11] in the tunneling regime by using bosonization methods. In Ref.[10], interactions between an E-MZI channel and an additional one outside the E-MZI were considered and the resulting resonant plasmon excitations were proposed as an origin of the puzzle. On the other hand, roles of the shot noise of an additional detecting channel were addressed [12,13] to understand similar lobes found in a related experiment [12].In this work, we propose an intrinsic mechanism for the puzzling behavior, which does not require additional channels outside the E-MZI. A key observation is that the shot noise at the input beam splitter of the E-MZI generates an ensemble of nonequilibrium electron density configurations in the two arms. Then the electron interaction within each arm induces configuration-specific phase shifts of an interfering electron, and the ensemble average of the phase shifts leads to nonequilibrium dephasing. The combined effect of the shot noise and the interaction results in lobe patterns and phase jumps, which agree with experimental data [2,4]. We use a wave-packet picture to describe the nonequilibrium density and treat the interaction phenomenologically at zero temperature. The inter-arm interaction is ignored.E-MZI setup -The E-MZI consists of two sources i = 1, 2, two drains i = 3, 4, two beam splitters j = a, b, and two arms l = u, d of length L l [ Fig. 1(a)]. The

Crossover between strong and weak measurement in interacting many-body systems

“…The oscillations found here and the physics of visibility lobes that was found experimentally [38] and studied theoretically [39][40][41] in the context of coherent transport through a MZI, are both related to interaction effects in an interferometry setup. To understand this similarity we employ a caricature semi-classical picture: a single particle wave-packet, whose energy components are in the interval eV 0,…”

“…When this single particle wavepacket interacts with a single electron in the detector (see the discussion preceding equation (2)), its phase shift is 0 . á ñ = p [39][40][41], splits into n and N n á ñin arms 3 and 4 respectively, with probability P n T R N n , n N n ⎛ ⎝ ⎜ ⎞…”

Visibility recovery by strong interaction in an electronic Mach-Zehnder interferometer

“…They capture the effects of the QPC's. On the other hand, the electron-electron interactions in the two interferometer arms are described, as in previous studies, 7,9,[13][14][15][16] by a capacitive interaction of the charging energy type,…”

“…Experiments on the interferometer have revealed nontrivial interaction-induced dephasing effects such as the so-called lobe structure 2-6 of the interference visibility under nonequilibrium. Different aspects of the dephasing effects have been theoretically studied in various ways of a bosonization approach, [8][9][10][11][12][13][14][15] a shot-noise argument, 11,16 an interedge interaction model, 10,11 and an exactly solvable model. 13,14 Whereas most previous studies dealt with the dephasing effects in the case that electrons are continuously injected, by dc bias voltage, into the Mach-Zehnder interferometer, here we examine a simpler problem where a single isolated electron wave packet is injected to the interferometer.…”

How to extract weak values from a mesoscopic electronic system

“…In that case, the width of an electron's wave packet is much smaller than the distance between two consecutive electrons. Moreover, we require that the time separation between successive injections of non-equilibrium electrons (τ V S1 2π /eV S1 is much larger than the electron's time-of-flight through the interferometer's arm [27]: τ V S1 τ f l . To reduce adverse decoherence effects one may consider the limit of low temperature, low voltage bias, and nearly symmetric interferometers (i.e., nearly equal arm lengths).…”