Direct Measurement of the Coherence Length of Edge States in the Integer Quantum Hall Regime

Abstract

We have determined the finite temperature coherence length of edge states in the Integer Quantum Hall Effect (IQHE) regime. This was realized by measuring the visibility of electronic Mach-Zehnder interferometers of different sizes, at filling factor 2. The visibility shows an exponential decay with the temperature. The characteristic temperature scale is found inversely proportional to the length of the interferometer arm, allowing to define a coherence length lϕ. The variations of lϕ with magnetic field are the same for all samples, with a maximum located at the upper end of the quantum hall plateau. Our results provide the first accurate determination of lϕ in the quantum Hall regime.PACS numbers: 03.65. Yz, 73.43.Fj, 73.23.Ad The understanding of the decoherence process is a major issue in solid state physics, especially in view of controlling entangled states for quantum information purposes. The edge states of the quantum Hall effect are known to present an extremely long coherence length l ϕ at low temperature [1], providing a useful tool for quantum interference experiments [2,3,4,5,6]. Surprisingly, very little is known on the exact value of this length and the mechanisms which reduce the coherence of edge states. This is in strong contrast with diffusive conductors, where weak localisation gives a powerful way to probe l ϕ . It has been shown, in this case, that electronelectron interactions are responsible for the finite coherence length at low temperatures. In the IQHE regime, the presence of a high magnetic field destroys any time reversal symmetry needed for weak localisation corrections, making such an investigation difficult. Furthermore, due to the uni-dimensionality of the edge states, electron-electron interactions may strongly modify the single particle picture and one can ask wether the notion of phase coherence length is still relevant and how it depends on temperature. In this letter, we show for the first time that one can define a phase coherence length, and that it is inversely proportional to the temperature. Though the energy redistribution length has been studied in the past [7,8],these scattering experiments do not measure the phase coherence, which requires observation of electron interference effects. So far, experiments have only been able to put a lower bound on l ϕ at low temperatures [2, 9, 10, 11]. The electronic Fabry-Pérot interferences occurring in ballistic quantum dots have been used since the early days of mesoscopic physics [9]. These first studies showed an exponential decay of the amplitude of the Aharonov-Bohm (AB) oscillations with temperature [10]. However, this decay was attributed to thermal smearing due to the contribution of thermally activated one particle energy levels of the dot. Furthermore, the size of the interferometers was not varied, nor was a Fourier analysis performed of the AB oscillations that could yield an estimation of l ϕ [12]. Quantum dot systems also implicate the possible interplay of Coulomb Blockade effects [13]. The Mach-Zender interf...

Dynamical control of interference using voltage pulses in the quantum regime

“…The device is close to the ones measured experimentally for example, in ref. 8 (although smaller owing to computational limitations) and simulated in DC in ref. 24.…”

“…A few works propose setups for 'flying qubits' [1][2][3][4][5][6] that encode the quantum information into the paths taken by the electrons. Those systems could be realized in Mach-Zehnder interferometers in the quantum Hall regime [7][8][9] or Aharonov-Bohm geometries 10 . Before designing any of those circuits, however, a necessary step is the understanding of the basic, potentially new, physics associated with the time-resolved dynamics in delocalized nanoelectronic systems.…”

Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2 period oscillations

“…The side gate sweep is therefore the preferred technique given its simpler interpretation. Although a complete theoretical understanding of edge state interference is presently emerging (B I Halperin and A Stern, personal communication), it has been demonstrated experimentally (12,13) that the area change achieved by using side-gate bias produces A-B oscillations in which the period directly reflects the charge of the edge channels. Attempts to assess the 5/2 quasiparticle charge and statistics through interferometry are therefore best served by employing a device capable of adjusting the area with a side gate while controlling the transmission independently with separately controlled qpcs.…”

“…Mach-Zehnder interferometer designs (12,13) Here we report interferometry studies using devices particularly designed for accommodating fragile FQH states, specifically the 5/2 state. FQH state confinement in an interferometer geometry is achieved here by using only top gate structures on ultra-high mobility, high-density samples for which the gate structures have minimal negative impact on the 2D electron quality.…”

Separation of neutral and charge modes in one-dimensional chiral edge channels

“…This mechanism is at the heart of the decoherence 9,10,13 and relaxation [14][15][16]12 of electronic excitations propagating in these systems. As such, it has been probed through Mach-Zehnder interferometry [17][18][19] or spectroscopy of edge channels [20][21][22] . This situation bears strong analogies with the spin-charge separation of conventional 1D wires, except that the two spin species are carried by two separated edge channels.…”