Two-particle entanglement in capacitively coupled Mach-Zehnder interferometers

Abstract

We propose and analyze a mesoscopic device producing on-demand entangled pairs of electrons. The system consists of two capacitively coupled Mach-Zehnder interferometers implemented in a quantum Hall structure. A pair of electron wave-packets is injected into the chiral edge states of two (of the four) incoming arms; scattering on the incoming interferometers splits the wave-packets into four components of which two interact. The resulting interaction phase associated with this component leads to the entanglement of the state; the latter is scattered at the outgoing beam splitter and analyzed in a Bell violation test measuring the presence of particles in the four outgoing leads. We study the two-particle case and determine the conditions to reach and observe full entanglement. We extend our two-particle analysis to include the underlying Fermi seas in the quantum Hall device; the change in shape of the wave-function, the generation of electron-hole pairs in the interaction regime, and a time delay between the pulses all reduce the degree of visible entanglement and the violation of the Bell inequality, effects which we analyze quantitatively. We determine the device settings optimizing the entanglement and the Bell test and find that violation is still possible in the presence of the Fermi seas, with a maximal Bell parameter reaching B = 2.18 > 2 in our setup.

Single-electron entanglement and nonlocality

“…We note that our results for the current and the zero-frequency noise do not depend on the pulse width Γ. As such, our measurement strategy based on equation (22) would also work with constant voltages as realized in the experiment by Neder et al [3], and the CHSH violation of equation (25) would be obtained. However, to unambiguously demonstrate single-electron entanglement, in line with the thought experiment described in section 3, it is important that only one electron from each source is traversing the interferometer at any given time.…”

“…The entanglement is detected by violating a Bell inequality [14,15] formulated in terms of zero-frequency current cross-correlations [16][17][18]. While early proposals focus on electron sources driven by static voltages, more recent works investigate the ondemand generation of entangled states using dynamic single-electron emitters [19][20][21][22][23].…”

Quantum computing through electron propagation in edge states of quantum spin Hall systems

“…26,33 It is also worth noting that, the decoherence caused by Coulomb interaction in the Luttinger liquids can be partly or even fully undone with the help of a suitable voltage pulse. 29,30 Consequently, the quantum computing scheme based on electronic spins seems rather promising within the QSH framework.…”

“…This suggests a twoqubit controlled phase gate can be implemented through the on-demand Coulomb interaction between electrons, which together with the two single-qubit gates can realize universal quantum computation. 27 Such Coulomb interaction between edges has recently been proposed to measure the which-path information 28 and generate orbital entanglement 29 in the coupled Mach-Zehnder interferometer setup composed by the edge states in the quantum Hall systems. Here we generalize the discussion to QSHs and utilize such an effect to perform quantum gate on the electronic spins.…”

“…[28][29][30] We now calculate the evolution of the two particle wave function. The interaction Hamiltonian in the interaction picture can be obtained as…”