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Register a new userTwo-electron coherence and its measurement in electron quantum optics
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Engineering and studying few-electron states in ballistic conductors is a key step towards understanding entanglement in quantum electronic systems. In this Letter, we introduce the intrinsic two-electron coherence of an electronic source in quantum Hall edge channels and relate it to two-electron wavefunctions and to current noise in an Hanbury Brown--Twiss interferometer. Inspired by the analogy with photon quantum optics, we propose to measure the intrinsic two-electron coherence of a source using low-frequency current correlation measurements at the output of a Franson interferometer. To illustrate this protocol, we discuss how it can distinguish between a time-bin entangled pure state and a statistical mixture of time shifted electron pairs.
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In this paper, we review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the usual case of photon quantum optics. Electron quantum optics aims at preparing, manipulating and measuring coherent single electron excitations propagating in ballistic conductors such as the edge channels of a 2DEG in the integer quantum Hall regime. Because of the Fermi statistics and the presence of strong interactions, electron quantum optics exhibits new features compared to the usual case of photon quantum optics. In particular, it provides a natural playground to understand decoherence and relaxation effects in quantum transport.
The recent developments of electron quantum optics in quantum Hall edge channels have given us new ways to probe the behavior of electrons in quantum conductors. It has brought new quantities called electronic coherences under the spotlight. In this paper, we explore the relations between electron quantum optics and signal processing through a global review of the various methods for accessing single- and two-electron coherences in electron quantum optics. We interpret electron quantum optics interference experiments as analog signal processing converting quantum signals into experimentally observable quantities such as current averages and correlations. This point of view also gives us a procedure to obtain quantum information quantities from electron quantum optics coherences. We illustrate these ideas by discussing two mode entanglement in electron quantum optics. We also sketch how signal processing ideas may open new perspectives for representing electronic coherences in quantum conductors and understand the properties of the underlying many-body electronic state.
We discuss a technique and a material system that enable the controlled realization of quantum entanglement between spin-wave modes of electron ensembles in two spatially separated pieces of semiconductor material. The approach uses electron ensembles in GaAs quantum wells that are located inside optical waveguides. Bringing the electron ensembles in a quantum Hall state gives selection rules for optical transitions across the gap that can selectively address the two electron spin states. Long-lived superpositions of these electron spin states can then be controlled with a pair of optical fields that form a resonant Raman system. Entangled states of spin-wave modes are prepared by applying quantum-optical measurement techniques to optical signal pulses that result from Raman transitions in the electron ensembles.
The quantum coherence of electronic quasiparticles underpins many of the emerging transport properties of conductors at small scales. Novel electronic implementations of quantum optics devices are now available with perspectives such as flying qubit manipulations. However, electronic quantum interferences in conductors remained up to now limited to propagation paths shorter than $30,mu$m, independently of the material. Here we demonstrate strong electronic quantum interferences after a propagation along two $0.1,$mm long pathways in a circuit. Interferences of visibility as high as $80%$ and $40%$ are observed on electronic analogues of the Mach-Zehnder interferometer of, respectively, $24,mu$m and $0.1,$mm arm length, consistently corresponding to a $0.25,$mm electronic phase coherence length. While such devices perform best in the integer quantum Hall regime at filling factor 2, the electronic interferences are restricted by the Coulomb interaction between copropagating edge channels. We overcome this limitation by closing the inner channel in micron-scale loops of frozen internal degrees of freedom, combined with a loop-closing strategy providing an essential isolation from the environment.
We demonstrate the extension of coherence between all four two-electron spin ground states of an InAs quantum dot molecule (QDM) via non-local suppression of nuclear spin fluctuations in both constituent quantum dots (QDs), while optically addressing only the upper QD transitions. Long coherence times are revealed through dark-state spectroscopy as resulting from nuclear spin locking mediated by the exchange interaction between the QDs. Lineshape analysis provides the first measurement of the quieting of the Overhauser field distribution correlating with reduced nuclear spin fluctuations.
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