Interactions and charge fractionalization in an electronic Hong-Ou-Mandel interferometer

Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer

Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel motifs that characterize the interplay of entanglement and quantum statistics: an 'entanglement pointer' and a 'statistics-induced entanglement entropy'. The two provide a quantitative description of the statistics-induced entanglement: (i) they are finite only in the presence of quantum entanglement underlined by quantum statistics and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, and anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements of auto-correlation and cross-correlation of current fluctuations of the scattered beams (following 'collisions'), we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.

Two electrons interacting at a mesoscopic beam splitter

The nonlinear response of a beam splitter to the coincident arrival of interacting particles enables numerous applications in quantum engineering and metrology. Yet, it poses considerable challenges to control interactions on the individual particle level. Here, we probe the coincidence correlations at a mesoscopic constriction between individual ballistic electrons in a system with unscreened Coulomb interactions and introduce concepts to quantify the associated parametric nonlinearity. The full counting statistics of joint detection allows us to explore the interaction-mediated energy exchange. We observe an increase from 50% up to 70% in coincidence counts between statistically indistinguishable on-demand sources and a correlation signature consistent with the independent tomography of the electron emission. Analytical modelling and numerical simulations underpin the consistency of the experimental results with Coulomb interactions between two electrons counterpropagating in a quadratic saddle potential. Coulomb repulsion energy and beam splitter dispersion define a figure of merit, which in this experiment is demonstrated to be sufficiently large to enable future applications, such as single-shot in-flight detection and quantum logic gates.

Anyonic Statistics Revealed by the Hong-Ou-Mandel Dip for Fractional Excitations

The fractional quantum Hall effect (FQHE) is known to host anyons, quasiparticles whose statistics is intermediate between bosonic and fermionic. We show here that Hong-Ou-Mandel (HOM) interferences between excitations created by narrow voltage pulses on the edge states of a FQHE system at low temperature show a direct signature of anyonic statistics. The width of the HOM dip is universally fixed by the thermal time scale, independently of the intrinsic width of the excited fractional wave packets. This universal width can be related to the anyonic braiding of the incoming excitations with thermal fluctuations created at the quantum point contact. We show that this effect could be realistically observed with periodic trains of narrow voltage pulses using current experimental techniques.

Partition of Two Interacting Electrons by a Potential Barrier

Scattering or tunneling of an electron at a potential barrier is a fundamental quantum effect. Electron-electron interactions often affect the scattering, and understanding of the interaction effect is crucial in detection of various phenomena of electron transport and their application to electron quantum optics. We theoretically study the partition and collision of two interacting hot electrons at a potential barrier. We predict their kinetic energy change by their Coulomb interaction during the scattering delay time inside the barrier. The energy change results in characteristic deviation of the partition probabilities from the noninteracting case. The derivation includes nonmonotonic dependence of the probabilities on the barrier height, which qualitatively agrees with recent experiments, and reduction of the fermionic antibunching.

Electronic Wave-Packets in Integer Quantum Hall Edge Channels: Relaxation and Dissipative Effects

We theoretically investigate the evolution of the peak height of energy-resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor equal to two. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energies. We investigate this quantity assuming a short-range capacitive coupling between the edges. Moreover, we also phenomenologically take into account the possibility of energy dissipation towards additional degrees of freedom—both linear and quadratic—in the injection energy. Through a comparison with recent experimental data, we rule out the non-dissipative case as well as a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate for describing the behavior of the quasi-particle peak at short enough propagation lengths.

Spectral features of voltage pulses in interacting helical channels

We investigate the interplay of voltage-driven excitations and electron-electron interactions in a pair of counterpropagating helical channels capacitively coupled to a time-dependent gate. By focusing on the non-equilibrium spectral properties of the system, we show how the spectral function is modified by external drives with different time profile in presence of Coulomb interactions. In particular, we focus on a Lorentzian drive and a square single pulse. In presence of strong enough electron-electron interactions, we find that both drives can result in minimal excitations, i.e. characterized by an excess spectral function with a definite sign. This is in contrast with what happens in the non-interacting case, where only properly quantized Lorentzian pulses are able to produce minimal excitations.

Quantum tomography of electrical currents

In quantum nanoelectronics, time-dependent electrical currents are built from few elementary excitations emitted with well-defined wavefunctions. However, despite the realization of sources generating quantized numbers of excitations, and despite the development of the theoretical framework of time-dependent quantum electronics, extracting electron and hole wavefunctions from electrical currents has so far remained out of reach, both at the theoretical and experimental levels. In this work, we demonstrate a quantum tomography protocol which extracts the generated electron and hole wavefunctions and their emission probabilities from any electrical current. It combines two-particle interferometry with signal processing. Using our technique, we extract the wavefunctions generated by trains of Lorentzian pulses carrying one or two electrons. By demonstrating the synthesis and complete characterization of electronic wavefunctions in conductors, this work offers perspectives for quantum information processing with electrical currents and for investigating basic quantum physics in many-body systems.

Coherent control of single electrons: a review of current progress

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

Minimal Excitations in the Fractional Quantum Hall Regime

We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury Brown-Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.

Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization

Coulomb interaction has a striking effect on electronic propagation in one-dimensional conductors. The interaction of an elementary excitation with neighbouring conductors favours the emergence of collective modes, which eventually leads to the destruction of the Landau quasiparticle. In this process, an injected electron tends to fractionalize into separated pulses carrying a fraction of the electron charge. Here we use two-particle interferences in the electronic analogue of the Hong-Ou-Mandel experiment in a quantum Hall conductor at filling factor 2 to probe the fate of a single electron emitted in the outer edge channel and interacting with the inner one. By studying both channels, we analyse the propagation of the single electron and the generation of interaction-induced collective excitations in the inner channel. These complementary pieces of information reveal the fractionalization process in the time domain and establish its relevance for the destruction of the quasiparticle, which degrades into the collective modes.

A charge injected into the edge of a correlated one-dimensional system can split into separate charge packages. Freulon et al. now study this electron fractionalization on the picosecond timescale using Hong-Ou-Mandel interferometry.

Partitioning of on-demand electron pairs

The on-demand generation and separation of entangled photon pairs are key components of quantum information processing in quantum optics. In an electronic analogue, the decomposition of electron pairs represents an essential building block for using the quantum state of ballistic electrons in electron quantum optics. The scattering of electrons has been used to probe the particle statistics of stochastic sources in Hanbury Brown and Twiss experiments and the recent advent of on-demand sources further offers the possibility to achieve indistinguishability between multiple sources in Hong-Ou-Mandel experiments. Cooper pairs impinging stochastically at a mesoscopic beamsplitter have been successfully partitioned, as verified by measuring the coincidence of arrival. Here, we demonstrate the splitting of electron pairs generated on demand. Coincidence correlation measurements allow the reconstruction of the full counting statistics, revealing regimes of statistically independent, distinguishable or correlated partitioning, and have been envisioned as a source of information on the quantum state of the electron pair. The high pair-splitting fidelity opens a path to future on-demand generation of spin-entangled electron pairs from a suitably prepared two-electron quantum-dot ground state.

Detection of spin entanglement via spin-charge separation in crossed Tomonaga-Luttinger liquids

We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLLs) realized, e.g., as two crossed nanowires or quantum Hall edge states. When injecting into each TLL one electron of opposite spin, the dc current measured after the crossing differs for singlet, triplet, or product states. This is a striking new non-Fermi liquid feature because the (mean) current in a noninteracting beam splitter is insensitive to spin entanglement. It can be understood in terms of collective excitations subject to spin-charge separation. This behavior may offer an easier alternative to traditional entanglement detection schemes based on current noise, which we show to be suppressed by the interactions.

Resonant edge magnetoplasmons and their decay in graphene

We investigate resonant edge magnetoplasmons (EMPs) and their decay in graphene by high-frequency electronic measurements. From EMP resonances in disk shaped graphene, we show that the dispersion relation of EMPs is nonlinear due to interactions, giving rise to the intrinsic decay of EMP wave packets. We also identify extrinsic dissipation mechanisms due to interaction with localized states in bulk graphene from the decay time of EMP wave packets. We indicate that, owing to the linear band structure and the sharp edge potential, EMP dissipation in graphene can be lower than that in GaAs systems.

Real-time decoherence of Landau and Levitov quasiparticles in quantum Hall edge channels

Quantum Hall edge channels at integer filling factor provide a unique test bench to understand the decoherence and relaxation of single-electron excitations in a ballistic quantum conductor. In this Letter, we obtain a full visualization of the decoherence scenario of energy (Landau)- and time (Levitov)-resolved single-electron excitations at filling factor ν = 2. We show that the Landau excitation exhibits a fast relaxation followed by spin-charge separation whereas the Levitov excitation only experiences spin-charge separation. We finally suggest to use Hong-Ou-Mandel-type experiments to probe specific signatures of these different scenarios.