Observing the universal screening of a Kondo impurity

The Kondo effect, deriving from a local magnetic impurity mediating electron-electron interactions, constitutes a flourishing basis for understanding a large variety of intricate many-body problems. Its experimental implementation in tunable circuits has made possible important advances through well-controlled investigations. However, these have mostly concerned transport properties, whereas thermodynamic observations - notably the fundamental measurement of the spin of the Kondo impurity - remain elusive in test-bed circuits. Here, with a novel combination of a 'charge' Kondo circuit with a charge sensor, we directly observe the state of the impurity and its progressive screening. We establish the universal renormalization flow from a single free spin to a screened singlet, the associated reduction in the magnetization, and the relationship between scaling Kondo temperature and microscopic parameters. In our device, a Kondo pseudospin is realized by two degenerate charge states of a metallic island, which we measure with a non-invasive, capacitively coupled charge sensor. Such pseudospin probe of an engineered Kondo system opens the way to the thermodynamic investigation of many exotic quantum states, including the clear observation of Majorana zero modes through their fractional entropy.

Observation of Edge Magnetoplasmon Squeezing in a Quantum Hall Conductor

Squeezing of the quadratures of the electromagnetic field has been extensively studied in optics and microwaves. However, previous works focused on the generation of squeezed states in a low impedance (Z_{0}≈50  Ω) environment. We report here on the demonstration of the squeezing of bosonic edge magnetoplasmon modes in a quantum Hall conductor whose characteristic impedance is set by the quantum of resistance (R_{K}≈25  kΩ), offering the possibility of an enhanced coupling to low-dimensional quantum conductors. By applying a combination of dc and ac drives to a quantum point contact, we demonstrate squeezing and observe a noise reduction 18% below the vacuum fluctuations. This level of squeezing can be improved by using more complex conductors, such as ac driven quantum dots or mesoscopic capacitors.

Quasiparticle Andreev scattering in the ν = 1/3 fractional quantum Hall regime

The scattering of exotic quasiparticles may follow different rules than electrons. In the fractional quantum Hall regime, a quantum point contact (QPC) provides a source of quasiparticles with field effect selectable charges and statistics, which can be scattered on an 'analyzer' QPC to investigate these rules. Remarkably, for incident quasiparticles dissimilar to those naturally transmitted across the analyzer, electrical conduction conserves neither the nature nor the number of the quasiparticles. In contrast with standard elastic scattering, theory predicts the emergence of a mechanism akin to the Andreev reflection at a normal-superconductor interface. Here, we observe the predicted Andreev-like reflection of an e/3 quasiparticle into a - 2e/3 hole accompanied by the transmission of an e quasielectron. Combining shot noise and cross-correlation measurements, we independently determine the charge of the different particles and ascertain the coincidence of quasielectron and fractional hole. The present work advances our understanding on the unconventional behavior of fractional quasiparticles, with implications toward the generation of novel quasi-particles/holes and non-local entanglements.

Relaxation and revival of quasiparticles injected in an interacting quantum Hall liquid

The one-dimensional, chiral edge channels of the quantum Hall effect are a promising platform in which to implement electron quantum optics experiments; however, Coulomb interactions between edge channels are a major source of decoherence and energy relaxation. It is therefore of large interest to understand the range and limitations of the simple quantum electron optics picture. Here we confirm experimentally for the first time the predicted relaxation and revival of electrons injected at finite energy into an edge channel. The observed decay of the injected electrons is reproduced theoretically within a Tomonaga-Luttinger liquid framework, including an important dissipation towards external degrees of freedom. This gives us a quantitative empirical understanding of the strength of the interaction and the dissipation.

Fractional statistics in anyon collisions

Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor ν = 1/m (where m is an odd integer) have been predicted to obey Abelian fractional statistics, with a phase ϕ associated with the exchange of two particles equal to π/m However, despite numerous experimental attempts, clear signatures of fractional statistics have remained elusive. We experimentally demonstrate Abelian fractional statistics at filling factor ν = ⅓ by measuring the current correlations resulting from the collision between anyons at a beamsplitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract ϕ = π/3, in agreement with predictions.

Electronic heat flow and thermal shot noise in quantum circuits

When assembling individual quantum components into a mesoscopic circuit, the interplay between Coulomb interaction and charge granularity breaks down the classical laws of electrical impedance composition. Here we explore experimentally the thermal consequences, and observe an additional quantum mechanism of electronic heat transport. The investigated, broadly tunable test-bed circuit is composed of a micron-scale metallic node connected to one electronic channel and a resistance. Heating up the node with Joule dissipation, we separately determine, from complementary noise measurements, both its temperature and the thermal shot noise induced by the temperature difference across the channel. The thermal shot noise predictions are thereby directly validated, and the electronic heat flow is revealed. The latter exhibits a contribution from the channel involving the electrons' partitioning together with the Coulomb interaction. Expanding heat current predictions to include the thermal shot noise, we find a quantitative agreement with experiments.

Transmitting the quantum state of electrons across a metallic island with Coulomb interaction

The Coulomb interaction generally limits the quantum propagation of electrons. However, it can also provide a mechanism to transfer their quantum state over larger distances. Here, we demonstrate such a form of electron teleportation across a metallic island. This effect originates from the low-temperature freezing of the island's charge Q which, in the presence of a single connected electronic channel, enforces a one-to-one correspondence between incoming and outgoing electrons. Such faithful quantum state imprinting is established between well-separated injection and emission locations and evidenced through two-path interferences in the integer quantum Hall regime. The additional quantum phase of 2πQ/e, where e is the electron charge, may allow for decoherence-free entanglement of propagating electrons, and notably of flying qubits.

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.

Chiral domain walls of Mn3Sn and their memory

Magnetic domain walls are topological solitons whose internal structure is set by competing energies which sculpt them. In common ferromagnets, domain walls are known to be of either Bloch or Néel types. Little is established in the case of Mn3Sn, a triangular antiferromagnet with a large room-temperature anomalous Hall effect, where domain nucleation is triggered by a well-defined threshold magnetic field. Here, we show that the domain walls of this system generate an additional contribution to the Hall conductivity tensor and a transverse magnetization. The former is an electric field lying in the same plane with the magnetic field and electric current and therefore a planar Hall effect. We demonstrate that in-plane rotation of spins inside the domain wall would explain both observations and the clockwise or anticlockwise chirality of the walls depends on the history of the field orientation and can be controlled.

Microwave photons emitted by fractionally charged quasiparticles

Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge q and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a dc voltage Vdc. We observe that only photons at frequencies f below qVdc/h are emitted. This threshold provides a direct and unambiguous determination of the charge q, and a signature of exclusion statistics. Derived initially within the Luttinger model, this feature is also predicted by universal non-equilibrium fluctuation relations which agree fully with our measurements. Our work paves the way for further exploration of anyonic statistics using microwave measurements.

Tunable quantum criticality and super-ballistic transport in a “charge” Kondo circuit

Quantum phase transitions (QPTs) are ubiquitous in strongly correlated materials. However, the microscopic complexity of these systems impedes the quantitative understanding of QPTs. We observed and thoroughly analyzed the rich strongly correlated physics in two profoundly dissimilar regimes of quantum criticality. With a circuit implementing a quantum simulator for the three-channel Kondo model, we reveal the universal scalings toward different low-temperature fixed points and along the multiple crossovers from quantum criticality. An unanticipated violation of the maximum conductance for ballistic free electrons is uncovered. The present charge pseudospin implementation of a Kondo impurity opens access to a broad variety of strongly correlated phenomena.

Controlling charge quantization with quantum fluctuations

In 1909, Millikan showed that the charge of electrically isolated systems is quantized in units of the elementary electron charge e. Today, the persistence of charge quantization in small, weakly connected conductors allows for circuits in which single electrons are manipulated, with applications in, for example, metrology, detectors and thermometry. However, as the connection strength is increased, the discreteness of charge is progressively reduced by quantum fluctuations. Here we report the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometre-scale metallic island to a circuit, we explore the complete evolution of charge quantization while scanning the entire range of connection strengths, from a very weak (tunnel) to a perfect (ballistic) contact. We observe, when approaching the ballistic limit, that charge quantization is destroyed by quantum fluctuations, and scales as the square root of the residual probability for an electron to be reflected across the quantum channel; this scaling also applies beyond the different regimes of connection strength currently accessible to theory. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization and in a universal square-root scaling, valid for all connection strengths, in agreement with expectations. Besides being pertinent for the improvement of single-electron circuits and their applications, and for the metal-semiconductor hybrids relevant to topological quantum computing, knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices.

Electron Phase Shift at the Zero-Bias Anomaly of Quantum Point Contacts

The Kondo effect is the many-body screening of a local spin by a cloud of electrons at very low temperature. It has been proposed as an explanation of the zero-bias anomaly in quantum point contacts where interactions drive a spontaneous charge localization. However, the Kondo origin of this anomaly remains under debate, and additional experimental evidence is necessary. Here we report on the first phase-sensitive measurement of the zero-bias anomaly in quantum point contacts using a scanning gate microscope to create an electronic interferometer. We observe an abrupt shift of the interference fringes by half a period in the bias range of the zero-bias anomaly, a behavior which cannot be reproduced by single-particle models. We instead relate it to the phase shift experienced by electrons scattering off a Kondo system. Our experiment therefore provides new evidence of this many-body effect in quantum point contacts.

Disorder-Induced Stabilization of the Quantum Hall Ferromagnet

We report on an absolute measurement of the electronic spin polarization of the ν=1 integer quantum Hall state. The spin polarization is extracted in the vicinity of ν=1 (including at exactly ν=1) via resistive NMR experiments performed at different magnetic fields (electron densities) and Zeeman energy configurations. At the lowest magnetic fields, the polarization is found to be complete in a narrow region around ν=1. Increasing the magnetic field (electron density) induces a significant depolarization of the system, which we attribute to a transition between the quantum Hall ferromagnet and the Skyrmion glass phase theoretically expected as the ratio between Coulomb interactions and disorder is increased. These observations account for the fragility of the polarization previously observed in high mobility 2D electron gas and experimentally demonstrate the existence of an optimal amount of disorder to stabilize the ferromagnetic state.

Tomonaga-Luttinger physics in electronic quantum circuits

In one-dimensional conductors, interactions result in correlated electronic systems. At low energy, a hallmark signature of the so-called Tomonaga–Luttinger liquids is the universal conductance curve predicted in presence of an impurity. A seemingly different topic is the quantum laws of electricity, when distinct quantum conductors are assembled in a circuit. In particular, the conductances are suppressed at low energy, a phenomenon called dynamical Coulomb blockade. Here we investigate the conductance of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance, and demonstrate a proposed link to Tomonaga–Luttinger physics. We reformulate and establish experimentally a recently derived phenomenological expression for the conductance using a wide range of circuits, including carbon nanotube data obtained elsewhere. By confronting both conductance data and phenomenological expression with the universal Tomonaga–Luttinger conductance curve, we demonstrate experimentally the predicted mapping between dynamical Coulomb blockade and the transport across a Tomonaga–Luttinger liquid with an impurity.

When physicists study the characteristics of quantum conductors they usually take great pains to limit the resistance of other elements in the system. But Jezouin et al. show that when a single quantum channel is measured in series with a resistor, it exhibits analogous characteristics to a Tomonaga–Luttinger liquid.

Epsilon-near-zero mode for active optoelectronic devices

The electromagnetic modes of a GaAs quantum well between two AlGaAs barriers are studied. At the longitudinal optical phonon frequency, the system supports a phonon polariton mode confined in the thickness of the quantum well that we call epsilon-near-zero mode. This epsilon-near-zero mode can be resonantly excited through a grating resulting in a very large absorption localized in the single quantum well. We show that the reflectivity can be modulated by applying a voltage. This paves the way to a new class of active optoelectronic devices working in the midinfrared and far infrared at ambient temperature.

Chargeless heat transport in the fractional quantum Hall regime

We demonstrate a direct approach to investigate heat transport in the fractional quantum Hall regime. At a filling factor of ν=4/3, we inject power at quantum point contacts and detect the related heating from the activated current through a quantum dot. The experiment reveals a chargeless heat transport from a significant heating that occurs upstream of the power injection point, in the absence of a concomitant electrical current. By tuning in situ the edge path, we show that the chargeless heat transport does not follow the reverse direction of the electrical current path along the edge. This unexpected heat conduction, whose mechanism remains to be elucidated, may play an important role in the physics of the fractional quantum Hall regime.

Quantum coherence engineering in the integer quantum Hall regime

We present an experiment where the quantum coherence in the edge states of the integer quantum Hall regime is tuned with a decoupling gate. The coherence length is determined by measuring the visibility of quantum interferences in a Mach-Zehnder interferometer as a function of temperature, in the quantum Hall regime at a filling factor 2. The temperature dependence of the coherence length can be varied by a factor of 2. The strengthening of the phase coherence at finite temperature is shown to arise from a reduction of the coupling between copropagating edge states. This opens the way for a strong improvement of the phase coherence of quantum Hall systems. The decoupling gate also allows us to investigate how interedge state coupling influences the quantum interferences' dependence on the injection bias. We find that the finite bias visibility can be decomposed into two contributions: a Gaussian envelope which is surprisingly insensitive to the coupling, and a beating component which, on the contrary, is strongly affected by the coupling.

Magneto-Transport Measurements on Si/Si1−xGex Resonant Tunneling Structures

We have investigated magneto-transport properties of differently strained Si/ Si1−xGex resonant tunneling devices. The built-in strain was either put in the Si layers, by means of a thick., relaxed Si1−xGex buffer layer, or in the Si1−xGex layers, in which case all Si1−xGex layers were grown below the critical thickness, and a Si1−xGex spacer layer with graded Ge content was used. Magnetic fields parallel to the interface have been employed to probe the in-plane dispersion in the quantum well. This is used to study the effect of band-mixing in the two strain configurations. A field perpendicular to the interface resolves some Landau level splitting. Most strikingly, however, is the similarity in the spectra with the case when the magnetic field is applied parallel to the interfaces. This indicates broadening of the levels, possibly due to scattering, and the importance of 3-dimensional band structure effects.

Tuning energy relaxation along quantum Hall channels

The chiral edge channels in the quantum Hall regime are considered ideal ballistic quantum channels, and have quantum information processing potentialities. Here, we demonstrate experimentally, at a filling factor of ν(L)=2, the efficient tuning of the energy relaxation that limits quantum coherence and permits the return toward equilibrium. Energy relaxation along an edge channel is controllably enhanced by increasing its transmission toward a floating Ohmic contact, in quantitative agreement with predictions. Moreover, by forming a closed inner edge channel loop, we freeze energy exchanges in the outer channel. This result also elucidates the inelastic mechanisms at work at ν(L)=2, informing us, in particular, that those within the outer edge channel are negligible.

Energy relaxation in the integer quantum Hall regime

We investigate the energy exchanges along an electronic quantum channel realized in the integer quantum Hall regime at a filling factor of νL=2. One of the two edge channels is driven out of equilibrium and the resulting electronic energy distribution is measured in the outer channel, after several propagation lengths 0.8  μm≤L≤30  μm. Whereas there are no discernible energy transfers toward thermalized states, we find efficient energy redistribution between the two channels without particle exchanges. At long distances L≥10  μm, the measured energy distribution is a hot Fermi function whose temperature is lower than expected for two interacting channels, which suggests the contribution of extra degrees of freedom. The observed short energy relaxation length challenges the usual description of quantum Hall excitations as quasiparticles localized in one edge channel.

Tuning decoherence with a voltage probe

We present an experiment where we tune the decoherence in a quantum interferometer using one of the simplest objects available in the physics of quantum conductors: an Ohmic contact. For that purpose, we designed an electronic Mach-Zehnder interferometer which has one of its two arms connected to an Ohmic contact through a quantum point contact. At low temperature, we observe quantum interference patterns with a visibility up to 57%. Increasing the connection between one arm of the interferometer to the floating Ohmic contact, the voltage probe, reduces quantum interference as it probes the electron trajectory. This unique experimental realization of a voltage probe works as a trivial which-path detector whose efficiency can be simply tuned by a gate voltage.

Noise dephasing in edge states of the integer quantum Hall regime

An electronic Mach-Zehnder interferometer is used in the integer quantum Hall regime at a filling factor 2 to study the dephasing of the interferences. This is found to be induced by the electrical noise existing in the edge states capacitively coupled to each other. Electrical shot noise created in one channel leads to phase randomization in the other, which destroys the interference pattern. These findings are extended to the dephasing induced by thermal noise instead of shot noise: it explains the underlying mechanism responsible for the finite temperature coherence time tau_{phi}(T) of the edge states at filling factor 2, measured in a recent experiment. Finally, we present here a theory of the dephasing based on Gaussian noise, which is found to be in excellent agreement with our experimental results.

Electrically injected cavity polaritons

We have realized an electroluminescent device operating in the light-matter strong-coupling regime based on a GaAs/AlGaAs quantum cascade structure embedded in a planar microcavity. At zero bias, reflectivity measurements show a polariton anticrossing between the intersubband transition and the cavity mode. Under electrical injection the spectral features of the emitted light change drastically, as electrons are resonantly injected in a reduced part of the polariton branches. Our experiments demonstrate that electrons can be selectively injected into polariton states up to room temperature.

Direct measurement of the coherence length of edge states in the integer quantum Hall regime

We have determined the finite temperature coherence length of edge states in the integer quantum Hall effect 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 one to define a coherence length l_(phi). The variations of l_(phi) 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 l_(phi) in the quantum Hall regime.

Experimental test of the dynamical coulomb blockade theory for short coherent conductors

We observed the recently predicted quantum suppression of dynamical Coulomb blockade on short coherent conductors by measuring the conductance of a quantum point contact embedded in a tunable on-chip circuit. Taking advantage of the circuit modularity we measured most parameters used by the theory. This allowed us to perform a reliable and quantitative experimental test of the theory. Dynamical Coulomb blockade corrections, probed up to the second conductance plateau of the quantum point contact, are found to be accurately normalized by the same Fano factor as quantum shot noise, in excellent agreement with the theoretical predictions.

Use of quantum-point-contact high-electron-mobility-transistors for time domain multiplexing of large arrays of high impedance low temperature bolometers

The use of a multiplexing readout for an array of bolometers simplifies the electronics and wiring, so making the readout of large arrays of bolometers (>100) feasible. Here we describe a time domain multiplexing technique and its performance based on the use of quantum-point-contact high-electron-mobility-transistors as low temperature (to approximately 100 mK) switches for measuring high impedance (5...70 MOmega) resistances and sensors. The presented system is well matched to ground based millimetric astronomy demands.

Intersubband electroluminescence from silicon-based quantum cascade structures

The quantum cascade laser, which uses electronic transitions within a single band of a semiconductor, constitutes a possible way to integrate active optical components into silicon-based technology. This concept necessitates a transition with a narrow linewidth and an upper state with a sufficiently long lifetime. We report the observation of intersubband electroluminescence from a p-type silicon/silicon-germanium quantum cascade structure, centered at 130 millielectron volts with a width of 22 millielectron volts, with the expected polarization, and discernible up to 180 kelvin. The nonradiative lifetime is found to depend strongly on the design of the quantum well structure, and is shown to reach values comparable to that of an equivalent GaInAs/AlInAs laser structure.

Analysis of the metallic phase of two-dimensional holes in SiGe in terms of temperature dependent screening

We find that temperature dependent screening can quantitatively explain the metallic behavior of the resistivity on the metallic side of the so-called metal-insulator transition in p-SiGe. Interference and interaction effects exhibit the usual insulating behavior which is expected to overpower the metallic background at sufficiently low temperatures. We find empirically that the concept of a Fermi liquid describes our system with its large interaction parameter r(s) approximately 8.