Current Cross Correlations Research Articles

Bell-state correlations of quasiparticle pairs in the nonlinear current of a local Fermi liquid

We study Bell-state correlations for quasiparticle pairs excited in nonlinear current through a double quantum dot in the Kondo regime. Exploiting the renormalized perturbation expansion in the residual interactions of the local Fermi liquid and Bell's inequality for cross correlation of spin currents through distinct conduction channels, we derive an asymptotically exact form of Bell's correlation for the double dot at low bias voltages. We find that pairs of quasiparticles and holes excited by the residual exchange interaction can violate Bell's inequality for the cross correlations of the spin currents.

Cross-correlations in a quantum dot Cooper pair splitter with ferromagnetic leads

We investigate Andreev transport through a quantum dot attached to two external ferromagnetic leads and one superconducting electrode. The transport properties of the system are studied by means of the real-time diagrammatic technique in the sequential tunneling regime. To distinguish various contributions to Andreev current we calculate the current cross-correlations, i.e. correlations between currents flowing through two junctions with normal leads. We analyze dependence of current cross-correlations on various parameters of the considered model, both in linear and nonlinear transport regimes. The processes and mechanisms leading to enhancement, suppression or sign change of current cross-correlations are examined and discussed. Interestingly, our results show that for specific transport regimes splitted Cooper pair results in two uncorrelated electrons. However, utilizing ferromagnetic leads instead of non-magnetic electrodes can result in positive current cross-correlations.

Chiral Majorana interference as a source of quantum entanglement

Interferometry is a powerful tool for entanglement production and detection in multiterminal mesoscopic systems. Here we propose a setup to produce, manipulate and detect entanglement in the electron-hole degree of freedom by exploiting Andreev reflection on chiral one-dimensional channels via interferometry. We study the best possible case in which two-particle interferometry produces superpositions of maximally entangled states. This is achieved by mixing chiral Dirac channels through chiral Majorana modes. We show that it is possible to extract entanglement witnesses through current cross-correlation measurements.

Peak-locking centroid bias in Shack–Hartmann wavefront sensing

Shack-Hartmann wavefront sensing relies on accurate spot centre measurement. Several algorithms were developed with this aim, mostly focused on precision, i.e. minimizing random errors. In the solar and extended scene community, the importance of the accuracy (bias error due to peak-locking, quantisation or sampling) of the centroid determination was identified and solutions proposed. But these solutions only allow partial bias corrections. To date, no systematic study of the bias error was conducted. This article bridges the gap by quantifying the bias error for different correlation peak-finding algorithms and types of sub-aperture images and by proposing a practical solution to minimize its effects. Four classes of sub-aperture images (point source, elongated laser guide star, crowded field and solar extended scene) together with five types of peak-finding algorithms (1D parabola, the centre of gravity, Gaussian, 2D quadratic polynomial and pyramid) are considered, in a variety of signal-to-noise conditions. The best performing peak-finding algorithm depends on the sub-aperture image type, but none is satisfactory to both bias and random errors. A practical solution is proposed that relies on the anti-symmetric response of the bias to the sub-pixel position of the true centre. The solution decreases the bias by a factor of ~7 to values of < 0.02 pix. The computational cost is typically twice of current cross-correlation algorithms.

Current cross-correlation in the Anderson impurity model with exchange interaction

We study spin-entanglement of the quasiparticles of the local Fermi liquid excited in nonlinear current through a quantum dot described by the Anderson impurity model with two degenerate orbitals coupled to each other via an exchange interaction. Applying the renormalized perturbation theory, we obtain the precise form of the cumulant generating function and cross-correlations for the currents with spin angled to arbitrary directions, up to third order in the applied bias voltage. It is found that the exchange interaction gives rise to spin-angle dependency in the cross-correlation between the currents through the two different orbitals, and also brings an intrinsic cross-correlation of currents with three different angular momenta.

Nonlocal Andreev entanglements and triplet correlations in graphene with spin-orbit coupling

Using a wavefunction Dirac Bogoliubov-de Gennes method, we demonstrate that the tunable Fermi level of a graphene layer in the presence of Rashba spin orbit coupling (RSOC) allows for producing an anomalous nonlocal Andreev reflection and equal spin superconducting triplet pairing. We consider a graphene junction of a ferromagnet-RSOC-superconductor-ferromagnet configuration and study scattering processes, the appearance of spin triplet correlations, and charge conductance in this structure. We show that the anomalous crossed Andreev reflection is linked to the equal spin triplet pairing. Moreover, by calculating current cross-correlations, our results reveal that this phenomenon causes negative charge conductance at weak voltages and can be revealed in a spectroscopy experiment, and may provide a tool for detecting the entanglement of the equal spin superconducting pair correlations in hybrid structures.

Current cross-correlations in double quantum dot based Cooper pair splitters with ferromagnetic leads

We investigate the current cross-correlations in a double quantum dot based Cooper pair splitter coupled to one superconducting and two ferromagnetic electrodes. The analysis is performed by assuming a weak coupling between the double dot and ferromagnetic leads, while the coupling to the superconductor is arbitrary. Employing the perturbative real-time diagrammatic technique, we study the Andreev transport properties of the device, focusing on the Andreev current cross-correlations, for various parameters of the model, both in the linear and nonlinear response regimes. Depending on parameters and transport regime, we find both positive and negative current cross-correlations. Enhancement of the former type of cross-correlations indicates transport regimes, in which the device works with high Cooper pair splitting efficiency, contrary to the latter type of correlations, which imply negative influence on the splitting. The processes and mechanisms leading to both types of current cross-correlations are thoroughly examined and discussed, giving a detailed insight into the Andreev transport properties of the considered device.

Hanbury Brown and Twiss noise correlations in a topological superconductor beam splitter

We study Hanbury-Brown and Twiss current cross-correlations in a three-terminal junction where a central topological superconductor (TS) nanowire, bearing Majorana bound states at its ends, is connected to two normal leads. Relying on a non-perturbative Green function formalism, our calculations allow us to provide analytical expressions for the currents and their correlations at subgap voltages, while also giving exact numerical results valid for arbitrary external bias. We show that when the normal leads are biased at voltages $V_1$ and $V_2$ smaller than the gap, the sign of the current cross-correlations is given by $-\mbox{sgn}(V_1 \, V_2)$. In particular, this leads to positive cross-correlations for opposite voltages, a behavior in stark contrast with the one of a standard superconductor, which provides a direct evidence of the presence of the Majorana zero-mode at the edge of the TS. We further extend our results, varying the length of the TS (leading to an overlap of the Majorana bound states) as well as its chemical potential (driving it away from half-filling), generalizing the boundary TS Green function to those cases. In the case of opposite bias voltages, $\mbox{sgn}(V_1 \, V_2)=-1$, driving the TS wire through the topological transition leads to a sign change of the current cross-correlations, providing yet another signature of the physics of the Majorana bound state.

Minimal Entanglement Witness from Electrical Current Correlations

Despite great efforts, an unambiguous demonstration of entanglement of mobile electrons in solid state conductors is still lacking. Investigating theoretically a generic entangler-detector setup, we here show that a witness of entanglement between two flying electron qubits can be constructed from only two current cross correlation measurements, for any nonzero detector efficiencies and noncollinear polarization vectors. We find that all entangled pure states, but not all mixed ones, can be detected with only two measurements, except the maximally entangled states, which require three. Moreover, detector settings for optimal entanglement witnessing are presented.

A full spectrum resamping method in polygon tunable laser-based swept-source optical coherence tomography

Swept-source optical coherence tomography (SS-OCT) has high sensitivity and signalnoise ratio compare with time-domain optical coherence tomography and spectral-domain optical coherence tomography. Therefore, SS-OCT is the form of Fourier domain optical coherence tomography predominantly used in experimental research and biomedical image. However, polygon tunable laser-based SS-OCT suffers sweep range fluctuation and spectral misplacement. Under certain circumstances, in the current resampling methods cross-correlation is widely used to align spectrum misplacement, and truncate A-lines in order to ensure the consistency of frequency-scanning range, which, however, degrades the image SNR and resolution. We use the Mach-Zehnder interference (MZI) signal to quantify and analyze this problem in two typical polygon tunable lasers. The periodical change of sweep range and spectrum misplacement show the instability derived from polygon mirror. The parallelism among unwrapped phase curves indicates that polygon tunable laser output spectra have consistent wavelength distributions, and thus it is suited to implement cross-correlation between MZI signals in time domain, and an unwrapped phase curve can represent the wavelength distribution of all A-lines.According to the above conclusions, we demonstrate a resampling method in which the zero-padding interpolation and cross-correlation are used to align A-lines in time domain and eliminate the residual phase noise caused by integer shift. Then the unwrapped phase curve that has a largest sweep range is used to resample all the aligned A-lines, and the interference signals can be fully utilized. The experiments for signal truncation and Pomelo fruit flesh indicate that the proposed method can improve image SNR but does not make the intensity image dislocated. The phase noise (3.9 mrad for a 49 dB SNR) from static mirror is close to theory limit after resampling, thus showing good phase stability and resampling precision. The proposed resampling method also needs less computational work than one-to-one resampling method because it only fits unwrapped phase curve and calculates interpolation coefficient once.

Separation of individual instrumental sounds in monaural music signals applying a modified Wiener filter on the time-frequency plane

This research seeks a signal processor for random processes which is suitable for distilling melodies played by a particular instrument from music ensemble. The proposed processor sequentially evaluates statistics of the mixture assuming a model of music sound and employs a modified Wiener filter so as to separate the mixture of time-variant and correlated random processes such as amplitude changing tones and same pitch tones by different instruments. The model of music sounds is assumed to be a weighted mixture of each standard tone, which is a typical tone of every pitch played by a particular instrument with invariant power, where the weight is called the amplitude factor corresponding to the standard tone. Thus, the proposed processor, at first, evaluates the current amplitude factors which are the the coordinates of the mixture where the standard tones form oblique basis. Then, according to evaluated coordinates of the mixture, its current autocorrelation and cross-correlation to each standard tone are calculated for obtaining the modified Wiener filter. Finally, the filter separates the mixture into individual tone, which is a component of a particular pitch played by an instrument with variant power, and combination of which provides a melody.

Detection of Majorana Kramers Pairs Using a Quantum Point Contact.

We propose a setup that integrates a quantum point contact (QPC) and a Josephson junction on a quantum spin Hall sample, experimentally realizable in InAs/GaSb quantum wells. The confinement due to both the QPC and the superconductor results in a Kramers pair of Majorana zero-energy bound states when the superconducting phases in the two arms differ by an odd multiple of π across the Josephson junction. We investigate the detection of these Majorana pairs with the integrated QPC, and find a robust switching from normal to Andreev scattering across the edges due to the presence of Majorana Kramers pairs. Such a switching of the current represents a qualitative signature where multiterminal differential conductances oscillate with alternating signs when the external magnetic field is tuned. We show that this qualitative signature is also present in current cross-correlations. Thus, the change of the backscattering current nature affects both conductance and shot noise, the measurement of which offers a significant advantage over quantitative signatures such as conductance quantization in realistic measurements.

Enhanced current noise correlations in a Coulomb-Majorana device

Majorana bound states (MBSs) nested in a topological nanowire are predicted to manifest nonlocal correlations in the presence of a finite energy splitting between the MBSs. However, the signal of the nonlocal correlations has not yet been detected in experiments. A possible reason is that the energy splitting is too weak and seriously affected by many system parameters. Here we investigate the charging energy induced nonlocal correlations in a hybrid device of MBSs and quantum dots. The nanowire that hosts the MBSs is assumed in proximity to a mesoscopic superconducting island with a finite charging energy. Each end of the nanowire is coupled to one lead via a quantum dot with resonant levels. With a floating superconducting island, the devices shows a negative differential conductance and giant super-Poissonian shot noise, due to the interplay between the nonlocality of the MBSs and dynamical Coulomb blockade effect. When the island is strongly coupled to a bulk superconductor, the current cross correlations at small lead chemical potentials are negative by tuning the dot energy levels. In contrast, the cross correlation is always positive in a non-Majorana setup. This difference may provide a signature for the existence of the MBSs.

Gate-tunable zero-frequency current cross correlations of the quartet state in a voltage-biased three-terminal Josephson junction

A three-terminal Josephson junction biased at opposite voltages can sustain a phase-sensitive dc-current carrying three-body static phase coherence, known as the "quartet current". We calculate the zero-frequency current noise cross-correlations and answer the question of whether this current is noisy (like a normal current in response to a voltage drop) or noiseless (like an equilibrium supercurrent in response to a phase drop). A quantum dot with a level at energy $\epsilon_0$ is connected to three superconductors $S_a$, $S_b$ and $S_c$ with gap $\Delta$, biased at $V_a=V$, $V_b=-V$ and $V_c=0$, and with intermediate contact transparencies. At zero temperature, nonlocal quartets (in the sense of four-fermion correlations) are noiseless at subgap voltage in the nonresonant dot regime $\epsilon_0/\Delta\gg 1$, which is demonstrated with a semi-analytical perturbative expansion of the cross-correlations. Noise reveals the absence of granularity of the superflow splitting from $S_c$ towards $(S_a,S_b)$ in the nonresonant dot regime, in spite of finite voltage. In the resonant dot regime $\epsilon_0/\Delta< 1$, cross-correlations measured in the $(V_a,V_b)$ plane should reveal an "anomaly" in the vicinity of the quartet line $V_a+V_b=0$, related to an additional contribution to the noise, manifesting the phase sensitivity of cross-correlations under the appearance of a three-body phase variable. Phase-dependent effective Fano factors $F_\varphi$ are introduced, defined as the ratio between the amplitudes of phase modulations of the noise and the currents. At low bias, the Fano factors $F_\varphi$ are of order unity in the resonant dot regime $\epsilon_0/\Delta< 1$, and they are vanishingly small in the nonresonant dot regime $\epsilon_0/\Delta\gg 1$.

Reprint of : Cross-correlations of coherent multiple Andreev reflections

We use the Landauer–Büttiker scattering theory for electronic transport to calculate the current cross-correlations in a voltage-biased three-terminal junction with all superconducting leads. At low bias voltage, when charge transport is due to coherent multiple Andreev reflections, we find large cross-correlations compared with their normal-state value. Furthermore, depending on the parameters that characterize the properties of the scattering region between the leads, the cross-correlations can reverse their sign with respect to the case of non-interacting fermionic systems.

Reprint of : Finite-frequency noise in a topological superconducting wire

In this paper we study the finite-frequency current cross-correlations for a topological superconducting nanowire attached to two terminals at one of its ends. Using an analytic 1D model we show that the presence of a Majorana bound state yields vanishing cross-correlations for frequencies larger than twice the applied transport voltage, in contrast to what is found for a zero-energy ordinary Andreev bound state. Zero cross-correlations at high frequency have been confirmed using a more realistic tight-binding model for finite-width topological superconducting nanowires. Finite-temperature effects have also been investigated.

Cross-correlations of coherent multiple Andreev reflections

We use the Landauer–Büttiker scattering theory for electronic transport to calculate the current cross-correlations in a voltage-biased three-terminal junction with all superconducting leads. At low bias voltage, when charge transport is due to coherent multiple Andreev reflections, we find large cross-correlations compared with their normal-state value. Furthermore, depending on the parameters that characterize the properties of the scattering region between the leads, the cross-correlations can reverse their sign with respect to the case of non-interacting fermionic systems.

Dynamical generation and detection of entanglement in neutral leviton pairs

The entanglement of coherently split electron-hole pairs in an electronic conductor is typically not considered accessible due to particle number conservation and fermionic super-selection rules. We demonstrate here that current cross-correlation measurements at the outputs of an electronic Mach-Zehnder interferometer can nevertheless provide a robust witness of electron-hole entanglement. Specifically, we consider neutral excitations generated by modulating the transmission of an unbiased quantum point contact periodically in time. For an optimized modulation profile, an entangled state with one positively-charged leviton (a hole) and one negatively-charged leviton (an electron) gets delocalized over the two paths of the interferometer and is detected at the output arms. We evaluate the influence of finite electronic temperatures and dephasing corresponding to recent experiments.

Currents and current correlations in a topological superconducting nanowire beam splitter

A beam splitter consisting of two normal leads coupled to one end of a topological superconducting nanowire via double quantum dot is investigated. In this geometry, the linear current cross-correlations at zero temperature change signs vs. the overlap between the two Majorana bound states hosted by the nanowire. Under symmetric bias voltages the net current flowing through the nanowire is noiseless. These two features highlight the fermionic nature of such exotic Majorana excitations though they are based on the superconductivity. Moreover, there exists a unique local particle-hole symmetry inherited from the self-Hermitian property of Majorana bound states, which is apparently scarce in other systems. We show that such particular symmetry can be revealed through measuring the currents under complementary bias voltages.

Majorana-assisted nonlocal electron transport through a floating topological superconductor

The nonlocal nature of the fermionic mode spanned by a pair of Majorana bound states in a one-dimensional topological superconductor has inspired many proposals aiming at demonstrating this property in transport. In particular, transport through the mode from a lead attached to the left bound state to a lead attached to the right will result in current cross-correlations. For ideal zero modes on a grounded superconductor, the cross-correlations are however completely suppressed in favor of purely local Andreev reflection. In order to obtain a non-vanishing cross-correlation, previous studies have required the presence of an additional global charging energy. Adding nonlocal terms in the form of a global charging energy to the Hamiltonian when testing the intrinsic nonlocality of the Majorana modes seems to be conceptually troublesome. Here, we show that a floating superconductor allows to observe nonlocal current correlations in the absence of charging energy. We show that the non-interacting and the Coulomb-blockade regime have the same peak conductance $e^2/h$ but different shot-noise power; while the shot noise is sub-Poissonian in the Coulomb-blockade regime in the large bias limit, Poissonian shot noise is generically obtained in the non-interacting case.