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We simulated the radiative response of the cavity quantum electrodynamics (QED) inductively coupled to the ring pierced by magnetic flux, and analyzed its spectral dependence to get insight into persistent current dynamics. Current fluctuations in the ring induce changes in the microwave resonator: shifting the resonant frequency and changing its damping. We use the linear response theory and calculate the current response function by means of the Green function technique. Our model contains two quantum dots which divide the ring into two arms with different electron transfers. There are two opposite (symmetric and asymmetric) components of the persistent current, which interplay can be observed in the response functions. The resonator reflectance shows characteristic shifts in the dispersive regime and avoided crossings at the resonance points. The magnitude of the resonator frequency shift is greater for coupling to the arm with higher transparency. Fluctuations of the symmetric component of the persistent current are relevant for a wide range of the Aharovov-Bohm phase $\phi$, while the asymmetric component becomes dominant close to $\phi\approx \pi$ (when the total persistent current changes its orientation), Comment: 5 pages, 4 figures, presented at European Conf. PHYSICS OF MAGNETISM 2023 (PM'23), June 26-30, Poznan, Poland

We simulated the radiative response of the cavity quantum electrodynamics (QED) coupled to the double quantum dot Cooper pair splitter and analyzed its spectral dependence to get insight into dynamics of the Cooper pair transfers. The model is confined to the energy subspace where two entangled electrons are transferred to two normal electrodes through the inter-dot singlet state on two proximitized quantum dots. Our research is focused on the Andreev scatterings in the subgap regime, for which the local charge susceptibility $\Pi(\omega_p)$ is derived, by means of Keldysh Green functions, in a whole bias voltage range. In particular, in the large voltage limit the spectrum of $\Pi(\omega_p)$ is expressed by a simple analytical formula, which shows various dissipation processes related with photon-induced transitions between the Andreev bound states., Comment: 7 pages, 4 figures

Transient electron dynamics and the Fano resonance formation over time in transport through a two quantum dot system in a T-shape geometry (2QD-T) are analysed for free electrons. Time evolution of the transport characteristics are different for a weak and a strong inter-dot coupling with respect to the dot-electrode coupling. When the dot-dot coupling is weak, we find that transport dynamics is governed by two channel tunneling processes with two different relaxation times and buildup of the Fano resonance is developed much slower, with the longer relaxation time. In the opposite limit, the transmission evolves with a single relaxation time, from the single peak resonance structure into the structure with two asymmetric peaks. One observes large dot-electrode charge oscillations, which can temporarily change direction of transient currents. We find also that the time evolution of entanglement is different in both coupling regimes; in particular rapid Rabi oscillations caused by coherent electron transfer between the 2QD states can be seen for the strong dot-dot coupling., Comment: 6 pages, 4 figures, presented at The European Conference Physics of Magnetism 2021

Exact analytical formulas are derived, by means of Keldysh Green functions, for currents and current correlation functions in a Cooper pair splitter modelled on a double quantum dot system coherently coupled to a superconductor and two normal metallic electrodes. Confining to the subspace with the inter-dot singlet we show perfect entanglement of split electrons in two separated crossed Andreev reflection processes. The studies are focused on the noise power spectrum in a whole bias voltage range. In particular, in the large voltage limit shot noise dominates and its spectrum exhibits two extraordinary side dips related to resonant inter-level current correlations caused by coherent electron-hole recombination processes accompanied by emission and absorption of photons. In the linear response limit we derived the frequency dependent admittance which shows different interference patterns for the cross and the auto current correlations., Comment: 12 pages, 5 figures

We present studies of quantum interference in a noise power spectrum in the system of two quantum dots (2QD) in a T-geometry. Performing the spectral decomposition we are able to separate local currents and distinguish between the intra- and inter-level current correlation contributions to the noise power spectrum. In particular, we analyzed the large bias regime and show that for a weak coupling of 2QD with the electrodes the noise power spectrum has dips at frequencies characteristic to inter-level excitations. For a strong coupling the electron transport changes its nature and the dynamics of the current correlations is different: there are two coherently coupled relaxators with different relaxation frequencies. These two regimes of current dynamics are separated by a quantum critical point, in which the noise power spectrum shows a specific frequency dependence. In the linear response limit the noise power spectrum is related to the admittance, which shows characteristics different, due to quantum interference, for the weak and strong coupling case., Comment: 4 pages, 2 figures, presented at The European Conference Physics of Magnetism 2021

Statistical properties of the electron transport flowing through nanostructures are strongly influenced by the interactions, geometry of the system and/or by type of the external electrodes. These factors affect not only the average current induced in the system but also contribute to fluctuations in the flux of charges and their correlations. Due to possible applications of the hybrid nano-systems, containing one or more superconducting electrodes, a detailed understanding of the flow of charge and its fluctuations seems to be of primary importance. Coulomb repulsion between electrons usually strongly affect the current-current correlation function. In this work we study the correlations in the charge flow through such interacting quantum dot contacted to one superconducting and two normal electrodes. This set-up allows for analysis of the Andreev scattering events in the correlations of currents flowing between external electrodes and, in particular, gives access to cross-correlations between currents from/to different normal electrodes. Our approach relies on the master equation technique, which properly captures the Coulomb interactions. We study the finite frequency correlations and find the relaxation processes, related to the high frequency charge and low frequency polarisation fluctuations. The multiterminal structure of here studied single electron device allows to analyze a competition between the intra- and inter-channel correlations. In the appropriate limit of the interacting quantum dot embedded between two normal electrodes our calculations quantitatively describe the recent experimental data on the frequency dependent correlations. This shows a promising potential of the method for description of the hybrid systems with superconducting electrode(s).

We present studies of the electron transport and circular currents induced by the bias voltage and the magnetic flux threading a ring of three quantum dots coupled with two electrodes. Quantum interference of electron waves passing through the states with opposite chirality plays a relevant role in transport, where one can observe Fano resonance with destructive interference. The quantum interference effect is quantitatively described by local bond currents and their correlation functions. Fluctuations of the transport current are characterized by the Lesovik formula for the shot noise, which is a composition of the bond current correlation functions. In the presence of circular currents, the cross-correlation of the bond currents can be very large, but it is negative and compensates for the large positive auto-correlation functions., Comment: 10 pages, 8 figures, minor improvments

We consider a model of two interacting always-on, exchange-only qubits for which controlled phase ($CPHASE$), controlled NOT ($CNOT$), quantum Fourier transform ($QFT$) and $SWAP$ operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the $CPHASE$ gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: $CNOT$, $QFT$ and $SWAP$. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations., Comment: 19 pages, 5 figures

We study generation and dynamics of an exchange spin qubit encoded in three coherently coupled quantum dots with three electrons. For two geometries of the system a linear and a triangular one, the creation and coherent control of the qubit states are performed by the Landau--Zener transitions. In the triangular case both the qubit states are equivalent and can be easily generated for particular symmetries of the system. If one of the dots is smaller than the others one can observe Rabi oscillations, that can be used for coherent manipulation of the qubit states. The linear system is easier to fabricate; however, then the qubit states are not equivalent, making qubit operations more difficult to control., Comment: 17 pages, 5 figures

The thermoelectric effects in three-terminal structures with a quantum dot are considered. We propose the experimentally consistent protocol for determination of the transport coefficients in terms of the local and non-local conductances and thermopowers that can be measured in two steps, applying the `four probe technique'. This proposal is compared with other approaches discussed so far in the literature. As an example we study in detail the thermopower induced by the superconducting electrode in a subgap regime which might be useful for analysis of novel hybrid devices.

We present a model of a qubit built of a three coherently coupled quantum dots with three spins in a triangular geometry. The qubit states are encoded in the doublet subspace and they are controlled by a gate voltage, which breaks the triangular symmetry of the system. We show how to prepare the qubit and to perform one qubit operations. A new type of the current blockade effect will be discussed. The blockade is related with an asymmetry of transfer rates from the electrodes to different doublet states and is used to read-out of the dynamics of the qubit state. Our research also presents analysis of the Rabi oscillations, decoherence and leakage processes in the doublets subspace., Comment: 13 pages, 8 figures

The interplay between various many body effects in a quantum dot attached to two normal and one superconducting lead is considered in the limit of large superconducting gap. By the proximity effect the superconducting lead induces pairing correlations on the quantum dot. In the subgap region one observes the anomalous tunneling via direct and crossed Andreev scattering, whereas the usual single particle electronic transfer is suppressed. The interactions of electrons on the dot leading to such phenomena as the Coulomb blockade and the Kondo effect severely modify the currents flowing in the system. In particular: (i) they prevent the existence of the negative differential conductance observed for non-interacting quantum dot over the whole range of voltages, (ii) affect the distribution of the currents as function of the applied voltage and (iii) lead to the appearance of additional low bias feature due to the formation of the Abrikosov-Suhl resonance. The non-local correlations in the Coulomb blockade regime are most pronounced for the particle-hole symmetric dot and thus can be easily tuned by means of gate voltage. They are observed even in the Kondo regime and dominate the behavior close to the Abrikosov-Suhl resonance showing convincingly that Kondo correlations do not destroy subtle entanglement between electrons., Comment: 14 pages, 10 figures, to appear in Phys. Rev. B

We show influence of electric field and magnetic flux on spin entanglement in an artificial triangular molecule build of coherently coupled quantum dots. In a subspace of doublet states an explicit relation of concurrence with spin correlation functions and chirality is presented. The electric field modifies super-exchange correlations, shifts many-electron levels (the Stark effect) as well as changes spin correlations. For some specific orientation of the electric field one can observe monogamy, for which one of the spins is separated from two others. Moreover, the Stark effect manifests itself in different spin entanglement for small and strong electric fields. A role of magnetic flux is opposite, it leads to circulation of spin supercurrents and spin delocalization., Comment: 7 pages, 8 figures

We analyze changes of the electronic structure of a triangular molecule under the influence of an electric field (i.e., the Stark effect). The effects of the field are shown to be anisotropic and include both a linear and a nonlinear part. For strong electron correlations, we explicitly derive exchange couplings in an effective spin Hamiltonian. For some conditions one can find a dark spin state, for which one of the spins is decoupled from the others. The model is also applied for studying electronic transport through a system of three coherently coupled quantum dots. Since electron transfer rates are anisotropic, the current characteristics are anisotropic as well, differing for small and large electric field., Comment: 7 pages, 5 figures

The transport properties of a octane-dithiol (ODT) molecule coupled to Au(001) leads are analyzed using density functional theory and non-equilibrium Green functions. It is shown that a symmetric molecule can turn into a diode under influence of a local electric field created by an external charged probe. The origin of the asymmetry of the current--voltage ($I-V$) dependence is traced back to the appearance of a probe induced quasi--local state in the pseudogap of the ODT molecule. The induced state affects electron transport, provided it is close to the Fermi level of the leads. An asymmetric placement of the charged probe along the alkane chain makes the induced quasi--local state in the energy gap very sensitive to the bias voltage and results in rectification of the current. The results based on DFT are supported by independent calculations using a simple one--particle model Hamiltonian., Comment: 7 pages, 6 figures

Current auto- and cross-correlations are studied in a system of two capacitively coupled quantum dots. We are interested in a role of Coulomb interaction in dynamical correlations, which occur outside the Coulomb blockade region (for high bias). After decomposition of the current correlation functions into contributions between individual tunneling events, we can show which of them are relevant and lead to sub-/supper-Poissonian shot noise and negative/positive cross-correlations. The results are differentiated for a weak and strong inter-dot coupling. Interesting results are for the strong coupling case when electron transfer in one of the channel is strongly correlated with charge drag in the second channel. We show that cross-correlations are non-monotonic functions of bias voltage and they are in general negative (except some cases with asymmetric tunnel resistances). This is effect of local potential fluctuations correlated by Coulomb interaction, which mimics the Pauli exclusion principle.

We investigate a dynamical Coulomb blockade effect and its role in the enhancement of current-current correlations in a three-terminal device with a multilevel splitter, as well as with two quantum dots. Spectral decomposition analysis shows that in the Y-terminal system with a two level ideal splitter, charge fluctuations at a level with a lowest outgoing tunneling rate are responsible for a super-Poissonian shot noise and positive cross-correlations. Interestingly, for larger source-drain voltages, electrons are transferred as independent particles, when three levels participate in transport, and double occupancy is allowed. We can explain compensation of the current correlations as the interplay between different bunching and antibunching processes by performing a spectral decomposition of the correlation functions for partial currents flowing through various levels. In the system with two quantum dots acting as a splitter, a long range feedback effect of fluctuating potentials leads to the dynamical Coulomb blockade and an enhancement of shot noise., Comment: 15 pages, 8 figures

We consider a model of a molecular junction made of BDT (benzene dithiol) molecule trapped between two Au(100) leads. Using the ab initio approach implemented in the SIESTA package we look for the optimal configuration of the molecule as a function of a distance between the leads. We find that for the distance long enough the energy of the system is minimized when the molecule is bonded asymmetricaly, i.e. chemisorbed to one of the leads, whereas for the distance shorter than 12 \AA the energy is minimized for the molecule sitting in the middle between the leads. We discuss possible consequences of the above findings for the transport properties of the junction.

We model a small quantum dot with a magnetic impurity by the Anderson Hamiltonian with a supplementary exchange interaction term. The transport calculations are performed by means of the Green functions within the equation of motion scheme, in which two decoupling procedures are proposed, for high and low temperatures, respectively. The paper focuses on the charge fluctuations for such a system, aspect not addressed before, as well as on the Kondo resonance. We show a specific role of the excited state, which can be observed in transport and in spin-spin correlations. Our studies show on a new many-body feature of the phase shift of transmitted electrons, which is manifested in a specific dip. In the Kondo regime, our calculations complement existing theoretical results. The system shows three Kondo peaks in the density of states: one at the Fermi energy and two side peaks, at a distance corresponding to the singlet-triplet level spacing. The existence of the central peak is conditioned by a degenerate state (the triplet) below the Fermi energy., Comment: 12 pages, 4 figures

Fano lineshapes in resonant transmission in a quantum dot imply interference between localized and extended states. The influence of the charge accumulated at the localized levels, which screens the external gate voltage acting on the conduction channel is investigated. The modified Fano q parameter and the resonant conduction is derived starting from a microscopic Hamiltonian. The latest experiments on "charge sensing" and ``Coulomb modified Fano sensing `` compare well with the results of the present model., Comment: 5 pages, 4 figures, RevTex style

Linear conductance across a large quantum dot via a single level e_0 with large hybridization to the contacts is strongly sensitive to quasi-bound states localized in the dot and weakly coupled to e_0. It oscillates with the gate voltage due to interference of the Fano type. At low temperature and Coulomb blockade, Kondo correlations damp the oscillations on an extended range of gate voltage values, by freezing the occupancy of the e_0 level itself. As a consequence, antiresonances of Fano origin are washed out. The results are in good correspondence with experimental data for a large quantum dot in the semi-open regime., Comment: 4 eps figures, RevTex format, revised version, to appear in Phys. Rev. Letters

We performed studies of coherent electronic transport through a single walled carbon nanotube. In the calculations multiple scattering on the contacts and interference processes were taken into account. Conductance is a composition of contributions from different channels. We studied also spin--dependent transport in the system with ferromagnetic electrodes. The magnetoresistance is large and shows large oscillations, it can be even negative in some cases., Comment: 6 pages, 4 figures, oral presentation at the XXXI International School on the Physics of Semiconducting Coumpounds, Jaszowiec 2002, to appear in the Acta Physica Polonica

Electronic transport through a quantum dot strongly coupled to electrodes is studied within a model with two conduction channels. It is shown that multiple scattering and interference of transmitted waves through both channels lead to Fano resonance associated with Kondo resonance. Interference effects are also pronouncedly seen in transport through the Aharonov-Bohm ring with the Kondo dot, where the current characteristics continuously evolve with the magnetic flux., Comment: 4 pages, 3 figures,a typing error has been corrected

Current and its noise in a ferromagnetic double tunnel barrier device with a small spacer particle were studied in the framework of the sequential tunneling approach. Analytical formulae were derived for electron tunneling through the spacer particle containing only a single energy level. It was shown that Coulomb interactions of electrons with a different spin orientation lead to an increase of the tunnel magnetoresistance. Interactions can also be responsible for the negative differential resistance. A current noise study showed, which relaxation processes can enhance or reduce fluctuations leading either to a super-Poissonian or a sub-Poissonian shot noise., Comment: 12 pages, 4 figures

A short review of correlated electrons in molecular systems has been performed. Main attention has been focussed on ET salts, which are the d=2 systems. They show the Mott transition in high temperatures and the transition from the antiferromagnetic to the superconducting phase in low temperatures, under a (chemical) pressure. Physical properties (the electrical resistivity, the specific heat, the magnetic susceptibility, the photoemission spectra, the optical conductivity) of ET salts have been compared with those ones in other strongly correlated systems. The optical conductivity is described in the framework of the Hubbard model, with a low frequency peak as an evidence for the Abrikosov-Suhl resonance., Comment: 9 pages, 4 figures, lecture given at the Conf. Molecular Crystals '98, Gdansk, Poland, September 9-12, 1998, to appear in Molecular Physics Reports

The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e. the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1 and d=$\infty$, by means of the (broken symmetry) Hartree-Fock approximations and, for d=$\infty$, by the slave-boson mean-field method. For d=1, at half-filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0 and q=Q ($\eta$-pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings is shrank with increasing lattice dimensionality d and for d=$\infty$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in the both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime., Comment: 16 pages, Revtex, 7 EPS figures included via epsf.sty, to appear in Phys. Rev. B, 01Mar99

The slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case of the hopping integral t equal to the correlated hopping integral X. The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any values of X and any electron concentration n. At the half-filled band (n=1) a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for n close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at n close to 0 and n close to 2. We found also that strong correlations change characteristics of the superconducting phase, e.g. the gap in the excitation spectrum has a nonexponential dependence close to the point of the phase transition., Comment: 13 pages, 24 Postscript figures (in 12 files)