Pair Tunneling Research Articles

MiTMoJCo: Microscopic Tunneling Model for Josephson Contacts

MiTMoJCo (Microscopic Tunneling Model for Josephson Contacts) is C code which aims to assist modeling of superconducting Josephson contacts based on the microscopic tunneling theory. The code offers implementation of a computationally demanding part of this calculation, that is evaluation of superconducting pair and quasiparticle tunnel currents from the given tunnel current amplitudes (TCAs) which characterize the junction material. MiTMoJCo comes with a library of pre-calculated TCAs for frequently used Nb-AlOx-Nb and Nb-AlN-NbN junctions, a Python module for developing custom TCAs, supplementary optimum filtration module for extraction of a constant component of a sinusoidal signal and examples of modeling few common cases of superconducting Josephson contacts. Program summaryProgram Title: MiTMoJCo: Microscopic Tunneling Model for Josephson ContactsProgram Files doi:http://dx.doi.org/10.17632/664k9g9zr7.1Licensing provisions: GPLv3Programming language: C, PythonNature of problem: Modeling superconducting Josephson contacts based on the microscopic tunneling theory; calculation and fitting of the tunnel current amplitudes.Solution method: Computationally efficient Odintsov–Semenov–Zorin algorithm is used to account for the memory effects in pair and quasiparticle tunnel currents.

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

In a recent work, Murmann et al (2015 Phys. Rev. Lett. 114 080402) have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two spin components. We first calculate Hubbard parameters using the finite-range interaction potentials of Jost and Kohn. In general, a finite range of interaction leads to on-site, inter-site, exchange and partial-exchange terms We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single- and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both fermionic and bosonic cases. But, quantum entanglement and quantum fluctuations are found to be markedly different for the two cases. We discuss atom-atom entanglement in two spatial modes corresponding to the two sites of the double-well. Our results show that the entanglement of a pair of spin-half fermions is always greater than that of spinless bosons; and when the fermions are maximally entangled the fluctuation in the two-mode phase difference is largely squeezed. In contrast, spinless bosons never exhibit phase squeezing, but shows squeezing in two-mode population imbalance depending on the system parameters.

Staggered ground states in an optical lattice

Non-standard Bose-Hubbard models can exhibit rich ground state phase diagrams, even when considering the one-dimensional limit. Using a self-consistent Gutzwiller diagonalisation approach, we study the mean-field ground state properties of a long-range interacting atomic gas in a one-dimensional optical lattice. We first confirm that the inclusion of long-range two-body interactions to the standard Bose-Hubbard model introduces density wave and supersolid phases. However, the introduction of pair and density-dependent tunnelling can result in new phases with two-site periodic density, single-particle transport and two-body transport order parameters. These staggered phases are potentially a mean-field signature of the known novel twisted superfluids found via a DMRG approach [PRA \textbf{94}, 011603(R) (2016)]. We also observe other unconventional phases, which are characterised by sign staggered order parameters between adjacent lattice sites.

Evidence of high-temperature exciton condensation in two-dimensional atomic double layers.

A Bose-Einstein condensate is the ground state of a dilute gas of bosons, such as atoms cooled to temperatures close to absolute zero1. With much smaller mass, excitons (bound electron-hole pairs) are expected to condense at considerably higher temperatures2-7. Two-dimensional van der Waals semiconductors with very strong exciton binding are ideal systems for the study of high-temperature exciton condensation. Here we study electrically generated interlayer excitons in MoSe2-WSe2 atomic double layers with a density of up to 1012 excitons per square centimetre. The interlayer tunnelling current depends only on the exciton density, which is indicative of correlated electron-hole pair tunnelling8. Strong electroluminescence arises when a hole tunnels from WSe2 to recombine with an electron in MoSe2. We observe a critical threshold dependence of the electroluminescence intensity on exciton density, accompanied by super-Poissonian photon statistics near the threshold, and a large electroluminescence enhancement with a narrow peak at equal electron and hole densities. The phenomenon persists above 100 kelvin, which is consistent with the predicted critical condensation temperature9-12. Our study provides evidence for interlayer exciton condensation in two-dimensional atomic double layers and opens up opportunities for exploring condensate-based optoelectronics and exciton-mediated high-temperature superconductivity13.

Topological ordering in the Majorana toric code

At zero temperature, a two-dimensional lattice of Majorana zero modes on mesoscopic superconducting islands exhibits a topologically-ordered toric code phase. Recently, a Landau field theory was used to describe the different phases of the aforementioned system and the phase-transitions separating them. While the field theory provides details on the properties of the system close to the phase-transitions, signatures of topological ordering in the different phases have not been computed. This is the primary goal of the current work. We describe a lattice gauge theory of the Majorana toric code in terms of $\mathrm{U}(1)$ matter fields coupled to an emergent $\mathbb{Z}_2$ gauge field. Subsequently, we use a generalized Wilson-loop order-parameter, the equal-time Fredenhagen-Marcu order parameter, to characterize the topological ordering in the different phases. Our computation provides evidence of the toric code phase both in the Mott insulator and the charge-$2e$ superconductor phases, while showing that the toric code phase disappears in the charge-$e$ superconductor phase. In addition, we perturbatively analyze the influence of Cooper pair tunneling on the topological gap of the toric code in the limit of strong charging energy and show that the toric code phase is, in fact, stabilized by the Cooper pair tunneling. Our results are relevant for experimental realizations of the Majorana toric code.

Josephson effect in the strontium titanate/lanthanum aluminate junction**Project supported by the National Natural Science Foundation of China (Grant No. 11675051) and China Scholarship Council (Grant No. 201506130054).

We report theoretical studies on the newly discovered novel Josephson effect and scanning tunneling spectroscopy (STS) at the interface of strontium titanate/lanthanum aluminate (STO/LAO). With a phenomenological boson–fermion model, the density of states is calculated and the results are consistent with the STS experiments. A typical calculation of Josephson effect is performed, and it is in qualitative agreement with the experiments. The calculations indicate that the gap states come from the pairing of quasi-particles with a finite total momentum and the Josephson current comes from the tunneling of quasi-particle pairs with zero momentum. The quasi-particles are Bogoliubov quasi-particles. Moreover, the fits using Kulikʼs formula imply that the Josephson junction at the STO/LAO interface has a point contact with the clean superconductor limit.

Quadrature Squeezing in Extended Two-Site Bose–Hubbard Model with Pair Tunneling

We analytically and numerically investigate quadrature squeezing in an extended two-site Bose–Hubbard model with pair tunneling by using the rotating-wave approximation. It is shown that single particle tunneling and the density-dependent tunneling have no influence on quadrature squeezing; the onsite interaction and the inter-well particle interactions effect the regime of squeezing under some conditions.

Momentum correlations of a few ultracold bosons escaping from an open well

The dynamical properties of a one-dimensional system of two and three bosons escaping from an open potential well are studied in terms of the momentum distributions of particles. In the case of a two-boson system, it is shown that the single- and two-particle momentum distributions undergo a specific transition as the interaction strength is tuned through the point where tunneling switches from the pair tunneling to the sequential one. Characteristic features in the momentum spectra can be used to quantitatively determine the participation of specific decay processes. A corresponding analysis is also performed for the three-boson system, showing a scheme for generalizations to higher particle numbers. For completeness, the time-dependent Tan's contact of the system is also examined and its dynamics is found to undergo a similar transition. The results provide insight into the dynamics of decaying few-body systems and offer potential interest for experimental research.

Charge control of blockade of Cooper pair tunneling in highly disordered TiN nanowires in an inductive environment

A central problem in understanding the superconductor-insulator transition in disordered superconductors is that the properties of grains and intergrain medium cannot be independently studied. Here we demonstrate an approach to the study of strongly disordered superconducting films by relying on the stochastic nature of the disorder probed by electrostatic gating in a restricted geometry. Charge tuning and magnetotransport measurements in quasihomogeneous TiN nanowires embedded in a superinductor environment allow us to classify different devices and distinguish between spontaneously formed Coulomb islands (with typical blockade voltage in the mV range) and homogeneous wires showing behavior indicative of coherent quantum phase slips (with significantly smaller blockade voltage).

Bright On-Demand Source of Antibunched Microwave Photons Based on Inelastic Cooper Pair Tunneling

The ability to generate single photons is not only an ubiquitous tool for scientific exploration with applications ranging from spectroscopy and metrology to quantum computing, but also an important proof of the underlying quantum nature of a physical process. In the microwave regime, emission of anti-bunched radiation has so far relied on coherent control of Josephson qubits, where precisely calibrated microwave pulses are needed, and the achievable bandwidth is limited by the anharmonicity of the qubit. Here, we demonstrate the operation of a bright on-demand source of quantum microwave radiation capable of emitting anti-bunched photons based on inelastic Cooper pair tunneling and driven by a simple DC voltage bias. It is characterized by its normalized second order correlation function of $g^{(2)}(0)\approx0.43$ corresponding to anti-bunching in the single photon regime. Our source can be triggered and its emission rate is tunable in situ exceeding rates obtained with current microwave single photon sources by more than one order of magnitude.

Tunneling of two interacting atoms from excited states

We consider a tunneling problem of two interacting cold atoms, with the even spatial symmetry, subject to an anharmonic optical trap and linear magnetic-field gradient. The atoms are initially, i.e. at t = 0, prepared in the two lowest excited states with respect to relative and center-of-mass motions. We calculate the energy spectrum for a wide range of the interatomic coupling strength g1D. In the limit of g1D → 0, an avoided crossing of the energy levels is revealed. For the dynamics, i.e. for t > 0, we observe monotonic and non-monotonic dependence of a tunneling rate as a function of g1D. We find a condition to observe a transition from uncorrelated to correlated pair tunneling as a function of g1D and a size of the external trap barrier. This system, although for lower energy levels, has been recently investigated in the deterministic Heidelberg experiment using two interacting 6Li atoms.

Andreev tunneling assisted suppression of Fano resonance in asymmetric parallel quantum dot system coupled to superconducting leads

Electronic transport through asymmetrically parallel coupled quantum dot system hybridized between conventional superconducting leads has been investigated theoretically in the Coulomb blockade regime by using Non-Equilibrium Green Function formalism. For resonant Cooper pair tunneling, the Andreev transmission probability and Josephson supercurrent (I−Vcharacteristics) have been presented for each configuration of coupled quantum dot system and for transition of coupled quantum dot system from series to symmetric parallel configuration. Superconducting order parameter regulates the Josephson Cooper pair tunneling in such a way that it initially enhances and then suppresses the resonant Cooper pair tunneling when system is tuned from series to symmetric parallel configuration. Furthermore, it has been found that the Fano effect, reported in asymmetric parallel configuration of CQD system, gets completely suppressed by Andreev tunneling for a particular value of superconducting order parameter and lead-dot coupling strength.

Optimal work extraction from quantum states by photo-assisted Cooper pair tunneling

The theory of quantum thermodynamics predicts fundamental bounds on work extraction from quantum states. As these bounds are derived in a very general and abstract setting, it is unclear how relevant they are in an experimental context, where control is typically limited. Here we address this question by showing that optimal work extraction is possible for a realistic engine. The latter consists of a superconducting circuit, where a LC-resonator is coupled to a Josephson junction. The oscillator state fuels the engine, providing energy absorbed by Cooper pairs, thus producing work in the form of an electrical current against an external voltage bias. We show that this machine can extract the maximal amount of work from all Gaussian and Fock states. Furthermore, we consider work extraction from a continuously stabilized oscillator state. In both scenarios, coherence between energy eigenstates is beneficial, increasing the power output of the machine. This is possible because the phase difference across the Josephson junction provides a phase reference.

Manipulating quantum coherence of charge states in interacting double-dot Aharonov–Bohm interferometers

We investigate the dynamics of charge-state coherence in a degenerate double-dot Aharonov–Bohm interferometer with finite inter-dot Coulomb interactions. The quantum coherence of the charge states is found to be sensitive to the transport setup configurations, involving both the single-electron impurity channels and the Coulomb-assisted ones. We numerically demonstrate the emergence of a complete coherence between the two charge states, with the relative phase being continuously controllable through the magnetic flux. Interestingly, a fully coherent charge qubit arises at the double-dots electron pair tunneling resonance condition, where the chemical potential of one electrode is tuned at the center between a single-electron impurity channel and the related Coulomb-assisted channel. This pure quantum state of charge qubit could be experimentally realized at the current–voltage characteristic turnover position, where differential conductance sign changes. We further elaborate the underlying mechanism for both the real-time and the stationary charge-states coherence in the double-dot systems of study.

Negative differential conductance in doped-silicon nanoscale devices with superconducting electrodes

We present a proof-of-concept nanoelectronics device with a negative differential conductance, an attractive from the applied viewpoint functionality. The device, characterized by the decreasing current with increasing voltage in a certain voltage region above a threshold bias of about several hundred millivolts, consists of two superconducting electrodes with an amorphous 10-nm-thick silicon interlayer doped by tungsten nano-inclusions. We show that small changes in the W content radically modify the shape of the trilayer current–voltage dependence and identify sudden conductance switching at a threshold voltage as an effect of Andreev fluctuators. The latter entities are two-level systems at the superconductor-doped silicon interface where a Cooper pair tunnels from a superconductor and occupies a pair of localized electronic states. We argue that in contrast to previously proposed devices, our samples permit very large-scale integration and are practically feasible.

A New Advance Classification Method for Surrounding Rock in Tunnels Based on the Set-Pair Analysis and Tunnel Seismic Prediction System

An advance optimized classification method is proposed to accurately predict the surrounding rock classification based on set pair analysis (SPA) and tunnel seismic prediction (TSP). Several factors that greatly affect rock mass classification are selected as evaluation indices of SPA based on analysis of TSP data. Evaluation indices are divided into five grades according to its response characteristics of seismic wave field, and their membership functions are proposed by using frequency statistical method. Entropy weight method is adopted to determine the weights of evaluation indices, and a SPA model is established for optimized classification of surrounding rock. Engineering application of Shimenya Tunnel of Yi-Ba Highway is taken as a case study, and proved that the evaluation indices are easy to obtain and the evaluation results are accurate and reliable. The SPA–TSP method can be further used for other tunnel engineering.

Cooper pair tunnelling and quasiparticle poisoning in a galvanically isolated superconducting double dot

We increase the isolation of a superconducting double dot from its environment by galvanically isolating it from any electrodes. We probe it using high frequency reflectometry techniques, find 2e-periodic behaviour, and characterise the energy structure of its charge states. By modelling the response of the device, we determine the time averaged probability that the device is poisoned by quasiparticles, and by comparing this with previous work, we conclude that quasiparticle exchange between the dots and the leads is an important relaxation mechanism.

Quantum tunnelling from vacuum in multidimensions

The tunnelling of virtual matter-antimatter pairs from the quantum vacuum in multidimensions is studied. We consider electric backgrounds as a linear combination of a spatial Sauter field and, interchangeably, certain weaker time dependent fields without poles in the complex plane such as the sinusoidal and Gaussian cases. Based on recent geometric considerations within the worldline formalism, we employ the relevant critical points in order to analytically estimate a characteristic threshold for the temporal inhomogeneity. We set appropriate initial conditions and apply additional symmetry constraints in order to determine the classical periodic paths in spacetime. Using these worldline instantons, we compute the corresponding leading order exponential factors showing large dynamical enhancement in general. We work out the main differences caused by the analytic structure of such composite backgrounds and also discuss the case with a strong temporal variation of Sauter-type.

Emission of Nonclassical Radiation by Inelastic Cooper Pair Tunneling.

We show that a properly dc-biased Josephson junction in series with two microwave resonators of different frequencies emits photon pairs in the resonators. By measuring auto- and intercorrelations of the power leaking out of the resonators, we demonstrate two-mode amplitude squeezing below the classical limit. This nonclassical microwave light emission is found to be in quantitative agreement with our theoretical predictions, up to an emission rate of 2 billion photon pairs per second.

From bare to renormalized order parameter in gauge space: Structure and reactions

The physical reason why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of pairing rotational bands, making use of simple BCS (constant matrix elements) or of many-body (Nambu-Gorkov (NG), nuclear field theory (NFT)) spectroscopic amplitudes, is not immediately obvious. Restoration of spontaneous symmetry breaking and associated emergent generalised rigidity in gauge space provides the answer, and points to a new emergence: a physical sum rule resulting from the intertwining of structure and reaction processes and closely connected with the central role induced pairing interaction plays in structure together with the fact that successive transfer dominates Cooper pair tunnelling.