Parity Of Ground State Research Articles

Singlet-Doublet Transitions of a Quantum Dot Josephson Junction Detected in a Transmon Circuit

We realize a hybrid superconductor-semiconductor transmon device in which the Josephson effect is controlled by a gate-defined quantum dot in an InAs-Al nanowire. Microwave spectroscopy of the transition spectrum of the transmon allows us to probe the ground-state parity of the quantum dot as a function of the gate voltages, the external magnetic flux, and the magnetic field applied parallel to the nanowire. The measured parity phase diagram is in agreement with that predicted by a single-impurity Anderson model with superconducting leads. Through continuous-time monitoring of the circuit, we furthermore resolve the quasiparticle dynamics of the quantum dot Josephson junction across the phase boundaries. Our results can facilitate the realization of semiconductor-based 0-π qubits and Andreev qubits.Received 28 February 2022Revised 23 May 2022Accepted 24 May 2022DOI:https://doi.org/10.1103/PRXQuantum.3.030311Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCircuit quantum electrodynamicsCoulomb blockadeHybrid quantum systemsImpurities in superconductorsJosephson effectKondo effectLifetimes & widthsProximity effectQuantum phase transitionsSpin-singlet pairingPhysical SystemsJosephson junctionsNanowiresQuantum dotsSemiconductorsSuperconducting qubitsSuperconductorsTechniquesMicrowave techniquesNumerical Renormalization GroupCondensed Matter, Materials & Applied PhysicsQuantum Information

Energy Levels and B(E2) Calculation for 50Fe Isotope Using F754 and F7mbz Interactions

In this work was calculated energy levels and reduced electric quadrupole transition probability B(E2) for 50Fe isotope using OXBASH code within the 1f7/2 shell and using the F754 and F7mbz effective interaction. 50Fe isotope contain 6 proton and 4 neutron out side 40Ca core in shell. In general, an acceptable agreement was obtained for a number of energy levels, and the total angular momentum and ground state parity were matched for all these isotopes, also new energy levels were obtained that have no practical values so far.

Aharonov-Bohm oscillations in phosphorene quantum rings: Mass anisotropy compensation by confinement potential

We consider the Aharonov-Bohm (AB) effect on a confined electron ground state in a quantum ring defined electrostatically within the phosphorene monolayer. The strong anisotropy of effective masses in phosphorene quenches ground-state oscillations for a circular ring because of interrupted persistent current circulation around the ring. An elliptic deformation of the confinement potential can compensate for the anisotropy of the effective masses and produce ground-state parity transformations with the AB periodicity. Moreover, a specific ratio of the semiaxes is determined for which the spectrum becomes identical to that of a circular quantum ring and an isotropic effective mass. We identify a generalized angular momentum operator which commutes with the continuum Hamiltonian for the chosen ratio of the semiaxes that closes the avoided crossings of energy levels for states of the same parity and spin. Ground-state oscillations for the two-electron ground state are also discussed.

Temperature induced shifts of Yu\u2013Shiba\u2013Rusinov resonances in nanowire-based hybrid quantum dots

The strong coupling of a superconductor to a spinful quantum dot results in Yu–Shiba–Rusinov discrete subgap excitations. In isolation and at zero temperature, the excitations are sharp resonances. In transport experiments, however, they show as broad differential conductance peaks. Here we obtain the lineshape of the peaks and their temperature dependence in superconductor–quantum dot–metal nanowire-based devices. Unexpectedly, we find that the peaks shift in energy with temperature, with the shift magnitude and sign depending on ground state parity and bias voltage. Additionally, we empirically find a power-law trend of the peak area versus temperature. These observations are not explained by current models.

Parity-to-charge conversion for readout of topological Majorana qubits

We theoretically study a scheme to distinguish the two ground states of a one-dimensional topological superconductor, which could serve as a basis for the readout of Majorana qubits. The scheme is based on parity-to-charge conversion, i.e., the ground-state parity of the superconductor is converted to the charge occupation on a tunnel-coupled auxiliary quantum dot. We describe how certain error mechanisms degrade the quality of the parity-to-charge conversion process. We consider (i) leakage due to a strong readout tunnel pulse, (ii) incomplete charge Rabi oscillations due to slow charge noise, and (iii) charge relaxation due to phonon emission and absorption. To describe these effects, we use simple model Hamiltonians based on the ideal Kitaev chain, and draw conclusions to generic one-dimensional topological superconductors wherever possible. In general, the effects of the error mechanisms can be minimized by choosing a smooth shape and an optimal strength for the readout tunnel pulse. In a case study based on InAs heterostructure device parameters, we estimate that the parity-to-charge conversion error is mainly due to slow charge noise for weak tunnel pulses and leakage for strong tunnel pulses.

Structure of the exotic He9 nucleus from the no-core shell model with continuum

The exotic $^9$He nucleus, which presents one of the most extreme neutron-to-proton ratios, belongs to the $N=7$ isotonic chain famous for the phenomenon of ground-state parity inversion with decreasing number of protons. Consequently, it would be expected to have an unnatural (positive) parity ground state similar to $^{11}$Be and $^{10}$Li. Despite many experimental and theoretical investigations, its structure remains uncertain. Apart from the fact that it is unbound, other properties including the spin and parity of its ground state and the very existence of additional low-lying resonances are still a matter of debate. In this work we study the properties of $^9$He by analyzing the $n+^8$He continuum in the context of the ab initio no-core shell model with continuum (NCSMC) formalism with chiral interactions as the only input. The NCSMC is a state-of-the-art approach for the ab initio description of light nuclei. With its capability to predict properties of bound states, resonances, and scattering states in a unified framework, the method is particularly well suited for the study of unbound nuclei such as $^9$He. Our analysis produces an unbound $^9$He nucleus. Two resonant states are found at the energies of ${\sim}1$ and ${\sim}3.5$ MeV, respectively, above the $n+^8$He breakup threshold. The first state has a spin-parity assignment of $J^{\pi} = {1/2}^-$ and can be associated with the ground state of $^9$He, while the second, broader state has a spin-parity of ${3/2}^-$. No resonance is found in the ${1/2}^+$ channel, only a very weak attraction. We find that the $^9$He ground-state resonance has a negative parity and thus breaks the parity-inversion mechanism found in the $^{11}$Be and $^{10}$Li nuclei of the same $N=7$ isotonic chain.

Detecting Majorana modes through Josephson junction ring-quantum dot hybrid architectures

Unequivocal signatures of Majorana zero energy modes in condensed matter systems and manipulation of the associated electron parity states are highly sought after for fundamental reasons as well as for the prospect of topological quantum computing. In this paper, we demonstrate that a ring of Josephson coupled topological superconducting islands threaded by magnetic flux and attached to a quantum dot acts as an excellent parity-controlled probe of Majorana mode physics. As a function of flux threading through the ring, standard Josephson coupling yields a Φ0=h/(2e) periodic features corresponding to 2π phase difference periodicity. In contrast, Majorana mode assisted tunneling provides additional features with 2Φ0 (4π phase difference) periodicity, associated with single electron processes. We find that increasing the number of islands in the ring enhances the visibility of the desired 4π periodic components in the groundstate energy. Moreover as a unique characterization tool, tuning the occupation energy of the quantum dot allows controlled groundstate parity changes in the ring, enabling a toggling between Φ0 and 2Φ0 periodicity.

CanAb InitioTheory Explain the Phenomenon of Parity Inversion inBe11?

The weakly bound exotic ^{11}Be nucleus, famous for its ground-state parity inversion and distinct n+^{10}Be halo structure, is investigated from first principles using chiral two- and three-nucleon forces. An explicit treatment of continuum effects is found to be indispensable. We study the sensitivity of the ^{11}Be spectrum to the details of the three-nucleon force and demonstrate that only certain chiral interactions are capable of reproducing the parity inversion. With such interactions, the extremely large E1 transition between the bound states is reproduced. We compare our photodisintegration calculations to conflicting experimental data and predict a distinct dip around the 3/2_{1}^{-} resonance energy. Finally, we predict low-lying 3/2^{+} and 9/2^{+} resonances that are not or not sufficiently measured in experiments.

Resonancelike enhancement in high-order above-threshold ionization of polyatomic molecules

We investigate the resonance-like enhancement (RLE) in high-order above-threshold ionization (ATI) spectra of the polyatomic molecules ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ and ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$. In the spectrum-intensity maps, strong and weak RLE areas emerge alternatively for both ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ and ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$ but in different sequences. Theoretical calculations using the strong-field approximation reproduce the experimental observation and analysis shows that the different characteristics of the two molecules can be attributed to interference effects of molecular orbitals with different symmetries. For ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$, the RLE structures are attributed to C--C centers of the highest occupied molecular orbital (HOMO) orbital. For ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$, in contrast, the C--C centers of the HOMO and HOMO-1 orbitals do not contribute to the RLE due to destructive interference but the hydrogen centers of the bonding HOMO-1 orbital give rise to the multiple RLE regions. In addition, clear experimental evidence of the existence of two types of the RLE and their dependence on the parity of ground state is shown. Our result, which strongly supports the channel-closing mechanism of the RLE, for the first time reveals the important role of low-lying orbitals and the differing roles of different atomic centers in the high-order ATI spectrum of molecules.

Quench dynamics and parity blocking in Majorana wires

We theoretically explore quench dynamics in a finite-sized topological fermionic p-wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, including the behavior of the Majorana end modes and the form of the tunnel coupling between them; a transfer matrix approach to analytically determine the locations of the zero energy contours where this coupling vanishes; and a Pfaffian approach to map the ground state parity in the associated phase diagram. We next study the quench dynamics resulting from initializing the system in a topological ground state and then dynamically tuning one of the parameters of the Hamiltonian. For this, we develop a dynamic quantum many-body technique that invokes a Wick’s theorem for Majorana fermions, vastly reducing the numerical effort given the exponentially large Hilbert space. We investigate the salient and detailed features of two dynamic quantities—the overlap between the time-evolved state and the instantaneous ground state (adiabatic fidelity) and the residual energy. When the parity of the instantaneous ground state flips successively with time, we find that the time-evolved state can dramatically switch back and forth between this state and an excited state even when the quenching is very slow, a phenomenon that we term ‘parity blocking’. This parity blocking becomes prominently manifest as non-analytic jumps as a function of time in both dynamic quantities.

Structure of Neutron-Rich Be Hyper Isotopes

The deformation change of \({^{9}_\Lambda}\) Be and the low-lying states of \({^{12}_{\Lambda}}\) Be are studied by using the antisymmetrized molecular dynamics for hypernuclei (HyperAMD). In \({^{9}_{\Lambda}}\) Be, the Λ hyperon in p orbit enhances nuclear quadrupole deformation, while the Λ hyperon in s orbit reduces it. In \({^{12}_{\Lambda}}\) Be, the ground state parity inverted in 11Be is reverted in \({^{12}_{\Lambda}}\) Be by adding a Λ hyperon as an impurity (impurity effect).

Two-channel Kondo phases and frustration-induced transitions in triple quantum dots

We consider a ring of three quantum dots mutually coupled by antiferromagnetic exchange interactions, and tunnel-coupled to two metallic leads: the simplest device in which the consequences of local frustration arising from internal degrees of freedom may be studied within a 2-channel environment. Two-channel Kondo (2CK) physics is found to predominate at low-energies in the mirror-symmetric systems considered, with a residual spin 1/2 overscreened by coupling to both leads. It is however shown that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot exchange couplings. In consequence a frustration-induced quantum phase transition occurs, the 2CK phases being separated by a quantum critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasi-degenerate local trimer states acts to destabilise the 2CK fixed points; and the critical fixed point is shown to consist of a free pseudospin together with effective 1-channel spin quenching, itself reflecting underlying channel-anisotropy in the inherently 2-channel system. Numerical renormalization group techniques and physical arguments are used to obtain a detailed understanding of the problem, including study of both thermodynamic and dynamical properties of the system.

Few-electron artificial molecules formed by laterally coupled quantum rings

We study artificial molecular states formed in laterally coupled double semiconductor nanorings by one, two, and three electrons. An interplay of the interring tunneling and the electron-electron interaction is described, as well as its consequences for the magnetization and charging properties of the system. It is shown that both the magnetic dipole moment generated by the double-ring structure and the chemical potential of the system as function of the external magnetic field strongly depend on the number of electrons and the interring barrier thickness. Both the magnetization and chemical potentials exhibit cusps at the magnetic fields inducing ground-state parity and/or spin transformations. The symmetry transformations are discussed for various tunnel coupling strengths, from rings coupled only electrostatically to the limit of coalesced rings. We find that in the ground states for rings of different radii the magnetic field transfers the electron charge from one ring to the other. The calculations are performed with the configuration-interaction method based on an approach of Gaussian functions centered on a rectangular array of points covering the studied structure. Electron-electron correlation is also discussed.

Wavelength dependence of channel-closing enhancements in high-order above-threshold ionization and harmonic generation

We investigate the laser-wavelength dependence of high-order above-threshold ionization and high-order harmonic generation rates. For both processes we have found pronounced enhancements in the spectra for those wavelengths for which the channel-closing condition is satisfied. These enhancements are explained in two complementary ways. One is in terms of the constructive interference of a large number of long quantum orbits, while the second interpretation is based on threshold anomalies. There are two types of these enhancements, which leave very different footprints in the spectra. When the ground-state parity of the atom changes, the two types are interchanged.

Energy- and angle-resolved photoelectron spectra of above-threshold ionization and detachment

We analyze strong-laser-field induced above-threshold ionization and above-threshold detachment processes within the strong-field approximation. Energy and angular distribution of photoelectrons are presented for two cases: (1) high-order above-threshold ionization of electrons from neutral atoms by a linearly polarized laser field and (2) above-threshold detachment of electrons from negative ions by a bicircular laser field. In particular, for the case (1) we compare the results obtained using a long pulse with the flat-top spatial intensity distribution in the laser focus with the results obtained using the Gaussian distribution. We also analyze the intensity-dependent resonant-like enhancements. We show that the position and shape of these enhancements strongly depend on the atomic ground state parity. The bicircular field of the case (2) consists of two counter-rotating circularly polarized fields having the frequencies rω and sω with integer r and s. The properties of the photoelectron spectra generated by such bicircular field are illustrated using an ω–4ω example. The spectra obtained are explained in terms of the interference of partial detachment amplitudes which correspond to different complex solutions of the saddle-point equations.

Intensity-dependent enhancements in high-order above-threshold ionization

The very pronounced intensity-dependent enhancements of groups of peaks of high-order above-threshold-ionization spectra of rare-gas atoms are investigated using an improved version of the strong-field approximation, which realistically models the respective atom. Two types of enhancements are found and explained in terms of constructive interference of the contributions of a large number of long quantum orbits. The first type is observed for intensities slightly below channel closings. Its intensity dependence is comparatively smooth and it is generated by comparatively few (of the order of 20) orbits. The second type occurs precisely at channel closings and exhibits an extremely sharp intensity dependence. It requires constructive interference of a very large number of long orbits (several hundreds) and generates cusps in the electron spectrum at integer multiples of the laser-photon energy. An interpretation of these enhancements as a threshold phenomenon is also given. An interplay of different types of the threshold anomalies is observed. The position of both types of enhancements, in the photoelectron-energy---laser-intensity plane, shifts to the next channel closing intensity with the change of the ground-state parity. The enhancements gradually disappear with decreasing laser pulse duration. This confirms the interpretation of enhancements as a consequence of the interference of long strong-laser-field-induced quantum orbits.

Large-scale prediction of the parity distribution in the nuclear level density and application to astrophysical reaction rates

A generalized method to calculate the excitation-energy dependent parity ratio in the nuclear level density is presented, using the assumption of Poisson distributed independent quasi particles combined with BCS occupation numbers. It is found that it is crucial to employ a sufficiently large model space to allow excitations both from low-lying shells and to higher shells beyond a single major shell. Parity ratios are only found to equilibrate above at least 5-10 MeV of excitation energy. Furthermore, an overshooting effect close to major shells is found where the parity opposite to the ground state parity may dominate across a range of several MeV before the parity ratio finally equilibrates. The method is suited for large-scale calculations as needed, for example, in astrophysical applications. Parity distributions were computed for all nuclei from the proton dripline to the neutron dripline and from Ne up to Bi. These results were then used to recalculate astrophysical reaction rates in a Hauser-Feshbach statistical model. Although certain transitions can be considerably enhanced or suppressed, the impact on astrophysically relevant reactions remains limited, mainly due to the thermal population of target states in stellar reaction rates.

David Allan Bromley

David Allan Bromley

The N = Z nucleus 76 Sr: Gamow-Teller strength and nuclear deformation

Challenged by recent theoretical work, a study of the $\beta^ + $ -EC decay of the N = Z even-even nucleus 76 Sr has been undertaken in order to assign the parent ground-state deformation. In this study 13 levels with $J^{\pi} = 1^{ + }$ have been located in 76 Rb. The beta-delayed proton emission has been observed for the first time in an N = Z even-even nucleus. The $\beta$ p branching ratio has been determined to be $(3.4 \pm 0.8)\cdot 10^{-5}$ . The 76 Sr half-life has been remeasured and a more precise value of $7.89 \pm 0.07$ s has been obtained. On the basis of the comparison of measured Gamow-Teller strength with calculated strength distributions for both oblate and prolate deformation, it is concluded that the 76 Sr has strong prolate deformation in the ground state.

Crossing the dripline to11Nusing elastic resonance scattering

The level structure of the unbound nucleus 11N has been studied by 10C+p elastic resonance scattering in inverse geometry with the LISE3 spectrometer at GANIL, using a 10C beam with an energy of 9.0 MeV/u. An additional measurement was done at the A1200 spectrometer at MSU. The excitation function above the 10C+p threshold has been determined up to 5 MeV. A potential-model analysis revealed three resonance states at energies 1.27 (+0.18-0.05) MeV (Gamma=1.44 +-0.2 MeV), 2.01(+0.15-0.05) MeV, (Gamma=0.84 +-$0.2 MeV) and 3.75(+-0.05) MeV, (Gamma=0.60 +-0.05 MeV) with the spin-parity assignments I(pi) =1/2+, 1/2- and 5/2+, respectively. Hence, 11N is shown to have a ground state parity inversion completely analogous to its mirror partner, 11Be. A narrow resonance in the excitation function at 4.33 (+-0.05) MeV was also observed and assigned spin-parity 3/2-.