Landau-Zener Effect Research Articles

Nonlinear two-level dynamics of quantum time crystals

A time crystal is a macroscopic quantum system in periodic motion in its ground state. In our experiments, two coupled time crystals consisting of spin-wave quasiparticles (magnons) form a macroscopic two-level system. The two levels evolve in time as determined intrinsically by a nonlinear feedback, allowing us to construct spontaneous two-level dynamics. In the course of a level crossing, magnons move from the ground level to the excited level driven by the Landau-Zener effect, combined with Rabi population oscillations. We demonstrate that magnon time crystals allow access to every aspect and detail of quantum-coherent interactions in a single run of the experiment. Our work opens an outlook for the detection of surface-bound Majorana fermions in the underlying superfluid system, and invites technological exploitation of coherent magnon phenomena – potentially even at room temperature.

Interplay of charge noise and coupling to phonons in adiabatic electron transfer between quantum dots

Long-distance transfer of quantum information in architectures based on quantum dot spin qubits will be necessary for their scalability. One way of achieving it is to simply move the electron between two quantum registers. Precise control over the electron shuttling through a chain of tunnel-coupled quantum dots is possible when interdot energy detunings are changed adiabatically. Deterministic character of shuttling is however endangered by coupling of the transferred electron to thermal reservoirs: sources of fluctuations of electric fields, and lattice vibrations. We theoretically analyse how the electron transfer between two quantum dots is affected by electron-phonon scattering, and interaction with sources of $1/f$ and Johnson charge noise in both detuning and tunnel coupling. The electron-phonon scattering turns out to be irrelevant in Si quantum dots, while a competition between the effects of charge noise and Landau-Zener effect leads to an existence of optimal detuning sweep rate, at which probability of leaving the electron behind is minimal. In GaAs quantum dots, on the other hand, coupling to phonons is strong enough to make the phonon-assisted processes of interdot transfer dominate over influence of charge noise. The probability of leaving the electron behind depends then monotonically on detuning sweep rate, and values much smaller than in silicon can be obtained for slow sweeps. However, after taking into account limitations on transfer time imposed by need for preservation of electron's spin coherence, minimal probabilities of leaving the electron behind in both GaAs- and Si-based double quantum dots turn out to be of the same order of magnitude. Bringing them down below $10^{-3}$ requires temperatures $\leq \! 100$ mK and tunnel couplings above $20$ $\mu$eV.

Microscopic description of α-decay as super-asymmetric fission

The fine structure of α-decay is treated with fission-like models. The single particle levels are calculated along a least action path connecting the ground state of the parent nucleus and the configuration of two spherical tangent nuclei. The probabilities to find different seniority-1 configurations are obtaining by solving the time-dependent pairing equations generalized by including the Landau-Zener effect and the Coriolis coupling. The theoretical results for the α-decay of 211Po and 211Bi are compared with experimental data showing a good agreement.

Fine structure of $$\alpha $$ decay from the time-dependent pairing equations

The $$\alpha $$ decay half-lives and the fine structure phenomenon are investigated with fission-like models. A superasymmetric fission path in a configuration space spanned by five degrees of freedom is determined in accordance with the least action principle. The deformation energy is evaluated within the macroscopic–microscopic approach while the inertia is obtained in the framework of the cranking model. The single particle levels schemes are calculated connecting the ground state of the parent nucleus and the asymptotic configuration of two separated nuclei. The probabilities to find different seniority configurations are obtained by solving time-dependent pairing equations generalized by including the Landau–Zener effect and the Coriolis coupling. The microscopic equations of motion for even numbers of particles are deduced, those for odd-nuclear systems being obtained in previous works. The models used in the calculations are reviewed within a detailed description. The microscopic equations of motion are solved by starting from the ground state configuration and arriving at the scission point. A description of all the possible configurations at scission together with their realization probabilities is given. By fitting the inter-nuclear velocity, the best agreement between experimental and theoretical hindrance factors is retained. The theoretical results for the $$\alpha $$ decay half-lives for $$^{211,212}$$ Po and $$^{211}$$ Bi are compared with experimental data showing discrepancies ranging over three orders of magnitude. The accuracy of the model concerning the calculations of the half-lives for different channels is discussed. The connections between the classical theories concerning the preformation of the $$\alpha $$ particle and the fission-like descriptions are highlighted.

Lefschetz-thimble inspired analysis of the Dykhne–Davis–Pechukas method and an application for the Schwinger Mechanism

Dykhne–Davis–Pechukas (DDP) method is a common approximation scheme for the transition probability in two-level quantum systems, as realized in the Landau–Zener effect, leading to an exponentially damping form comparable to the Schwinger pair production rate. We analyze the foundation of the DDP method using a modern complex technique inspired by the Lefschetz-thimble method. We derive an alternative and more adaptive formula that is useful even when the DDP method is inapplicable. As a benchmark, we study the modified Landau–Zener model and compare results from the DDP and our methods. We then revisit a derivation of the Schwinger Mechanism of particle production under electric fields using the DDP and our methods. We find that the DDP method gets worse for the Sauter type of short-lived electric pulse, while our method is still a reasonable approximation. We also study the Dynamically Assisted Schwinger Mechanism in two methods.

Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions

We reveal that topological Josephson junctions provide a natural platform for the interplay between the Josephson effect and the Landau-Zener effect through a two-level system formed by coupled Majorana modes. We build a quantum resistively shunted junction (RSJ) model by modifying the standard textbook RSJ model to take account of the two-level system from the Majorana modes at the junction. We show that the dynamics of the two-level system is governed by a nonlinear Schr\"odinger equation and solve the equations analytically via a mapping to a classical dynamical problem. This nonlinear dynamics leads to hysteresis in the I-V characteristics, which can give a quantitative explanation to recent experiments. We also predict the coexistence of two interference patterns with periods $h/e$ and $h/2e$ in topological superconducting quantum interference devices.

Fine structure of 211Bi α-decay from Coriolis coupling

The α-decay is considered as a superasymmetric fission process. A fragmentation path is obtained by mean of the least action principle in a configuration space spanned by five degrees of freedom. The potential barrier is obtained within the macroscopic-microscopic model while the effective mass and the momentum of inertia within the cranking approach. The single-particle wave functions and the single-particle energies are supplied by the Woods-Saxon two-center shell model. The fine structure of 211Bi α-decay is treated within a set of generalized time-dependent pairing equations that takes into account the Landau-Zener effect and the Coriolis coupling. A low value of the internuclear collective velocity was used. The theoretical results showed a good agreement with the experimental data. Essentially, in the framework of the formalism, the fine structure for the 211Bi is due to the occurrence of the Coriolis coupling.

Fine structure of α decay from the variational principle

Starting from the variational principle, the time-dependent pairing equations are generalized by including the Landau-Zener effect and the Coriolis coupling. A system of microscopic equations of motion for configuration mixing is deduced, allowing the determination of quantities that have the same meaning as the preformation factors of the $\ensuremath{\alpha}$ particle. These equations are solved in order to reproduce the hindrance factors of the $\ensuremath{\alpha}$ decay of an odd-$A$ mass nucleus. The $\ensuremath{\alpha}$ decay of $^{211}\mathrm{Po}$ is treated as a superasymmetric fission process, by following the rearrangement of the nuclear orbitals from the parent ground state up to the scission configuration. The probabilities of finding the excited states of the daughter at scission are obtained from the microscopic equations of motion. The intensities of the transitions to the excited states of the daughter were evaluated theoretically. The experimental data were compared with the theoretical findings. A very good agreement was obtained. A mean value of the tunneling velocity of about $2\ifmmode\times\else\texttimes\fi{}{10}^{4}$ fm/fs was extracted.

Nonlinear targeted energy transfer and macroscopic analog of the quantum Landau–Zener effect in coupled granular chains

In this work, we present an analytical and numerical approach for analyzing the passive nonlinear targeted energy transfer—TET—in weakly coupled granular media. In particular, we consider two weakly coupled uncompressed granular chains of semi-infinite extent, composed of perfectly elastic spherical beads under Hertzian interactions, mounted on linear elastic foundations. One of the chains is regarded as the ‘excited’ chain, whereas the other is designated as the ‘absorbing’ chain and is initially at rest. We study two different mechanisms for TET in this class of strongly nonlinear granular media: (i) by decoupling the chains taking into account the relative phases of the propagating breathers in the two chains, and (ii) through stratification of the coupling between the two chains leading to macro-scale realization of the analog of the quantum Landau–Zener tunneling quantum effect in space. Each mechanism provides an efficient way for eventual spatial localization of energy in the absorbing granular chain; the second mechanism is especially interesting since it provides an example of macroscopic realization of the analog of a quantum effect for passive energy transfer. Numerical simulations fully validate the theoretical analysis and results.

CONFIGURATION MIXING AND DISSIPATION FROM THE TIME-DEPENDENT PAIRING EQUATIONS

The time-dependent pairing equations are developed to include the Landau–Zener effect and a pair breaking mechanism. The new formalism provide information about the configuration mixing and the dissipation for a dynamical evolution of a nuclear system. A formula for a nonadiabatic cranking inertia is also deduced. Results concerning cluster decay and fission processes are presented.

Strong dissipation regime in nuclear disintegrations

The coupling of collective degrees of freedom with the microscopic ones causes dissipation and a modification of the adiabatic potential. The term dissipation usually refers to exchange of energy (either linear or angular momentum) by all kind of damping from collective motion to intrinsic heat. A measure of the dissipated energy can be obtained solving the time dependent pairing equations. In this presentation, a generalization of the time dependent pairing equations is presented by including the Landau-Zener effect in the superfluid model. These new equations allows a mixing of seniority one configurations that allows us to obtain a ground state at the end of the process. An application concerning the 14C emission is offered and its fine structure is explained. These new equations are furthermore used to evidence a dynamical pair breaking effect that could explain the fine odd-even effect in cold fission. Finally, the time dependent pairing equations are used to deduce a model for non-adiabatic cranking inertia.

Dissipative regime in low energy fission

Abstract In this presentation, a generalization of the time dependent pairing equations is presented by including the Landau-Zener effect in the superfluid model. These new equations allows a mixing of seniority one configurations that allows us to obtain a ground state at the end of the process. An application concerning the C-14 emission is offered and its fine structure is explained. These new equations are furthermore used to evidence a dynamical pair breaking effect that could explain the fine odd-even effect in cold fission. The partition of the dissipated energy between the two fission fragments will be also modeled. Finally, the time dependent pairing equations are used to deduce a model for non-adiabatic cranking inertia.

Time-dependent pairing equations for seniority-one nuclear systems

When the time-dependent Hartree-Fock-Bogoliubov intrinsic equations of motion are solved in the case of seniority-one nuclear systems, the unpaired nucleon remains on the same orbital. The blocking effect hinders the possibility to skip from one orbital to another. This unpleasant feature is by-passed with a new set of pairing time-dependent equations that allows the possibility that the unpaired nucleon changes its single-particle level. These equations generalize the time-dependent Hartree-Fock-Bogoliubov equations of motion by including the Landau-Zener effect. The derivation of these new equations is presented in detail. These equations are applied to the case of a superasymmetric fission process, that is, to explain the fine structure the $^{14}\mathrm{C}$ emission from $^{233}\mathrm{Ra}$. In this context, a new version of the Woods-Saxon model extended for two-center potentials is used.

Landau-Zener effect in fission

A model that takes into account the Landau-Zener promotion mechanism during fission was developed recently. The structures observed in the subthreshold neutron-induced fission of $^{232}\mathrm{Th}$ are investigated employing this model. Theoretical single-particle excitations of a phenomenological two-humped barrier are determined by solving a system of coupled differential equations for the motion along the optimal fission path. A rather good agreement with experimental data is obtained using a small number of independent parameters. It is predicted that the structure at 1.4 and 1.6 MeV is mainly dominated by a spin 3/2 partial cross section with a small admixture of spin 1/2, while the structure at 1.7 MeV is given by a large partial cross section of spin 5/2.

Boost-invariant mean field approximation and the nuclear Landau-Zener effect

We investigate the relation between time-dependent Hartree-Fock (TDHF) states and the adiabatic eigenstates by constructing a boost-invariant single-particle Hamiltonian. The method is numerically realized within a full three-dimensional TDHF which includes all the terms of the Skyrme energy functional and without any symmetry restrictions. The study of free translational motion of a nucleus demonstrates the validity of the concept of boost-invariant and adiabatic TDHF states. The interpretation is further corroborated by the test case of fusion of 16 O + 16 O. As a first application, we present a study of the nuclear Landau-Zener effect on a collision of 4 He + 16 O.

Dynamical single-particle effects in the threshold fission cross section

A new formalism intended to simulate the cross section of the threshold neutron induced fission is proposed. The barriers corresponding to excited intrinsic single-particle states are taken explicitly into account. The radial coupling damping is treated within the Landau–Zener effect while the second-well damping due to re-emission in other channels is treated within an imaginary potential. In this context, the excitations are strongly dependent on the internuclear velocity between the two nascent fragments, and therefore managed by the dynamics of the system. An example of the neutron induced fission cross section of 234U is given.

Many-body Landau-Zener effect at fast sweep

The asymptotic staying probability $P$ in the Landau-Zener effect with interaction is analytically investigated at fast sweep $\ensuremath{\epsilon}=\ensuremath{\pi}{\ensuremath{\Delta}}^{2}∕(2\ensuremath{\hbar}v)⪡1$. We have rigorously calculated the value of ${I}_{0}$ in the expansion $P\ensuremath{\cong}1\ensuremath{-}\ensuremath{\epsilon}+{\ensuremath{\epsilon}}^{2}∕2+{\ensuremath{\epsilon}}^{2}{I}_{0}$ for arbitrary couplings and relative resonance shifts of individual tunneling particles. The results essentially differ from those of the mean-field approximation. It is shown that strong long-range interactions such as dipole-dipole interaction generate huge values of ${I}_{0}$ because a flip of one particle strongly influences many others. However, in the presence of strong static disorder, making the resonances for individual particles shifted with respect to each other, the influence of interactions is strongly reduced. In molecular magnets the main source of static disorder is the coupling to nuclear spins. Our calculations using the actual shape of the ${\mathrm{Fe}}_{8}$ crystal studied in the Landau-Zener experiments [Wernsdorfer et al., Europhys. Lett. 50, 552 (2000)] yield a value of ${I}_{0}$ that is in good agreement with the value extracted from the experimental data.

Interference effect in the Landau-Zener tunneling of the antiferromagnetically coupled dimer of single-molecule magnets

Two antiferromagnetically coupled tunneling systems compose a minimal model exhibiting the effect of the quantum-mechanical phase in the Landau-Zener effect. It is shown that the averaged staying probability oscillates versus the resonance shift between the two particles, as well as versus the sweeping rate. Such a resonance shift can be produced in ${\mathrm{Mn}}_{4}$ dimers by the gradient of the magnetic field.

Landau–Zener Effect in Superfluid Nuclear Systems

The Landau–Zener effect is generalized for many-body systems with pairing residual interactions. The microscopic equations of motion are obtained and the 14C decay of 223Ra spectroscopic factors are deduced. An asymmetric nuclear shape parametrization given by two intersected spheres is used. The single particle level scheme is determined in the frame of the superasymmetric two-center shell model. The deformation energy is computed in the microscopic–macroscopic approximation. The penetrabilities are obtained within the WKB approximation. The fine structure of the cluster decay analyzed in the frame of this formalism gives a very good agreement with the experimental ratio of partial half-lives for transition to the first excited state and to the ground state.

Superradiance from crystals of molecular nanomagnets.

We show that crystals of molecular nanomagnets can exhibit giant magnetic relaxation due to the Dicke superradiance of electromagnetic waves. Rigorous theory is presented that combines superradiance with the Landau-Zener effect.