Adiabatic Limit Research Articles

Influence of zonal flow and density on resistive drift wave turbulent transport

The generations of zonal flow (ZF) and density (ZD) and their feedback on the resistive drift wave turbulent transport are investigated within the modified Hasegawa-Wakatani model. With proper normalization, the system is only controlled by an effective adiabatic parameter, α, where the ZF dominates the collisional drift wave (DW) turbulence in the adiabatic limit α>1. By conducting direct numerical simulations, we found that the ZF can significantly reduce the transport by trapping the DWs in the vicinities of its extrema for α>1, whereas the ZD itself has little impact on the turbulence but can only assist ZF to further decrease the transport by flattening the local plasma density gradient.

Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

As discussed in Bahns et al. (2015) fundamental physical principles suggests that, close to cosmological singularities, the effective Planck length diverges, hence a “quantum point” becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This conclusion is supported by converging evidences in two different approaches to interacting quantum fields on Quantum Spacetime: (1) as the Planck length diverges, the field operators evaluated at a “quantum point” converge to zero, and so do the lowest order expressions for interacting fields in the Yang Feldman approach; (2) in the same limit, we find convergence of the interacting vacuum to the free one at all perturbative orders. The latter result is obtained using the adaptation, performed in Doplicher et al. (2020), of the methods of perturbative Algebraic Quantum Field Theory to Quantum Spacetime, through a novel picture of the effective Lagrangian, which maintains the ultraviolet finiteness of the perturbation expansion and allows one to prove also the existence of the adiabatic limit. It remains an open question whether the S matrix itself converges to unity and whether the limit in which the effective Planck length diverges is a unique initial condition or an unreachable limit, and only different asymptotics matter.

Probabilistic hysteresis from a quantum-phase-space perspective

\emph{Probabilistic hysteresis} is a manifestation of irreversibility in a small, isolated classical system [Sci. Rep. 9, 14169]: after a slow cyclic sweep of a control parameter, the probability that a microcanonical ensemble returns to the neighborhood of its initial energy is significantly below one. A similar phenomenon has recently been confirmed in a corresponding quantum system for not too small particle number $N$. Quantum-classical correspondence has been found to be non-trivial in this case, however; the rate at which the control parameter changes must not be extremely slow and the initial distribution of energies must not be too narrow. In this paper we directly compare the quantum and classical forms of probabilistic hysteresis by making use of the Husimi quantum phase space formalism. In particular we demonstrate that the classical ergodization mechanism, which is a key ingredient in classical probabilistic hysteresis, can lead to a breakdown of quantum-classical correspondence rather than to quantum ergodization. As a result strong quantum effects in the long-term evolution are present, even though the quantum corrections in the equations of motion are proportional to $1/N$ and therefore would naively seem to be small. We also show, however, that quantum ergodization is restored by averaging over energies, so that for sufficient initial energy width and not-too-slow sweep rate the classical results are recovered after all. Finally we show that the formal incommutability of the classical and adiabatic limits in our system, leading to the breakdown of quantum-classical correspondence in the quasi-static limit, is due to macroscopic quantum tunneling through a large energetic barrier. This explains the extremely slow sweep rates needed to reach the quantum adiabatic limit that were reported in our previous work.

Comprehensive Benchmark Results for the Accuracy of Basis Sets for Anharmonic Molecular Vibrations.

The accuracy and convergence of a series of commonly used split-valence electronic basis sets are systematically investigated for the anharmonic molecular vibrational spectroscopic calculations using the second-order perturbative corrected vibrational self-consistent field theory. A series of 18 split-valence basis sets with increasing flexibility is assessed in conjunction with MP2 and density functional theory (DFT)-based dispersion-corrected B3LYP potentials and applied to a set of molecular systems with different electronic and vibrational characteristics. The computed fundamental transitions and intensities are compared with the experimental values to assess the accuracy of different basis sets. Comparisons with high levels of Dunning basis sets, aug-cc-pVQZ along with def2-TZVPP and aug-pc-2 type basis sets, are also tested to check the convergence. A full statistical error analysis has been performed, assessing the success and failure of each basis set in terms of both accuracy and precision. The general statement "the bigger the basis, the better the results" is not strictly followed for bigger basis sets that are nearly converged to the adiabatic ab initio limit. It is found that the basis set hierarchy holds good for minimal basis sets up to polarized double-ζ basis sets. Beyond that, the improvements in comparison to experimental results or with very high end aug-cc-pVQZ and others are found rather slow. Finally, a prescription regarding the choice of a basis set for a suitable balance between accuracy and the computational time is given, which can be further used to investigate specific normal modes and large molecules as a blackbox.

Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Considering two non-interacting qubits in the context of open quantum systems, it is well known that their common environment may act as an entangling agent. In a perturbative regime the influence of the environment on the system dynamics can effectively be described by a unitary and a dissipative contribution. For the two-spin Boson model with (sub-) Ohmic spectral density considered here, the particular unitary contribution (Lamb shift) easily explains the buildup of entanglement between the two qubits. Furthermore it has been argued that in the adiabatic limit, adding the so-called counterterm to the microscopic model compensates the unitary influence of the environment and, thus, inhibits the generation of entanglement. Investigating this assertion is one of the main objectives of the work presented here. Using the hierarchy of pure states (HOPS) method to numerically calculate the exact reduced dynamics, we find and explain that the degree of inhibition crucially depends on the parameter s determining the low frequency power law behavior of the spectral density J(ω)∼ωse−ω/ωc. Remarkably, we find that for resonant qubits, even in the adiabatic regime (arbitrarily large ωc), the entanglement dynamics is still influenced by an environmentally induced Hamiltonian interaction. Further, we study the model in detail and present the exact entanglement dynamics for a wide range of coupling strengths, distinguish between resonant and detuned qubits, as well as Ohmic and deep sub-Ohmic environments. Notably, we find that in all cases the asymptotic entanglement does not vanish and conjecture a linear relation between the coupling strength and the asymptotic entanglement measured by means of concurrence. Further we discuss the suitability of various perturbative master equations for obtaining approximate entanglement dynamics.

Heuristic model for sum frequency generation in chirped quasi-phase-matching gratings with application to selective, cascaded harmonic generation.

The use of chirped quasi-phase-matching (CQPM) for cascaded harmonic generation (CHG) in a single crystal has gained attraction in recent years. CHG involves multiple stages of second harmonic and sum frequency generation processes, of which their complex dynamics in CQPM structures are not well understood when far from the adiabatic limit. This subsequently poses a challenge to design CQPM structures for the optimization of higher order harmonic generation via cascaded processes. In this paper, we derive a heuristic model with analytical expressions for the approximation of the efficiency, location and length of second harmonic and sum frequency generation processes in CQPM structures in the non-adiabatic, fully nonlinear regime (i.e. with pump depletion). With the developed model, we present a design framework to create cascaded CQPM structures for the generation of any arbitrary harmonic with efficiency close to 100%.

Majorana-based quantum computing in nanowire devices

The boundary of topological superconductors might lead to the appearance of Majorana edge modes, whose non-trivial exchange statistics can be used for topological quantum computing. In branched nanowire networks one can exchange Majorana states by time-dependently tuning topologically non-trivial parameter regions. In this work, we simulate the exchange of four Majorana modes in T-shaped junctions made out of p-wave superconducting Rashba wires. We derive concrete experimental predictions for (quasi-)adiabatic braiding times and determine geometric conditions for successful Majorana exchange processes. Contrary to the widespread opinion, we show for the first time that in the adiabatic limit the gating time needs to be smaller than the inverse of the squared superconducting order parameter and scales linearly with the gating potential. Further, we show how to circumvent the formation of additional Majorana modes in branched nanowire systems, arising at wire intersection points of narrow junctions. Finally, we propose a multi qubit setup, which allows for universal and in particular topologically protected quantum computing.

Uniform adiabatic limit of Benney type systems

In this paper, we show that solutions of the cubic nonlinear Schrödinger equation are asymptotic limit of solutions to the Benney system. Due to the special characteristic of the one-dimensional transport equation, same result is obtained for solutions of the one-dimensional Zakharov and 1d-Zakharov–Rubenchik systems. Convergence is reached in the topology \(L^2({\mathbb R})\times L^2({\mathbb R})\) and with an approximation in the energy space \(H^1({\mathbb R})\times L^2({\mathbb R})\). In the case of the Zakharov system, this is achieved without the condition \(\partial _t n(x,0) \in \dot{H}^{-1}({\mathbb R})\) for the wave component, improving previous results.

Direct observation of time-asymmetric breakdown of the standard adiabaticity around an exceptional point

Recent study on topological operations around an exceptional point singularity has shown remarkably robust chiral processes that potentially create time-asymmetric or nonreciprocal systems and devices. Nevertheless, direct observation of the entire dynamics in the courses of the topological operations has not been revealed in experiments thus far. Here, we report a comprehensive experimental study on fully time-resolved dynamic-state evolution passages during encircling-an-exceptional-point operations. Using dynamically tunable electrical oscillators, we create a self-intersecting eigenvalue topology with an unprecedented accuracy and experimentally confirm that the time-asymmetric breakdown of the standard adiabaticity is indeed unavoidable when the system encircles an exceptional point in the canonical adiabatic limit. We further discuss the impact of parasitic noises on the time-asymmetric mode-transfer performance and subsequent considerations for practical design requirements.

Theory of wave-packet transport under narrow gaps and spatial textures: Nonadiabaticity and semiclassicality

We generalise the celebrated semiclassical wavepacket approach from the adiabatic to the non-adiabatic regime. A unified description covering both of these regimes is particularly desired for systems with spatially varying band structures where band gaps of various sizes are simultaneously present, e.g. in moir\'{e} patterns. For a single wavepacket, alternative to the previous derivation by Lagrangian variational approach, we show that the same semiclassical equations of motion can be obtained by introducing a spatial-texture-induced force operator similar to the Ehrenfest theorem. For semiclassically computing the current, the ensemble of wavepackets based on adiabatic dynamics is shown to well correspond to a phase-space fluid for which the fluid's mass and velocity are two distinguishable properties. This distinction is not inherited to the ensemble of wavepackets with the non-adiabatic dynamics. We extend the adiabatic kinetic theory to the non-adiabatic regime by taking into account decoherence, whose joint action with electric field favours certain form of inter-band coherence. The steady-state density matrix as a function of the phase-space variables is then phenomenologically obtained for calculating the transport current. The result, applicable with a finite electric field, expectedly reproduces the known adiabatic limit by taking the electric field to be infinitesimal, and therefore attains a unified description from the adiabatic to the non-adiabatic situations.

Non-adiabatic Hall effect at Berry curvature hot spot

Hot spot of Berry curvature is usually found at Bloch band anti-crossings, where the Hall effect due to the Berry phase can be most pronounced. With small gaps there, the adiabatic limit for the existing formulations of Hall current can be exceeded in a moderate electric field. Here we present a theory of non-adiabatic Hall effect, capturing non-perturbatively the across gap electron-hole excitations by the electric field. We find a general connection between the field induced electron-hole coherence and intrinsic Hall velocity. In coherent evolution, the electron-hole coherence can manifest as a sizeable ac Hall velocity. When environmental noise is taken into account, its joint action with the electric field favors a form of electron-hole coherence that is function of wavevector and field only, leading to a dc non-linear Hall effect. The Hall current has all odd order terms in field, and still retains the intrinsic role of the Berry curvature. The quantitative demonstration uses the example of gapped Dirac cones, and our theory can be used to describe the bulk pseudospin Hall current in insulators with gapped edge such as graphene and 2D MnBi2Te4.

Effect of mediated interactions on a Hubbard chain in mixed-dimensional fermionic cold atoms

Cold atom experiments can now realize mixtures where different components move in different spatial dimensions. We investigate a fermion mixture where one species is constrained to move along a one-dimensional lattice embedded in a two-dimensional lattice populated by another species of fermions, and where all bare interactions are contact interactions. By focusing on the one-dimensional fermions, we map this problem onto a model of fermions with non-local interactions on a chain. The effective interaction is mediated by the two-dimensional fermions and is both attractive and retarded, the form of which can be varied by changing the density of the two-dimensional fermions. By using the functional renormalization group in the weak-coupling and adiabatic limit, we show that the one-dimensional fermions can be controlled to be in various density-wave, or spin-singlet or triplet superconducting phases.

Quantum Control beyond the Adiabatic Regime in 2D Curved Matter-Wave Guides.

The propagation of matter waves in curved geometry is relevant for ion transport, atomtronics and electrons in nanowires. Curvature effects are usually addressed within the adiabatic limit and treated via an effective potential acting on the manifold to which the particles are strongly confined. However, the strength of the confinements that can be achieved experimentally are limited in practice, and the adiabatic approximation often appears too restrictive for realistic guides. Here, we work out a design method for 2D sharply bent waveguides beyond this approximation using an exact inverse-engineering technique. The efficiency of the method is confirmed by the resolution of the 2D nonlinear Schrödinger equation in curved geometry. In this way, we realize reflectionless and ultrarobust curved guides, even in the presence of interactions. Here, the transverse stability is improved by several orders of magnitude when compared to circular guides of similar size.

Nonadiabatic charge pumping across two superconductors connected through a normal metal region by periodically driven potentials

Periodically driven systems exhibit resonance when the difference between an excited state energy and the ground state energy is an integer multiple of ℏ times the driving frequency. On the other hand, when a superconducting phase difference is maintained between two superconductors, subgap states appear which carry a Josephson current. A driven Josephson junction therefore opens up an interesting avenue where the excitations due to applied driving affect the current flowing from one superconductor to the other. Motivated by this, we study charge transport in a superconductor–normal metal–superconductor junction where oscillating potentials are applied to the normal metal region. We find that for small amplitudes of the oscillating potential, driving at one site reverses the direction of current at the superconducting phase differences when difference between the subgap eigenenergies of the undriven Hamiltonian is integer multiple of ℏ times the driving frequency. For larger amplitudes of oscillating potential, driving at one site exhibits richer features. We show that even when the two superconductors are maintained at same superconducting phase, a current can be driven by applying oscillating potentials to two sites in the normal metal differing by a phase. We find that when there is a nonzero Josephson current in the undriven system, the local peaks and valleys in current of the system driven with an amplitude of oscillating potential smaller than the superconducting gap indicates sharp excitations in the system. In the adiabatic limit, we find that charge transferred in one time period diverges as a powerlaw with pumping frequency when a Josephson current flows in the undriven system. Our calculations are exact and can be applied to finite systems. We discuss possible experimental setups where our predictions can be tested.

Polaron transformations in the realistic model of the strongly correlated electron system

Electron-phonon coupling, diagonal in a real space formulation, leads to polaron paradigm of smoothly varying properties. However, fundamental changes, namely the singular behavior of polarons, occur if non-diagonal pairing is involved into consideration. The study of polaron transformations and related properties of matter is of particular interest for realistic models, since competition between diagonal and non-diagonal electron-phonon contributions in the presence of other strong interactions can result in unconventional behavior of the system. Here we consider the multiband pd-model of cuprate superconductors with electron-phonon interaction and analyze the features of the systems that are caused by the competition of diagonal and non-diagonal electron-phonon contributions in the limit of strong electron correlations. Using the polaronic version of the generalized tight-binding method, we describe the evolution of the band structure, Fermi surface, density of states at Fermi level, and phonon spectral function in the space of electron-phonon parameters ranging from weak to strong coupling strength of the adiabatic limit. On the phase diagram of polaron properties we reveal two quantum phase transitions and show how electron-phonon interaction gives rise to Fermi surface transformation (i) from hole pockets to Fermi arcs and (ii) from hole to electron type of conductivity. We also demonstrate the emergence of new states in the phonon spectral function of the polaron and discuss their origin.

Nonlinear oscillations of non-neutral plasmas in a time-dependent harmonic trap

A non-neutral plasma is confined in a quasi-1D device and described by a fluid model. The use of the Lagrangian variables method together with a certain Ansatz for the velocity field reduces the problem essentially to ordinary differential equations satisfied by a scale function. In the case of thermal dominated plasma, the governing equation is the Pinney equation, having a close connection with the time-dependent harmonic oscillator. For a slowly varying frequency of the trap potential, an approximate solution is derived and shown to be accurate in the adiabatic limit. In the case of negligible thermal effects, the resulting non-homogeneous time-dependent oscillator equation for the scale function is also approximately solved, in the adiabatic limit. The validity conditions of the thermal dominated and Coulomb dominated cases are determined. The results are applied to a confined antiproton plasma, with implication on antimatter atom experiments.

A general non-adiabatic quantum instanton approximation.

We present a general quantum instanton approach to calculating reaction rates for systems with two electronic states and arbitrary values of the electronic coupling. This new approach, which we call the non-adiabatic quantum instanton (NAQI) approximation, reduces to Wolynes theory in the golden rule limit and to a recently proposed projected quantum instanton method in the adiabatic limit. As in both of these earlier theories, the NAQI approach is based on making a saddle point approximation to the time integral of a reactive flux autocorrelation function, although with a generalized definition of the projection operator onto the product states. We illustrate the accuracy of the approach by comparison with exact rates for one dimensional scattering problems and discuss its applicability to more complex reactions.

Effect of confined one-gluon-exchange potential and instanton-induced interaction on nucleon–nucleon interaction

The effect of confined one-gluon-exchange potential and instanton-induced interaction potential in the singlet (1S0) and triplet (3S1) channels for nucleon–nucleon interaction has been investigated in the framework of the relativistic harmonic model using the resonating group method in the adiabatic limit with the Born–Oppenheimer approximation. The contributions of the different components of the interaction potentials have been analyzed.

Speeding up the creation of coherent superposition states by shortcut-to-adiabaticity means

We propose protocols of loop stimulated Raman shortcut-to-adiabatic passage (STIRSAP) and modified-STIRSAP to speed up the creation of arbitrary high fidelity coherent superposition states (F≃0.999). In loop- and modified-STIRSAP protocols, the nonadiabatic coupling between the dark and bright states can be canceled by an additional microwave pulse and modified pump and Stokes pulses, respectively. As a result of dark state rotation, the creation of preselected coherent superposition states can be achieved beyond the adiabatic limit. Compared with the stimulated Raman adiabatic passage (STIRAP) protocol, the evolution time of the creation of coherent superposition states can be shortened. Our numerical calculations agree well with the theoretical analysis in the partial dressed-state picture.

Nonadiabatic storage of short light pulses in an atom-cavity system

We demonstrate the storage of $5$ ns light pulses in a single rubidium atom coupled to a fiber-based optical resonator. Our storage protocol addresses a regime beyond the conventional adiabatic limit and approaches the theoretical bandwidth limit. We extract the optimal control laser pulse properties from a numerical simulation of our system and measure storage efficiencies of $(8.2\pm 0.6)~\%$, in close agreement with the maximum expected efficiency. Such well-controlled and high-bandwidth atom-photon interfaces are key components for future hybrid quantum networks.