Nonadiabatic Phase Research Articles

Phase-Matched High-Harmonic Generation under Nonadiabatic Conditions: Model and Experiment

Nonadiabatic phase matching of high-harmonic generation (HHG) driven by few-cycle laser pulses is essential for extending harmonic energy and generating isolated attosecond pulses. However, understanding nonadiabatic HHG is challenging due to the complex interplay of various optical phases driven by temporally and spatially varying laser fields. Theoretical calculations typically rely on computationally demanding 3-dimensional simulations, which can make it difficult to extract the essential features of nonadiabatic HHG. In this work, we develop a computationally efficient 2-dimensional model that directly considers various phase contributions of HHG. Our model can well explain the experimentally observed pressure- and intensity-dependent behaviors of different harmonic orders. By appropriately parameterizing the single-atom response, our model can also estimate the variation of HHG spectra under different driving conditions. Our model can provide an efficient tool for the design and optimization of HHG-based applications.

Extension of the bright high-harmonic photon energy range via nonadiabatic critical phase matching

The concept of critical ionization fraction has been essential for high-harmonic generation, because it dictates the maximum driving laser intensity while preserving the phase matching of harmonics. In this work, we reveal a second, nonadiabatic critical ionization fraction, which substantially extends the phase-matched harmonic energy, arising because of the strong reshaping of the intense laser field in a gas plasma. We validate this understanding through a systematic comparison between experiment and theory for a wide range of laser conditions. In particular, the properties of the high-harmonic spectrum versus the laser intensity undergoes three distinctive scenarios: (i) coincidence with the single-atom cutoff, (ii) strong spectral extension, and (iii) spectral energy saturation. We present an analytical model that predicts the spectral extension and reveals the increasing importance of the nonadiabatic effects for mid-infrared lasers. These findings are important for the development of high-brightness soft x-ray sources for applications in spectroscopy and imaging.

The rate of thermodynamic cost against adiabatic and nonadiabatic fluctuations of a single gene circuit in Drosophila embryos

We study the stochastic dynamics of the externally regulating gene circuit as an example of an eve-skipped gene stripe in the development of Drosophila. Three gene regulation regimes are considered: an adiabatic phase when the switching rate of the gene from the OFF to ON state is faster than the rate of mRNA degradation; a nonadiabatic phase when the switching rate from the OFF to ON state is slower than that of the mRNA degradation; and a bursting phase when the gene switching is fast and transcription is very fast, while the ON state probability is very low. We found that the rate of thermodynamic cost quantified by the entropy production rate can suppress the fluctuations of the gene circuit. A higher (lower) rate of thermodynamic cost leads to reduced (increased) fluctuations in the number of gene products in the adiabatic (nonadiabatic) regime. We also found that higher thermodynamic cost is often required to sustain the emergence of more gene states and, therefore, more heterogeneity coming from genetic mutations or epigenetics. We also study the stability of the gene state using the mean first passage time from one state to another. We found the monotonic decrease in time, i.e., in the stability of the state, in the transition from the nonadiabatic to adiabatic regimes. Therefore, as the higher rate of thermodynamic cost suppresses the fluctuations, higher stability requires higher thermodynamics cost to maintain.

Dissipative Floquet dynamical quantum phase transition

Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time-driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical nonadiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.

Nonadiabatic Phase Transition with Broken Chiral Symmetry.

We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations, which support nonadiabatic transitions. Nevertheless, we find that the excitations on one of the chain sublattices are suppressed in the nearly adiabatic regime exponentially. Thus, we reveal a coherent mechanism to induce exponentially large density separation for different quasiparticles.

Effects of microphysical processes on the rapid intensification of Super-Typhoon Meranti

Typhoon Meranti (2016) underwent extreme rapid intensification (RI) over the western North Pacific (WNP), just before its landfall in Fujian Province, China. In this study, the extreme RI, track, and structures of the inner core and spiral cloud bands of Meranti were simulated, reasonably realistically, using WRF-ARW (the Advanced Research version of the Weather Research and Forecasting model). Firstly, the convective bursts (CBs) and associated microphysical processes were analyzed in detail to evaluate the probable mechanism responsible for the RI of Meranti. The results showed that Meranti experienced RI over the warm ocean with high ocean heat content and decreasing environmental vertical shear. The onset of RI was triggered by CBs, which penetrated the upper troposphere, leading to upper-tropospheric warming and the formation of an upper-level warm core. Diagnosis of the complete Q-vector showed that the CBs of the inner core were jointly triggered by the dynamic forcing of the frontogenesis and the non-adiabatic phase transition process. Further analysis of the heat budget of microphysical processes revealed that the condensation process (accounting for 76.3% of the total heating rate of the warming processes) played a leading role for CBs in the lower and middle troposphere, while the deposition process (accounting for 19% of the total heating rate of the warming processes) was a critical factor of the CBs in the upper level of the troposphere.

Low-frequency spectroscopy for quantum multilevel systems

A periodically driven quantum system with avoided-level crossing experiences both non-adiabatic transitions and wave-function phase changes. These result in coherent interference fringes in the system's occupation probabilities. For qubits, with repelling energy levels, such interference, named after Landau-Zener-Stuckelberg-Majorana, displays arc-shaped resonance lines. We demonstrate that in the case of a multi-level system with an avoided-level crossing of the two lower levels, the shape of the resonances can change from convex arcs to concave heart-shaped and harp-shaped resonance lines. In this way, the shape of such resonance fringes is defined by the whole spectrum, providing insight on the slow-frequency system spectroscopy. As a particular example, we consider this for valley-orbit silicon quantum dots.

Exact spin-orbit qubit manipulation

We consider exactly solvable manipulation of spin-qubits confined in a moving harmonic trap and in the presence of the time dependent Rashba interaction. Non-adiabatic Anandan phase for cyclic time evolution is compared to the Wilczek-Zee adiabatic counterpart. It is shown that the ratio of these two phases can for a chosen system be any real number. Next we demonstrate the possibility of arbitrary qubit transformation in a ring with spin-orbit interaction. Finally, we present an example of exact analysis of spin-orbit dynamics influenced by the Ornstein-Uhlenbeck coloured noise.

Classical analog of Stückelberg interferometry in a two-coupled-cantilever–based optomechanical system

We present the realization of a St\uckelberg interferometer with two mechanical modes in a two-coupled-cantilever--based optomechanical system. By optically tuning the frequency of one cantilever inside a cavity, we show that nonadiabatic crossing of the mechanical modes twice creates the interference fringes of the mechanical oscillations as a result of coherent splitting and subsequent recombination of the oscillations. By measuring the nonadiabatic phase acquired at the transition, we unveil an in-depth analog between the two-mode and quantum two-level systems. With this interferometry-based technique, transferring of oscillation between spatially separated cantilevers is achieved with 97% efficiency.

Nonadiabatic quantum phase transition in a trapped spinor condensate

We study the effect of an external harmonic trapping potential on an outcome of the non-adiabatic quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 atomic condensate. Previously, we demonstrated that the dynamics of an untrapped system exhibits double universality with two different scaling laws appearing due to conservation of magnetization. We show that in the presence of a trap double universality persists. However, the corresponding scaling exponents are strongly modified by transfer of local magnetization across the system. The values of these exponents cannot be explained by the effect of causality alone, as in the spinless case. We derive the appropriate scaling laws based on a slow diffusive-drift relaxation process in the local density approximation.

Continuum model for chiral induced spin selectivity in helical molecules.

A minimal model is exactly solved for electron spin transport on a helix. Electron transport is assumed to be supported by well oriented p(z) type orbitals on base molecules forming a staircase of definite chirality. In a tight binding interpretation, the spin-orbit coupling (SOC) opens up an effective π(z) - π(z) coupling via interbase p(x,y) - p(z) hopping, introducing spin coupled transport. The resulting continuum model spectrum shows two Kramers doublet transport channels with a gap proportional to the SOC. Each doubly degenerate channel satisfies time reversal symmetry; nevertheless, a bias chooses a transport direction and thus selects for spin orientation. The model predicts (i) which spin orientation is selected depending on chirality and bias, (ii) changes in spin preference as a function of input Fermi level and (iii) back-scattering suppression protected by the SO gap. We compute the spin current with a definite helicity and find it to be proportional to the torsion of the chiral structure and the non-adiabatic Aharonov-Anandan phase. To describe room temperature transport, we assume that the total transmission is the result of a product of coherent steps.

Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas

A general theoretical framework for investigating the nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or comparable to the wave–particle trapping period. In this limit, both theoretical and numerical simulation studies show that nonadiabatic frequency chirping and phase locking could lead to secular resonant particle transport on meso- or macro-scales. The interplay between mode structures and resonant particles then provides the crucial ingredient to properly understand and analyze the nonlinear dynamics of Alfvén wave instabilities excited by nonperturbative energetic particles in burning fusion plasmas. Analogies with autoresonance in nonlinear dynamics and with superradiance in free-electron lasers are also briefly discussed.

Adiabatic and Non-Adiabatic Berry Phases in Generalized J-C Model of Multi-Photon Process

We derive the adiabatic and non-adiabatic Berry phases in the generalized Jaynes—Cummings model of multi-photon process. The results show that the adiabatic Berry phase is kept a constant π independent of all the parameters, while the non-adiabatic approximate Berry phase is parameter-dependent, proportional to the average photon number m, and tends to be constant with the increasing detuning. In the case of exact n-photon resonance and an integer ratio of m/n, the two results coincide with each other, otherwise there appears an additional non-trivial phase factor.

Quantum path control in harmonic generation by temporal shaping of few-optical-cycle pulses in ionizing media

Temporal reshaping of the electric field of few-optical-cycle pulses in a low-density ionizing gas has been used to achieve control of the electron trajectories in the process of high-order harmonic generation. As a result of such a quantum path control mechanism, isolated or multiple attosecond pulses have been produced, depending on the carrier-envelope phase of the driving field. In particular, complete spectral tunability of the harmonic peaks over the whole spectral range has been demonstrated. Experimental results have been interpreted using a nonadiabatic three-dimensional propagation model and a nonadiabatic stationary phase model.

Constructing effective one-body dynamics with numerical energy flux for intermediate-mass-ratio inspirals

A new scheme for computing dynamical evolutions and gravitational radiations for intermediate-mass-ratio inspirals (IMRIs) based on an effective one-body (EOB) dynamics plus Teukolsky perturbation theory is built in this paper. In the EOB framework, the dynamic essentially affects the resulted gravitational waveform for a binary compact star system. This dynamic includes two parts. One is the conservative part, which comes from effective one-body reduction. The other part is the gravitational backreaction, which contributes to the shrinking process of the inspiral of a binary compact star system. Previous works used an analytical waveform to construct this backreaction term. Since the analytical form is based on post-Newtonian expansion, the consistency of this term is always checked by numerical energy flux. Here, we directly use numerical energy flux by solving the Teukolsky equation via the frequency-domain method to construct this backreaction term. The conservative correction to the leading order terms in mass-ratio is included in the deformed-Kerr metric and the EOB Hamiltonian. We try to use this method to simulate not only quasicircular adiabatic inspiral, but also the nonadiabatic plunge phase. For several different spinning black holes, we demonstrate and compare the resulted dynamical evolutions and gravitational waveforms.

Suppression of nonadiabatic phases by a non-Markovian environment: Easier observation of Berry phases

We consider a two-level system coupled to a highly non-Markovian environment when the coupling axis rotates with time. The environment may be quantum (for example a bosonic bath or a spin bath) or classical (such as classical noise). We show that an Anderson orthogonality catastrophe suppresses transitions, so that the system's instantaneous eigenstates (parallel and antiparallel to the coupling axis) can adiabatically follow the rotation. These states thereby acquire Berry phases; geometric phases given by the area enclosed by the coupling axis. Unlike in earlier proposals for environment-induced Berry phases, here there is little decoherence, so one does not need a decoherence-free subspace. Indeed we show that this Berry phase should be much easier to observe than a conventional one because it is not masked by either the dynamic phase or the leading nonadiabatic phase. The effects that we discuss should be observable in any qubit device where one can drive three parameters in the Hamiltonian with strong man-made noise.

Shaping of attosecond pulses by phase-stabilized polarization gating

We demonstrate that the characteristics of the high-order harmonic spectra generated by few-cycle carrier-envelope phase-stabilized pulses can be finely adjusted by controlling the time-dependent ellipticity. The experimental measurements show evidence for the generation of single, pairs, and trains of attosecond pulses by controlling the time window of linear polarization of the driving pulses. The influence of the carrier-envelope phase on the generation process in different confinement configurations is interpreted and analyzed using a nonadiabatic stationary phase model. We show that the xuv emission depends critically on particular aspects of the fundamental electric field that allows us to steer the electron trajectories on the time scale of tens of attoseconds.

Preliminary results on the determination of the theoretical nonadiabatic observable phase lag (ψT) using VIRGO color photometry

AbstractThe helioseismic instruments aboard the SOHO satellite make it possible to measure solar oscillations as variations of the irradiance (VIRGO) or as variations of the photospheric velocity (GOLF). Theoretically, phase differences between different photometric bands are expected to be around 0 degrees over the p‐mode frequency range. By using VIRGO (red) and VIRGO (blue) data, we find a mean phase shift of 8.05 ± 1.81°, whereas by using VIRGO (green) and VIRGO (blue) data, we got a mean value of –1.04 ± 0.19°. Hence, when the analysis includes the VIRGO infrared range, the Sun's atmosphere does not follow an exact adiabatic behavior. In this study, we use the phase shifts obtained by VIRGO (green) and VIRGO (blue) to determine the non‐adiabatic parameter phase lag (ψT) as a function of frequency. To this aim, we applied the non radial linearized formula put in the complex form by Garrido: we found a mean value of ψT = 179.95°. The lowest value being ψT = 179.90°, the departure from theoretical predictions is less then a tenth of a degree over the entire p mode frequency range. We can state that the solar atmosphere has a behavior close to the adiabatic case, when the phase shifts and amplitude ratios are computed using VIRGO (green) and VIRGO (blue) data. Nevertheless this small deviation is significant. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Quench-induced trapping of magnetic flux in annular Josephson junctions

The aim of the project is to investigate spontaneous symmetry breaking in non-adiabatic phase transitions (Kibble-Zurek processes). A long and narrow annular Josephson tunnel junction is subjected to repeated thermal quenches through the normal-superconducting transition. The quench rate is varied over 4 orders of magnitude. After the quench the result of the spontaneous production of topological defects, trapped fluxons, is unambiguously observed as zero-field steps in the DC I-V characteristic of the junction. A power-law scaling behavior of trapping probability versus quench rate is found with a critical exponent of 0.5 (within experimental error). The main experimental challenges are to generate many identical quenches with accurate cooling rate, to automate data analysis and acquisition, and to suppress external magnetic fields and noise by passive magnetic shielding and compensation.

Zurek–Kibble Symmetry Breaking Process in Superconducting Rings; Spontaneous Fluxon Formation in Annular Josephson Tunnel Junctions

We report on new investigations of spontaneous symmetry breaking in non-adiabatic phase transitions. This Zurek-Kibble (ZK) process is mimicked in solid state systems by trapping of magnetic flux quanta, fluxons, in a long annular Josephson tunnel junction quenched through the normal-superconducting transition. A trapped fluxon unambiguously is detected as a zero-field step in the DC I-V characteristic. Experimentally we plot the fluxon trapping probability versus the quench rate, varied over 4 decades. An allometric scaling behavior is found. By fitting to the theoretical curve we get sigma sime 0.5 for the ZK critical scaling exponent sigma, which does not agree with an earlier theoretical prediction of sigma = 0.25. A novel theory based on the proximity effect leading to sigma = 0.50 has been proposed. The dependence of the gap voltage on temperature is measured and used for precise monitoring of the fast temperature variation during the quench.