It is shown that the fidelity, a basic notion of quantum information science, may be used to characterize quantum phase transitions, regardless of what type of internal order is present in quantum many-body states. If the fidelity of two given states vanishes, then there are two cases: (1) they are in the same phase if the distinguishability results from irrelevant local information; or (2) they are in different phases if the distinguishability results from relevant long-distance information. The different effects of irrelevant and relevant information are quantified, which allows us to identify unstable and stable fixed points (in the sense of renormalization group theory). A physical implication of our results is the occurrence of the orthogonality catastrophe near the transition points.

Fidelity and quantum phase transitions

We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. An exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of ground states occurs, associated with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist in an open chain in the time-reversal symmetry-unbroken region, demonstrating the bulk-edge correspondence in such a non-Hermitian system.

Topological phases in a Kitaev chain with imbalanced pairing

The complex Swift-Hohenberg equation (CSHE) has been widely studied in recent years. It is a more real model in the mode-locked fiber laser with the saturable absorber due to the addition of the diffraction term compared with the complex Ginzburg-Landau equation. In this work, the dynamics process of the traditional soliton and M−type soliton pulses in the mode-locked fiber laser is demonstrated based on the CSHE model with higher-order nonlinear effects. The results show that with the increase of the small signal gain coefficient, the number of soliton molecules adds gradually. Under the same transmission conditions, the transmission of M−type solitons in the laser are more stable than that of single solitons. By adding the self-steepening effect, it can be found that the time-domain shift due to higher-order dispersion effects is compensated. The self-frequency shift effect caused by the Raman scattering can produce not only time domain shift, but also frequency domain shift. Moreover, the addition of higher-order diffraction term can describe the spectral response of multiple peaks, and makes the pulse spectrum show the asymmetric propagation in the transmission process. Finally, the increase of the length of the single-mode fiber on the right side of the gain fiber in the optical circuit will not only shift the center position of the output pulse backward, but also make the pulse energy show a ladder type downward trend. 

Influence of higher-order nonlinear effects on optical solitons of the complex Swift-Hohenberg model in the mode-locked fiber laser

Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-environment interaction. A simple and paradigmatic example of non-Hermitian transport, originally introduced by Hatano and Nelson two decades ago [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996)], is the hopping dynamics of a quantum particle on a one-dimensional tight-binding lattice in the presence of an imaginary vectorial potential. The imaginary gauge field can prevent Anderson localization via non-Hermitian delocalization, opening up a mobility region and realizing robust transport immune to disorder and backscattering. Like for robust transport of topologically protected edge states in quantum Hall and topological insulator systems, non-Hermitian robust transport in the Hatano-Nelson model is unidirectional. However, there is not any physical impediment to observe robust bidirectional non-Hermitian transport. Here it is shown that in a quasi-one-dimensional zigzag lattice, with non-Hermitian (imaginary) hopping amplitudes and a synthetic gauge field, robust transport immune to backscattering can occur bidirectionally along the lattice.

Non-Hermitian bidirectional robust transport

Multi-layer metal films such as metallic coatings on metal substrate are important elements in modern engineering applications. Specifically, gold-coated metal mirrors are widely used in high-power laser systems. This work studies microscopic energy deposition and transport processes during short-pulse laser heating of multi-layer metals: the absorption of radiation energy by free electrons and the energy exchange between electrons and the lattice. The results show that multi-layer metals present very different thermal responses from single-layer metals during the heating process. In a gold and chromium multi-layer film, although laser energy is absorbed by free electrons in the top gold coating layer, most of the absorbed energy is converted into lattice energy not in the gold layer but rather in the underlying chromium layer. The underlying chromium layer reduces the lattice-temperature rise of the top gold layer significantly during short-pulse laser heating, suggesting a new way to increase the resistance of mirrors to thermal damage in applications of high-power lasers.

Femtosecond laser heating of multi-layer metals--I. analysis

We study quantum phase transitions in non-Hermitian XY and transverse-field Ising spin chains, in which the non-Hermiticity arises from the imaginary magnetic field. Analytical and numerical results show that at exceptional points, coalescing eigenstates in these models are close to W, distant Bell, and GHZ states, which can be steady states in the dynamical preparation scheme proposed by Lee et al. [T. E. Lee et al., Phys. Rev. Lett. 113, 250401 (2014)]. By selecting proper initial states, numerical simulations demonstrate the time evolution process to the target states with high fidelity.

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Generation of Bell, W , and Greenberger-Horne-Zeilinger states via exceptional points in non-Hermitian quantum spin systems

A conventional quantum phase transition (QPT) not only occurs at zero temperature, but also exhibits finite-temperature quantum criticality. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the finite-temperature quantum criticality in a non-Hermitian $\mathcal{PT}$-symmetric Ising model. We present the complete set of exact eigenstates of the non-Hermitian Hamiltonian, based on which the mixed-state fidelity in the context of biorthogonal bases is calculated. Analytical and numerical results show that the fidelity approach to finite-temperature QPT can be extended to the non-Hermitian Ising model. This paves the way for experimental detection of quantum criticality in a complex-parameter plane.

Finite-temperature quantum criticality in a complex-parameter plane

The dynamics of optical soliton molecules in ultrafast lasers can reveal the intrinsic self-organized characteristics of dissipative systems. The photonic time-stretch dispersive Fourier transformation (TS-DFT) technology provides an effective method to observe the internal motion of soliton molecules real time. However, the evolution of complex soliton molecular structures has not been reconstructed from TS-DFT data satisfactorily. We train a residual convolutional neural network (RCNN) with simulated TS-DFT data and validate it using arbitrarily generated TS-DFT data to retrieve the separation and relative phase of solitons in three- and six-soliton molecules. Then, we use RCNNs to analyze the experimental TS-DFT data of three-soliton molecules in a passive mode-locked laser. The solitons can exhibit different phase evolution processes and have compound vibration frequencies simultaneously. The phase evolutions exhibit behavior consistent with single-shot autocorrelation results. Compared with autocorrelation methods, the RCNN can obtain the actual phase difference and analyze soliton molecules comprising more solitons and almost equally spaced soliton pairs. This study provides an effective method for exploring complex soliton molecule dynamics.

Analysis of real-time spectral interference using a deep neural network to reconstruct multi-soliton dynamics in mode-locked lasers

In passively mode-locked fiber lasers (PMLFLs), the dissipative solitons (DSs) can self-organize to form complex structures through delicate interactions. However, it is still elusive to control these soliton structures by external influences. We here find that at a certain critical power, the location between two soliton molecules can be controlled by a slow modulated pump power. After applying the pump power with periodic fluctuation, two soliton molecules oscillate from the state of soliton molecular complex to stable distribution with maximum inter-molecular separation. During this process, the internal structure of each soliton molecule keeps steady. The slow gain depletion and recovery mechanism which plays a dominant role affects the motion of soliton molecules. These results could further expand the molecular analogy of spectroscopy and stimulate the development of optical information storage and processing.

Oscillatory self-organization dynamics between soliton molecules induced by gain fluctuation.

In this article, we design a long short-term memory (LSTM) scheme, combined with dense networks, to realize soliton dynamics prediction in passively mode-locked fiber lasers. Based on the particle characteristic of soliton interaction, we propose to use the separation and relative phase between solitons as characteristic parameters to model and predict the dynamics. The network predicted soliton collision and soliton molecule dynamics accurately. This scheme of precoding physical information with subsequent dynamics prediction not only introduces new prospects for the laser self-optimization algorithm, but also brings new insights for the modeling of nonlinear systems and description of soliton interactions.

Caiyun Li

Papers

Generation of Bell, W , and Greenberger-Horne-Zeilinger states via exceptional points in non-Hermitian quantum spin systems

Finite-temperature quantum criticality in a complex-parameter plane

Analysis of real-time spectral interference using a deep neural network to reconstruct multi-soliton dynamics in mode-locked lasers

Oscillatory self-organization dynamics between soliton molecules induced by gain fluctuation.

Soliton Molecule Dynamics Evolution Prediction Based on LSTM Neural Networks