arXiv subjects

Hui Zhai

Publications and source records attributed to Hui Zhai.

At least 55 records · Page 3Linked to original sources

arXiv2021

Maximum Energy Growth Rate in Dilute Quantum Gases

In this letter we study how fast the energy density of a quantum gas can increase in time, when the inter-atomic interaction characterized by the $s$-wave scattering length $a_\text{s}$ is increased from zero with arbitrary time dependence. We show that, at short time, the energy density can at most increase as $\sqrt{t}$, which can be achieved when the time dependence of $a_\text{s}$ is also proportional to $\sqrt{t}$, and especially, a universal maximum energy growth rate can be reached when $a_\text{s}$ varies as $2\sqrt{\hbar t/(πm)}$. If $a_\text{s}$ varies faster or slower than $\sqrt{t}$, it is respectively proximate to the quench process and the adiabatic process, and both result in a slower energy growth rate. These results are obtained by analyzing the short time dynamics of the short-range behavior of the many-body wave function characterized by the contact, and are also confirmed by numerical solving an example of interacting bosons with time-dependent Bogoliubov theory. These results can also be verified experimentally in ultracold atomic gases.

cond-mat.quant-gas↗

arXiv2021

Page Curve from Non-Markovianity

In this letter, we use the exactly solvable Sachdev-Ye-Kitaev model to address the issue of entropy dynamics when an interacting quantum system is coupled to a non-Markovian environment. We find that at the initial stage, the entropy always increases linearly matching the Markovian result. When the system thermalizes with the environment at a sufficiently long time, if the environment temperature is low and the coupling between system and environment is weak, then the total thermal entropy is low and the entanglement between system and environment is also weak, which yields a small system entropy in the long-time steady state. This manifestation of non-Markovian effects of the environment forces the entropy to decrease in the later stage, which yields the Page curve for the entropy dynamics. We argue that this physical scenario revealed by the exact solution of the Sachdev-Ye-Kitaev model is universally applicable for general chaotic quantum many-body systems and can be verified experimentally in near future.

cond-mat.str-el↗

arXiv2021

Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System

In this letter we point out that the Lindblad spectrum of a quantum many-body system displays a segment structure and exhibits two different energy scales in the strong dissipation regime. One energy scale determines the separation between different segments, being proportional to the dissipation strength, and the other energy scale determines the broadening of each segment, being inversely proportional to the dissipation strength. Ultilizing a relation between the dynamics of the second Rényi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short- and the long-time dynamics of the second Rényi entropy starting from a generic initial state. This gives rise to opposite behaviors, that is, as the dissipation strength increases, the short-time dynamics becomes faster and the long-time dynamics becomes slower. We also interpret the quantum Zeno effect as specific initial states that only occupy the Lindblad spectrum around zero, for which only the broadening energy scale of the Lindblad spectrum matters and gives rise to suppressed dynamics with stronger dissipation. We illustrate our theory with two concrete models that can be experimentally verified.

cond-mat.quant-gas↗

arXiv2021

Expressivity of Quantum Neural Networks

In this work, we address the question whether a sufficiently deep quantum neural network can approximate a target function as accurate as possible. We start with simple but typical physical situations that the target functions are physical observables, and then we extend our discussion to situations that the learning targets are not directly physical observables, but can be expressed as physical observables in an enlarged Hilbert space with multiple replicas, such as the Loshimidt echo and the Renyi entropy. The main finding is that an accurate approximation is possible only when the input wave functions in the dataset do not exhaust the entire Hilbert space that the quantum circuit acts on, and more precisely, the Hilbert space dimension of the former has to be less than half of the Hilbert space dimension of the latter. In some cases, this requirement can be satisfied automatically because of the intrinsic properties of the dataset, for instance, when the input wave function has to be symmetric between different replicas. And if this requirement cannot be satisfied by the dataset, we show that the expressivity capabilities can be restored by adding one ancillary qubit where the wave function is always fixed at input. Our studies point toward establishing a quantum neural network analogy of the universal approximation theorem that lays the foundation for expressivity of classical neural networks.

cond-mat.dis-nn↗

arXiv2020

Scrambling Ability of Quantum Neural Networks Architectures

In this letter we propose a general principle for how to build up a quantum neural network with high learning efficiency. Our stratagem is based on the equivalence between extracting information from input state to readout qubit and scrambling information from the readout qubit to input qubits. We characterize the quantum information scrambling by operator size growth, and by Haar random averaging over operator sizes, we propose an averaged operator size to describe the information scrambling ability for a given quantum neural network architectures, and argue this quantity is positively correlated with the learning efficiency of this architecture. As examples, we compute the averaged operator size for several different architectures, and we also consider two typical learning tasks, which are a regression task of a quantum problem and a classification task on classical images, respectively. In both cases, we find that, for the architecture with a larger averaged operator size, the loss function decreases faster or the prediction accuracy in the testing dataset increases faster as the training epoch increases, which means higher learning efficiency. Our results can be generalized to more complicated quantum versions of machine learning algorithms.

cond-mat.dis-nn↗

arXiv2020

The Bayesian Committee Approach for Computational Physics Problems

In this work, we propose a method for efficient learning of a multi-dimensional function. This method combines the Bayesian neural networks and the query-by-committee method. A committee made of deep Bayesian neural networks not only can provide uncertainty of the prediction but also can provide the discrepancy between committee members. Both the uncertainty and the discrepancy are large in the regions where the target function varies rapidly, and therefore, both quantities can be used to guide sampling data to such regions. In this way, we can learn a function accurately with the number of queried data points much less than uniform sampling. Here we test our method with two examples. One example is to find a rare phase in a phase diagram, which is separated from other phases by a second-order phase transition. In this example, the target function is the susceptibility function, and since the divergence of the susceptibility function locates the phase diagram, the task of searching such a phase perfectly matches the advantage of our method. Another example is to learn the distribution function for Monte Carlo integration of a high-dimensional function. In both examples, we show that our method performs significantly efficiently than uniform sampling. Our method can find broad applications in computational scientific problems.

physics.comp-ph↗

arXiv2020

Stability of Time-Reversal Symmetry Protected Topological Phases

In a closed system, it is well known that the time-reversal symmetry can lead to Kramers degeneracy and protect nontrivial topological states such as quantum spin Hall insulator. In this letter we address the issue whether these effects are stable against coupling to environment, provided that both environment and the coupling to environment also respect the time-reversal symmetry. By employing a non-Hermitian Hamiltonian with the Langevin noise term and ultilizing the non-Hermitian linear response theory, we show that the spectral functions for Kramers degenerate states can be split by dissipation, and the backscattering between counter-propagating edge states can be induced by dissipation. The latter leads to the absence of accurate quantization of conductance in the case of quantum spin Hall effect. As an example, we demonstrate this concretely with the Kane-Mele model. Our study could also be extended to interacting topological phases protected by the time-reversal symmetry.

cond-mat.mes-hall↗

arXiv2020

Disconnecting a Traversable Wormhole: Universal Quench Dynamics in Random Spin Models

Understanding strongly interacting quantum matter and quantum gravity are both important open issues in theoretical physics, and the holographic duality between quantum field theory and gravity theory nicely brings these two topics together. Nevertheless, direct connections between gravity physics and experimental observations in quantum matter are still rare. Here we utilize the gravity physics picture to understand quench dynamics experimentally observed in a class of random spin models realized in several different quantum systems, where the dynamics of magnetization are measured after the external polarization field is suddenly turned off. Two universal features of the magnetization dynamics, namely, a slow decay described by a stretched exponential function and an oscillatory behavior, are respectively found in different parameter regimes across different systems. This work addresses the issues of generic conditions under which these two universal features can occur, and we find that a natural answer to this question emerges in the gravity picture. By the holographic duality bridged by a model proposed by Maldacena and Qi, the quench dynamics after suddenly turning off the external polarization field is mapped to disconnecting an eternal traversable wormhole. Our studies show that insight from gravity physics can help unifying different experiments in quantum systems.

cond-mat.quant-gas↗

arXiv2020

Density Dependent Spin-Orbit Coupling in Degenerate Quantum Gases

In this letter we propose a method to realize a kind of spin-orbit coupling in ultracold Bose and Fermi gases whose format and strength depend on density of atoms. Our method combines two-photon Raman transition and periodical modulation of spin-dependent interaction, which gives rise to the direct Raman process and the interaction assisted Raman process, and the latter depends on density of atoms. These two processes have opposite effects in term of spin-momentum locking and compete with each other. As the interaction modulation increases, the system undergoes a crossover from the direct Raman process dominated regime to the interaction assisted Raman process dominated regime. For this crossover, we show that for bosons, both the condensate momentum and the chirality of condensate wave function change sign, and for fermions, the Fermi surface distortion is inverted. We highlight that there exists an emergent spatial reflection symmetry in the crossover regime, which can manifest itself universally in both Bose and Fermi gases. Our method paves a way to novel phenomena in a non-abelian gauge field with intrinsic dynamics.

cond-mat.quant-gas↗

arXiv2020

Machine Learning Identification of Impurities in the STM Images

In this work we train a neural network to identify impurities in the experimental images obtained by the scanning tunneling microscope measurements. The neural network is first trained with large number of simulated data and then the trained neural network is applied to identify a set of experimental images taken at different voltages. We use the convolutional neural network to extract features from the images and also implement the attention mechanism to capture the correlations between images taken at different voltages. We note that the simulated data can capture the universal Friedel oscillation but cannot properly describe the non-universal physics short-range physics nearby an impurity, as well as noises in the experimental data. And we emphasize that the key of this approach is to properly deal these differences between simulated data and experimental data. Here we show that even by including uncorrelated white noises in the simulated data, the performance of neural network on experimental data can be significantly improved. To prevent the neural network from learning unphysical short-range physics, we also develop another method to evaluate the confidence of the neural network prediction on experimental data and to add this confidence measure into the loss function. We show that adding such an extra loss function can also improve the performance on experimental data. Our research can inspire future similar applications of machine learning on experimental data analysis.

cond-mat.str-el↗

arXiv2020

Dynamical Kosterlitz-Thouless Theory for Two-Dimensional Ultracold Atomic Gases

In this letter we develop a theory for the first and second sound in a two-dimensional atomic superfluid across the superfluid transition based on the dynamic Koterlitz-Thouless theory. We employ a set of modified two-fluid hydrodynamic equations which incorporate the dynamics of the quantised vortices, rather than the conventional ones for a three-dimensional superfluid. As far as the sound dispersion equation is concerned, the modification is essentially equivalent to replacing the static superfluid density with a frequency dependent one, renormalised by the frequency dependent "dielectric constant" of the vortices. This theory has two direct consequences. First, because the renormalised superfluid density at finite frequencies does not display discontinuity across the superfluid transition, in contrast to the static superfluid density, the sound velocities vary smoothly across the transition. Second, the theory includes dissipation due to free vortices, and thus naturally describes the sound-to-diffusion crossover for the second sound in the normal phase. With only one fitting parameter, our theory gives a perfect agreement with the experimental measurements of sound velocities across the transition, as well as the quality factor in the vicinity of the transition. The predictions from this theory can be further verified by future experiments.

cond-mat.quant-gas↗

arXiv2020

High Temperature Virial Expansion to Universal Quench Dynamics

High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from non-interacting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for low-momentum part with $k k^*$, where $k^*$ is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of $k^*λ$ that agrees perfectly with the experiment, with $λ$ being the thermal de Broglie wave length. We also find a jump of the half-way relaxation time across $k^*λ$ and the non-monotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the long-time steady state thermalizes or not, and we find that this state does thermalize except for the very high momentum tail with $kλ\gg 1$. Our framework can also be applied to quench dynamics in other systems.

cond-mat.quant-gas↗

arXiv2020

Information Scrambling in Quantum Neural Networks

The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wavefunction into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information, a quantity recently developed to characterize information scrambling, to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks.

cond-mat.dis-nn↗

arXiv2020

Many-Body Localization from Dynamical Gauge Fields

A recent experiment [Nature Physics 10, 1 (2019)] has realized a dynamical gauge system with $\mathbb{Z}_2$ gauge symmetry in a double-well potential. In this work we propose a method to generalize this model from a single double well to a one-dimensional chain. We show that although there is no disordered potential in the original model, the phenomenon of many-body localization can occur. The key ingredient is that different symmetry sectors with different local gauge charges play the role of different disorder configurations, which becomes clear after exactly mapping our model to a transverse Ising model in a random longitudinal field. We show that both the ergodic regime and the many-body localized regime exist in this model from four different metrics, which include level statistics, volume law versus area law of entanglement entropy of eigenstates, quench dynamics of entanglement entropy and physical observables.

cond-mat.quant-gas↗

arXiv2020

Active Learning Approach to Optimization of Experimental Control

In this work we present a general machine learning based scheme to optimize experimental control. The method utilizes the neural network to learn the relation between the control parameters and the control goal, with which the optimal control parameters can be obtained. The main challenge of this approach is that the labeled data obtained from experiments are not abundant. The central idea of our scheme is to use the active learning to overcome this difficulty. As a demonstration example, we apply our method to control evaporative cooling experiments in cold atoms. We have first tested our method with simulated data and then applied our method to real experiments. We demonstrate that our method can successfully reach the best performance within hundreds of experimental runs. Our method does not require knowledge of the experimental system as a prior and is universal for experimental control in different systems.

cond-mat.quant-gas↗

arXiv2020

Active Learning Algorithm for Computational Physics

In large-scale computation of physics problems, one often encounters the problem of determining a multi-dimensional function, which can be time-consuming when computing each point in this multi-dimensional space is already time-demanding. In the work, we propose that the active learning algorithm can speed up such calculations. The basic idea is to fit a multi-dimensional function by neural networks, and the key point is to make the query of labeled data economically by using a stratagem called "query by committee". We present the general protocol of this fitting scheme, as well as the procedure of how to further compute physical observables with the fitted functions. We show that this method can work well with two examples, which are quantum three-body problem in atomic physics and the anomalous Hall conductivity in condensed matter physics, respectively. In these examples, we show that one reaches an accuracy of few percent error for computing physical observables with less than $10\%$ of total data points compared with uniform sampling. With these two examples, we also visualize that by using the active learning algorithm, the required data are added mostly in the regime where the function varies most rapidly, which explains the mechanism for the efficiency of the algorithm. We expect broad applications of our method on various kind of computational physics problems.

cond-mat.quant-gas↗

arXiv2019

Non-Hermitian Linear Response Theory

Linear response theory lies at the heart of quantum many-body physics because it builds up connections between the dynamical response to an external probe and correlation functions at equilibrium. Here we consider the dynamical response of a Hermitian system to a non-Hermitian probe, and we develop a non-Hermitian linear response theory that can also relate this dynamical response to equilibrium properties. As an application of our theory, we consider the real-time dynamics of momentum distribution induced by one-body and two-body dissipations. We find that, for many cases, the dynamics of momentum occupation and the width of momentum distribution obey the same universal function, governed by the single-particle spectral function. We also find that, for critical state with no well-defined quasi-particles, the dynamics are slower than normal state and our theory provides a model independent way to extract the critical exponent. We apply our results to analyze recent experiment on the Bose-Hubbard model and find surprising good agreement between theory and experiment. We also propose to further verify our theory by carrying out a similar experiment on a one-dimensional Luttinger liquid.

cond-mat.quant-gas↗

arXiv2019

Universal Dynamics of a Degenerate Bose Gas Quenched to Unitarity

Motivated by an unexpected experimental observation from the Cambridge group, [Eigen {\it et al.,} Nature {\bf563}, 221 (2018)], we study the evolution of the momentum distribution of a degenerate Bose gas quenched from the weakly interacting to the unitarity regime. For the two-body problem, we establish a relation that connects the momentum distribution at a long time to a sub-leading term in the initial wave function. For the many-body problem, we employ the time-dependent Bogoliubov variational wave function and find that, in certain momentum regimes, the momentum distribution at long times displays the same exponential behavior found by the experiment. Moreover, we find that this behavior is universal and independent of the short-range details of the interaction potential. Consistent with the relation found in the two-body problem, we also numerically show that this exponential form is hidden in the same sub-leading term of the Bogoliubov wave function in the initial stages. Our results establish a consistent picture to understand the universal dynamics observed in the Cambridge experiment.

cond-mat.quant-gas↗