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The recent breakthrough of realizing the Bose-Einstein condensate of polar molecules and degenerate Fermi molecules in three dimensions relies crucially on the microwave shielding technique, which strongly suppresses the collision loss between molecules. In this letter, we show that the cooperation of microwave shielding and dipolar interaction naturally leads to the emergence of a synthetic gauge field. Unlike that studied in cold atoms before, this gauge field couples to the relative motion of every two molecules instead of single-particle motion, therefore being a mutual gauge field. In this case, every molecule carrying a synthetic charge sees the other molecule as carrying the source of the magnetic field, and the spatial distribution of the magnetic field is reminiscent of a solenoid attached to the molecule. In other words, in addition to microwave-shielded interaction, another part of the interaction between two molecules behaves as a charge interacting with a solenoid, which was missed in the previous discussion. We argue that the physical manifestation of this gauge field is breaking time-reversal symmetry in the collective spatial motion of molecules. Finally, we discuss the challenges in quantitatively studying such a quantum many-body system., Comment: 6 pages, 4 figures

We report the first experimental observation of dissipation-driven coherent quantum many-body oscillation, and this oscillation is manifested as the coherent exchange of atoms between the thermal and the condensate components in a three-dimensional partially condensed Bose gas. Firstly, we observe that the dissipation leads to two different atom loss rates between the thermal and the condensate components, such that the thermal fraction increases as dissipation time increases. Therefore, this dissipation process serves as a tool to uniformly ramp up the system's temperature without introducing extra density excitation. Subsequently, a coherent pair exchange of atoms between the thermal and the condensate components occurs, resulting in coherent oscillation of atom numbers in both components. This oscillation, permanently embedded in the atom loss process, is revealed clearly when we inset a duration of dissipation-free evolution into the entire dynamics, manifested as an oscillation of total atom number at the end. Finally, we also present a theoretical calculation to support this physical mechanism, which simultaneously includes dissipation, interaction, finite temperature, and harmonic trap effects. Our work introduces a highly controllable dissipation as a new tool to control quantum many-body dynamics., Comment: 11 pages, 5 figures, 1 table

In the zoo of emergent symmetries in quantum many-body physics, the previously unrealized emergent spacetime supersymmetry (SUSY) is particularly intriguing. Although it was known that spacetime SUSY could emerge at the (1+1)d tricritical Ising transition, an experimental realization is still absent. In this letter, we propose to realize the tricritical Ising transition with Rydberg atom arrays, taking advantage of the reconfigurability of these systems. In such systems, the spacetime SUSY manifests itself in the respective correlation functions of a bosonic mode and its fermionic partner. However, the correlation function of the fermionic mode inevitably involves a string operator, making direct measurement challenging in the conventional setting. Here, we utilize the analog--digital hybrid nature of the Rydberg atom arrays, which can simulate a physical Hamiltonian and perform a digital quantum circuit on the same platform, to measure the correlation function of the fermionic mode. This hybridized protocol provides an experimentally feasible way to reveal the hidden structure of the spacetime SUSY that emerges at the tricritical Ising transition., Comment: 7 pages, 3 figures

Universality often emerges in low-energy equilibrium physics of quantum many-body systems, despite their microscopic complexity and variety. Recently, there has been a growing interest in studying far-from-equilibrium dynamics of quantum many-body systems. Such dynamics usually involves highly excited states beyond the traditional low-energy theory description. Whether universal behaviors can also emerge in such non-equilibrium dynamics is a central issue at the frontier of quantum dynamics. Here we report the experimental observation of universal dynamics by monitoring the spin depolarization process in a solid-state NMR system described by an ensemble of randomly interacting spins. The spin depolarization can be related to temporal spin-spin correlation functions at high temperatures. We discover a remarkable phenomenon that these correlation functions obey a universal functional form. This experimental fact helps us identify the dominant interacting processes in the spin depolarization dynamics that lead to this universality. Our observation demonstrates the existence of universality even in non-equilibrium dynamics at high temperatures, thereby complementing the well-established universality in low-energy physics., Comment: 10 pages, 4 figures; Supplementary Information 26 pages, 11 figures, 2 tables

The work intends to extend the moir\'e physics to three dimensions. Three-dimensional moir\'e patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a structure currently unachievable in solid-state materials. We give the commensurate conditions under which the three-dimensional moir\'e pattern features a periodic structure, termed a three-dimensional moir\'e crystal. We emphasize a key distinction of three-dimensional moir\'e physics: in three dimensions, the twist operation generically does not commute with the rotational symmetry of the original lattice, unlike in two dimensions, where these two always commute. Consequently, the moir\'e crystal can exhibit a crystalline structure that differs from the original underlying lattice. We demonstrate that twisting a simple cubic lattice can generate various crystal structures. This capability of altering crystal structures by twisting offers a broad range of tunability for three-dimensional band structures.

Topological band theory has been studied for free fermions for decades, and one of the most profound physical results is the bulk-boundary correspondence. Recently a trend in topological physics is extending topological classification to mixed state. Here, we focus on Gaussian mixed states where the modular Hamiltonians of the density matrix are quadratic free fermion models and can be classified by topological invariants. The bulk-boundary correspondence is then manifested as stable gapless modes of the modular Hamiltonian and degenerate spectrum of the density matrix. In this letter, we show that these gapless modes can be detected by the full counting statistics, mathematically described by a function introduced as F({\theta}). We show that a divergent derivative at {\theta} = {\pi} probes the gapless modes in the modular Hamiltonian. We can introduce a topological indicator whose quantization to unity senses topologically nontrivial mixed states. We present the physical intuition of these results and also demonstrate these results with concrete models in both one- and two-dimensions. Our results pave the way for revealing the physical significance of topology in mixed states., Comment: 7pages, 3figures

In closed systems, the celebrated Lieb-Schultz-Mattis (LSM) theorem states that a one-dimensional locally interacting half-integer spin chain with translation and spin rotation symmetry cannot have a non-degenerate gapped ground state. However, the applicability of this theorem is diminished when the system interacts with a bath and loses its energy conservation. In this letter, we propose that the LSM theorem can be revived in the entanglement Hamiltonian when the coupling to bath renders the system short-range correlated. Specifically, we argue that the entanglement spectrum cannot have a non-degenerate minimum, isolated by a gap from other states. We further support the results with numerical examples where a spin-$1/2$ system is coupled to another spin-$3/2$ chain serving as the bath. Compared with the original LSM theorem which primarily addresses UV--IR correspondence, our findings unveil that the UV data and topological constraints also have a pivotal role in shaping the entanglement in open quantum many-body systems., Comment: 6 pages, 4 figures

Topological charge pumping occurs in the adiabatic limit, and the non-adiabatic effect due to finite ramping velocity reduces the pumping efficiency and leads to deviation from quantized charge pumping. In this work, we discuss the relation between this deviation from quantized charge pumping and the entanglement generation after a pumping circle. In the simplest setting, we show that purity $\mathcal{P}$ of the half system reduced density matrix equals to $\mathcal{R}$ defined as $(1-\kappa)^2+\kappa^2$, where $\kappa$ denotes the pumping efficiency. In generic situations, we argue $\mathcal{P}<\mathcal{R}$ and the pumping efficiency can provide an upper bound for purity and, therefore, a lower bound for generated entanglement. To support this conjecture, we propose a solvable pumping scheme in the Rice--Mele--Hubbard model, which can be represented as brick-wall type quantum circuit model. With this pumping scheme, numerical calculation of charge pumping only needs to include at most six sites, and therefore, the interaction and the finite temperature effects can be both included reliably in the exact diagonalization calculation. The numerical results using the solvable pumping circle identify two regimes where the pumping efficiency is sensitive to ramping velocity and support the conjecture $\mathcal{P}<\mathcal{R}$ when both interaction and finite temperature effects are present., Comment: 5 pages, 3 figures

In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the autocorrelation function. In particular, we focus on a particular kind of operator complexity called the Krylov complexity. We find that a set of Lanczos coefficients $\{b_n\}$ computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations, which are otherwise impossible. When the time axis is scaled by $b_1$, different autocorrelation functions obey a universal function form at short time. We further propose a characteristic parameter deduced from $\{b_n\}$ that can largely determine the behavior of autocorrelations at the intermediate time. This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time. We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations. We emphasize that these universal behaviors are held across different operators and different physical systems., Comment: 5 pages, 3 figures

When the Fermi Hubbard model was first introduced sixty years ago, one of the original motivations was to understand correlation effects in itinerant ferromagnetism. In the past two decades, ultracold Fermi gas in an optical lattice has been used to study the Fermi Hubbard model. However, the metallic ferromagnetic correlation was observed only in a recent experiment using frustrated lattices, and its underlying mechanism is not clear yet. In this letter, we point out that, under the particle--hole transformation, the single-particle ground state can exhibit double degeneracy in such a frustrated lattice. Therefore, the low-energy state exhibits valley degeneracy, reminiscent of multi-orbit physics in ferromagnetic transition metals. The local repulsive interaction leads to the valley Hund's rule, responsible for the observed ferromagnetism. We generalize this mechanism to distorted honeycomb lattices and square lattices with flux. This mechanism was first discussed by M\"uller-Hartmann in a simpler one-dimension model. However, this mechanism has not been widely discussed and has not been related to experimental observations before. Hence, our study not only explains the experimental findings but also enriches our understanding of itinerant ferromagnetism., Comment: 6 pages, 5 figures

The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution. We solve this problem for the fermionic Gaussian state and for the modular Hamiltonian being a quadratic operator of a set of fermionic operators. When these conditions are satisfied, along with a nontrivial topological classification of the symmetry class of the modular Hamiltonian, a topological transition can occur as time evolves. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class with U(1) symmetry and the DIII class without U(1) symmetry. By a finite size scaling, we show that this density matrix topology transition occurs at a finite time. We also present the physical signature of this transition., Comment: 8 pages, 2 figure

Gauge theory and thermalization are both foundations of physics and nowadays are both topics of essential importance for modern quantum science and technology. Simulating lattice gauge theories (LGTs) realized recently with ultracold atoms provides a unique opportunity for carrying out a correlated study of gauge theory and thermalization in the same setting. Theoretical studies have shown that an Ising quantum phase transition exists in this implemented LGT, and quantum thermalization can also signal this phase transition. Nevertheless, it remains an experimental challenge to accurately determine the critical point and controllably explore the thermalization dynamics in the quantum critical regime due to the lack of techniques for locally manipulating and detecting matter and gauge fields. Here, we report an experimental investigation of the quantum criticality in the LGT from both equilibrium and non-equilibrium thermalization perspectives by equipping the single-site addressing and atom-number-resolved detection into our LGT simulator. We accurately determine the quantum critical point agreed with the predicted value. We prepare a $|Z_{2}\rangle$ state deterministically and study its thermalization dynamics across the critical point, leading to the observation that this $|Z_{2}\rangle$ state thermalizes only in the critical regime. This result manifests the interplay between quantum many-body scars, quantum criticality, and symmetry breaking., Comment: 6+4 pages, 4+7 figures

Krylov complexity is a novel measure of operator complexity that exhibits universal behavior and bounds a large class of other measures. In this letter, we generalize Krylov complexity from a closed system to an open system coupled to a Markovian bath, where Lindbladian evolution replaces Hamiltonian evolution. We show that Krylov complexity in open systems can be mapped to a non-hermitian tight-binding model in a half-infinite chain. We discuss the properties of the non-hermitian terms and show that the strengths of the non-hermitian terms increase linearly with the increase of the Krylov basis index $n$. Such a non-hermitian tight-binding model can exhibit localized edge modes that determine the long-time behavior of Krylov complexity. Hence, the growth of Krylov complexity is suppressed by dissipation, and at long-time, Krylov complexity saturates at a finite value much smaller than that of a closed system with the same Hamitonian. Our conclusions are supported by numerical results on several models, such as the Sachdev-Ye-Kitaev model and the interacting fermion model. Our work provides insights for discussing complexity, chaos, and holography for open quantum systems., Comment: 8 pages, 5 figures, a mistake in the operator Lindblad equation is corrected

Majorana zero modes form as intrinsic defects in an odd-orbital one-dimensional superconductor thus motivating the search for such materials in the pursuit of Majorana physics. Here, we present combined experimental results and first principles calculations which suggest that quasi-one-dimensional K$_2$Cr$_3$As$_3$ may be such a superconductor. Using inelastic neutron scattering we probe the dynamic spin-susceptibilities of K$_2$Cr$_3$As$_3$ and K$_2$Mo$_3$As$_3$ and show the presence of antiferromagnetic spin-fluctuations in both compounds. Below the superconducting transition, these fluctuations gap in K$_2$Mo$_3$As$_3$ but not in K$_2$Cr$_3$As$_3$. Using first principles calculations, we show that these fluctuations likely arise from nesting on one dimensional features of the Fermi surface. Considering these results we propose that while K$_2$Mo$_3$As$_3$ is a conventional superconductor, K$_2$Cr$_3$As$_3$ is likely a spin-triplet, and consequently, topological superconductor., Comment: 8 pages, 4 figures

In this letter, we propose how to measure the quantized nonlinear transport using two-dimensional ultracold atomic Fermi gases in a harmonic trap. This scheme requires successively applying two optical pulses in the left and lower half-planes and then measuring the number of extra atoms in the first quadrant. In ideal situations, this nonlinear density response to two successive pulses is quantized, and the quantization value probes the Euler characteristic of the local Fermi sea at the trap center. We investigate the practical effects in experiments, including finite pulse duration, finite edge width of pulses, and finite temperature, which can lead to deviation from quantization. We propose a method to reduce the deviation by averaging measurements performed at the first and third quadrants, inspired by symmetry considerations. With this method, the quantized nonlinear response can be observed reasonably well with experimental conditions readily achieved with ultracold atoms., Comment: 7 pages, 3 figures, expanded introduction, added an appendix, added new references, accepted by Quantum

The one-dimensional lattice Schwinger model has recently been realized by using bosons in optical lattices. This model contains both confinement and deconfinement phases, whose phase diagram is controlled by the mass of the matter field and the topological angle. Since varying the mass of matter field is straightforward experimentally, we propose how to tune the topological angle, allowing accessing the entire phase diagram. We propose that direct experimental evidence of confinement and deconfinement can be obtained by measuring whether a physical charge is localized around a fixed gauge charge to screen it. We also discuss the PXP model realized in the Rydberg atoms array, which is equivalent to the lattice Schwinger model when all local gauge charges are fixed as zero. Although the gauge charges are fixed, we can alternatively probe the confinement and the deconfinement in the PXP model by studying the relative motion of a pair of a physical charge and an anti-charge. Our scheme can be directly implemented in these two relevant experimental platforms of ultracold atom quantum simulators., Comment: 8 pages, 6 figures

The Rydberg blockade induces strongly correlated many-body effects in Rydberg atom arrays, including rich ground-state phases and many-body scar states in the excitation spectrum. In this letter, we propose a composite spin representation that can provide a unified description for major features in this system. The composite spin combines Rydberg excitation and the auxiliary fermions, which are introduced to implement the Rydberg blockade constraint automatically. First, we focus on the PXP model describing one-dimensional arrays with the Rydberg blocking radius being a lattice spacing. Using composite spins, the ground state is simply a ferromagnetic product state of composite spins, and the magnon excitations of these composite spins can accurately describe the many-body scar states and signal the quantum phase transition driven by detuning. Then, we show that Rydberg atom arrays with different blocking radii can share a universal description of the composite spin representation, and the difference between different blockade radii can be absorbed in the formation of composite spins., Comment: 6 pages, 5 figures

Recently the Rydberg blockade effect has been utilized to realize quantum spin liquid on the kagome lattice. Evidence of quantum spin liquid has been obtained experimentally by directly measuring non-local string order. In this letter, we report a BCS-type variational wave function study of the spin liquid state in this model. This wave function is motivated by mapping the Rydberg blockade model to a lattice gauge theory, where the local gauge conservations replace the role of constraints from the Rydberg blockade. We determine the variational parameter from the experimental measurement of the Rydberg atom population. Then we compare the predictions of this deterministic wave function with the experimental measurements of non-local string order. Combining the measurements on both open and closed strings, we extract the fluctuations only associated with the closed-loop as an indicator of the topological order. The prediction from our wave function agrees reasonably well with the experimental data without any fitting parameter. Our variational wave function provides a simple and intuitive picture of the quantum spin liquid in this system that can be generalized to various generalizations of the current model., Comment: 7 pages, 4 figures

Analytic continuation maps imaginary-time Green's functions obtained by various theoretical/numerical methods to real-time response functions that can be directly compared with experiments. Analytic continuation is an important bridge between many-body theories and experiments but is also a challenging problem because such mappings are ill-conditioned. In this work, we develop a neural network-based method for this problem. The training data is generated either using synthetic Gaussian-type spectral functions or from exactly solvable models where the analytic continuation can be obtained analytically. Then, we applied the trained neural network to the testing data, either with synthetic noise or intrinsic noise in Monte Carlo simulations. We conclude that the best performance is always achieved when a proper amount of noise is added to the training data. Moreover, our method can successfully capture multi-peak structure in the resulting response function for the cases with the best performance. The method can be combined with Monte Carlo simulations to compare with experiments on real-time dynamics.

Ramping a physical parameter is one of the most common experimental protocols in studying a quantum system, and ramping dynamics has been widely used in preparing a quantum state and probing physical properties. Here, we present a novel method of probing quantum many-body correlation by ramping dynamics. We ramp a Hamiltonian parameter to the same target value from different initial values and with different velocities, and we show that the first-order correction on the finite ramping velocity is universal and path-independent, revealing a novel quantum many-body correlation function of the equilibrium phases at the target values. We term this method as the non-adiabatic linear response since this is the leading order correction beyond the adiabatic limit. We demonstrate this method experimentally by studying the Bose-Hubbard model with ultracold atoms in three-dimensional optical lattices. Unlike the conventional linear response that reveals whether the quasi-particle dispersion of a quantum phase is gapped or gapless, this probe is more sensitive to whether the quasi-particle lifetime is long enough such that the quantum phase possesses a well-defined quasi-particle description. In the Bose-Hubbard model, this non-adiabatic linear response is significant in the quantum critical regime where well-defined quasi-particles are absent. And in contrast, this response is vanishingly small in both superfluid and Mott insulators which possess well-defined quasi-particles. Because our proposal uses the most common experimental protocol, we envision that our method can find broad applications in probing various quantum systems., Comment: 7 pages for main text. Science Bulletin (2022)

In this letter, we study the PXP Hamiltonian with an external magnetic field that exhibits both quantum scar states and quantum criticality. It is known that this model hosts a series of quantum many-body scar states violating quantum thermalization at zero magnetic field, and it also exhibits an Ising quantum phase transition driven by finite magnetic field. Although the former involves the properties of generic excited states and the latter concerns the low-energy physics, we discover two surprising connections between them, inspired by the observation that both states possess log-volume law entanglement entropies. First, we show that the quantum many-body scar states can be tracked to a set of quantum critical states, whose nature can be understood as pair-wisely occupied Fermi sea states. Second, we show that the partial violation of quantum thermalization diminishes in the quantum critical regime. We envision that these connections can be extended to general situations and readily verified in existing cold atom experimental platforms., Comment: 6 pages, 5 figures

Quantum chaos in hermitian systems concerns the sensitivity of long-time dynamical evolution to initial conditions. The skin effect discovered recently in non-hermitian systems reveals the sensitivity to the spatial boundary condition even deeply in bulk. In this letter, we show that these two seemingly different phenomena can be unified through space-time duality. The intuition is that the space-time duality maps unitary dynamics to non-unitary dynamics and exchanges the temporal direction and spatial direction. Therefore, the space-time duality can establish the connection between the sensitivity to the initial condition in the temporal direction and the sensitivity to the boundary condition in the spatial direction. Here we demonstrate this connection by studying the space-time duality of the out-of-time-ordered commutator in a concrete chaotic hermitian model. We show that the out-of-time-ordered commutator is mapped to a special two-point correlator in a non-hermitian system in the dual picture. For comparison, we show that this sensitivity disappears when the non-hermiticity is removed in the dual picture., Comment: 5 pages, 3 figures; supplmentary material 8 pages, 2 figures

The Floquet Hamiltonian has often been used to describe a time-periodic system. Nevertheless, because the Floquet Hamiltonian depends on a micro-motion parameter, the Floquet Hamiltonian with a fixed micro-motion parameter cannot faithfully represent a driven system, which manifests as the anomalous edge states. Here we show that an accurate description of a Floquet system requires a set of Hamiltonian exhausting all values of the micro-motion parameter, and this micro-motion parameter can be viewed as an extra synthetic dimension of the system. Therefore, we show that a $d$-dimensional Floquet system can be described by a $d+1$-dimensional static Hamiltonian, and the advantage of this representation is that the periodic boundary condition is automatically imposed along the extra-dimension, which enables a straightforward definition of topological invariants. The topological invariant in the $d+1$-dimensional system can ensure a $d-1$-dimensional edge state of the $d$-dimensional Floquet system. Here we show two examples where the topological invariant is a three-dimensional Hopf invariant. We highlight that our scheme of classifying Floquet topology on the micro-motion space is different from the previous classification of Floquet topology on the time space., Comment: 6 pages, 3 figures

Because of the unique physical properties and potential applications, the exploration of quantum materials with diverse symmetry-protected topological states has attracted considerable interest in the condensed-matter community in recent years. Most of the topologically nontirvial materials identified thus far have two-dimensional or three-dimensional structural characteristics, while the quasi-one-dimensional (quasi-1D) analogs are rare. Here we report on anisotropic magnetoresistance, Hall effect, and quantum de Haas$-$van Alphen (dHvA) oscillations in TaPtTe$_5$ single crystals, which possess a layered crystal structure with quasi-1D PtTe$_2$ chains. TaPtTe$_5$ manifests an anisotropic magnetoresistance and a nonlinear Hall effect at low temperatures. The analysis of the dHvA oscillations reveals two major oscillation frequencies (63.5 T and 95.2 T). The corresponding light effective masses and the nonzero Berry phases suggest the nontrivial band topology in TaPtTe$_5$, which is further corroborated by the first-principles calculations. Our results suggest that TaPtTe$_5$, in analogy with its sister compounds TaPdTe$_5$ and TaNiTe$_5$, is another quasi-1D material hosting topological Dirac fermions., Comment: There are some errors in the current vertion. After proper modifications, updated manuscript will be resubmitted

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 $2\sqrt{\hbar t/(\pi m)}$. 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., Comment: 5 pages main text plus 5 pages supplementary

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 R\'enyi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short- and the long-time dynamics of the second R\'enyi 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., Comment: 5 pages, 4 figures

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., Comment: 5 pages, 3 figures

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.

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.

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., Comment: 5 pages, 5 figures

Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between these two limits; that is, there exist situations that the solution to a class of interacting hydrodynamic equations with certain initial conditions can be exactly constructed from the dynamics of noninteracting ideal gases. We analytically provide three such examples. The first two examples focus on scale-invariant systems, which generalize fermionization to the hydrodynamics of strongly interacting systems, and determine specific initial conditions for perfect density oscillations in a harmonic trap. The third example recovers the dark soliton solution in a one-dimensional Bose condensate. The results can explain a recent puzzling experimental observation in ultracold atomic gases by the Paris group and make further predictions for future experiments. We envision that extensive examples of such an ideal-gas approach to hydrodynamics can be found by systematical numerical search, which can find broad applications in different problems in various subfields of physics., Comment: 10 pages, 4 figures

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., Comment: 5+7 pages, 1+2 figures

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., Comment: 9 pages, 4 figures + supplementary

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., Comment: 4 pages

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., Comment: 5 page, 5 figures

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., Comment: 11 pages, 4 figures

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 $kk^*$, where $k^*$ is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of $k^*\lambda$ that agrees perfectly with the experiment, with $\lambda$ being the thermal de Broglie wave length. We also find a jump of the half-way relaxation time across $k^*\lambda$ 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 $k\lambda\gg 1$. Our framework can also be applied to quench dynamics in other systems., Comment: 6 pages, 4 figures

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., Comment: 7 pages, 6 figures

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.

Hayden and Preskill proposed a thought experiment that Bob can recover the information Alice throws into a black hole if he has a quantum computer entangled with the black hole, and Yoshida and Kitaev recently proposed a concrete decoding scheme. The parallel question is that after a small system is thermalized with a large system, how one can decode the initial state information with the help of two entangled many-body systems. Here we propose to realize this protocol in a physical system of two Dicke models, with two cavity fields prepared in a thermofield double state. We show that the Yoshida-Kitaev protocol allows us to read out the initial spin information after it is scrambled into the cavity. We show that the readout efficiency reaches a maximum when the model parameter is tuned to the regime where the system is the most chaotic, characterized by the shortest scrambling time in the out-of-time-ordered correlation function. Our proposal opens up the possibility of discussing this profound thought experiment in a realistic setting., Comment: 5 pages, 4 figures

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., Comment: 6+3 pages, 3 figures; v2: supplementary material added

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., Comment: 6 pages, 4 figures + 9 pages of supplemental material