Many-body Quantum Research Articles

Quantum force sensing by digital twinning of atomic Bose-Einstein condensates

High sensitivity detection plays a vital role in science discoveries and technological applications. While intriguing methods utilizing collective many-body correlations and quantum entanglements have been developed in physics to enhance sensitivity, their practical implementation remains challenging due to rigorous technological requirements. Here, we propose an entirely data-driven approach that harnesses the capabilities of machine learning, to significantly augment weak-signal detection sensitivity. In an atomic force sensor, our method combines a digital replica of force-free data with anomaly detection technique, devoid of any prior knowledge about the physical system or assumptions regarding the sensing process. Our findings demonstrate a significant advancement in sensitivity, achieving an order of magnitude improvement over conventional protocols in detecting a weak force of approximately 10−25N. The resulting sensitivity reaches 1.7(4)×10−25N/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.7(4)\ imes 1{0}^{-25}\\,{{{{{{{\\rm{N}}}}}}}}/\\sqrt{{{{{{{{\\rm{Hz}}}}}}}}}$$\\end{document}. Our machine learning-based signal processing approach does not rely on system-specific details or processed signals, rendering it highly applicable to sensing technologies across various domains.

Fewer Measurements from Shadow Tomography with N-Representability Conditions.

Classical shadow tomography provides a randomized scheme for approximating the quantum state and its properties at reduced computational cost with applications in quantum computing. In this Letter we present an algorithm for realizing fewer measurements in the shadow tomography of many-body systems. Accelerated tomography of the two-body reduced density matrix (2-RDM) is achieved by combining classical shadows with necessary constraints for the 2-RDM to represent an N-body system, known as N-representability conditions. We compute the ground-state energies and 2-RDMs of hydrogen chains and the N_{2} dissociation curve. The results demonstrate a significant reduction in the number of measurements with important applications to quantum many-body simulations on near-term quantum devices.

Statistics of Local Level Spacings in Single- and Many-Body Quantum Chaos.

We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their ratios which uniquely identify the global symmetries of a quantum system and its internal-chaotic or regular-dynamics. These findings, which offer a new framework to monitor single- and many-body quantum systems, are corroborated by numerical experiments performed for zeros of the Riemann zeta function, spectra of irrational rectangular billiards, and many-body spectra of the Sachdev-Ye-Kitaev Hamiltonians.

From many-body quantum dynamics to the Hartree–Fock and Vlasov equations with singular potentials

In a combined mean-field and semiclassical regime, we consider the time evolution of N fermions interacting through singular pair interaction potentials of the form \pm |x-y|^{-a} , which includes the Coulomb and gravitational interactions. We prove that the many-body dynamics of mixed states are well approximated by solutions of the Hartree–Fock and Vlasov equations in terms of Schatten norms. The errors in these approximations are expressed in terms of the expected number of particles, N , and the Planck constant, h . For cases where a\in(0,1/2) , we obtain local-in-time results when N^{-1/2}\ll h \leq N^{-1/3} . Notably, this leads to the derivation of the Vlasov equation with singular potentials. For cases where a\in[1/2,1] , our results hold only within a small time scale or require an N -dependent cut-off. A fundamental ingredient in our analysis is the propagation of regularity for solutions to the Hartree–Fock equation uniformly in the Planck constant, which holds for a\in(0,1] .

Unsupervised learning of quantum many-body scars using intrinsic dimension

Quantum many-body scarred systems contain both thermal and non-thermal scar eigenstates in their spectra. When these systems are quenched from special initial states which share high overlap with scar eigenstates, the system undergoes dynamics with atypically slow relaxation and periodic revival. This scarring phenomenon poses a potential avenue for circumventing decoherence in various quantum engineering applications. Given access to an unknown scar system, current approaches for identification of special states leading to non-thermal dynamics rely on costly measures such as entanglement entropy. In this work, we show how two dimensionality reduction techniques, multidimensional scaling and intrinsic dimension estimation, can be used to learn structural properties of dynamics in the PXP model and distinguish between thermal and scar initial states. The latter method is shown to be robust against limited sample sizes and experimental measurement errors.

Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration

Collective neutrino oscillations are typically studied using the lowest-order quantum kinetic equation, also known as the mean-field approximation. However, some recent quantum many-body simulations suggest that quantum entanglement among neutrinos may be important and may result in flavor equilibration of the neutrino gas. In this work, we develop new quantum models for neutrino gases in which any pair of neutrinos can interact at most once in their lifetimes. A key parameter of our models is γ=μΔz, where μ is the neutrino coupling strength, which is proportional to the neutrino density, and Δz is the duration over which a pair of neutrinos can interact each time. Our models reduce to the mean-field approach in the limit γ→0 and achieve flavor equilibration in time t≫(γμ)−1. These models demonstrate the emergence of coherent flavor oscillations from the particle perspective and may help elucidate the role of quantum entanglement in collective neutrino oscillations. Published by the American Physical Society 2024

Selective Detection of Dynamics-Complete Set of Correlations via Quantum Channels.

Correlations of fluctuations are essential to understanding many-body systems and key information for advancing quantum technologies. To fully describe the dynamics of a physical system, all time-ordered correlations (TOCs), i.e., the dynamics-complete set of correlations are needed. The current measurement techniques can only access a limited set of TOCs, and there has been no systematic and feasible solution for extracting the dynamic-complete set of correlations hitherto. Here we propose a platform-universal protocol to selectively detect arbitrary types of TOCs via quantum channels. In our method, the quantum channels are synthesized with various controls, and engineer the evolution of a sensor-target system along a specific path that corresponds to a desired correlation. Using nuclear magnetic resonance, we experimentally demonstrate this protocol by detecting a specific type of fourth-order TOC that has never been accessed previously. We also show that the knowledge of the TOCs can be used to significantly improve the precision of quantum optimal control. Our method provides a new toolbox for characterizing the quantum many-body states and quantum noise, and hence for advancing the fields of quantum sensing and quantum computing.

A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems

We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate Γ of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues {λα}α=1n of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size n→∞ it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of λ’s at each time t and for each size n. Two relevant regimes emerge: at short times tΓ=O(1), the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the n→∞ limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times tΓ=O(n), one enters instead a regime in which the eigenvalues are exponentially separated log(λα/λβ)=O(Γt/n), but fluctuations ∼O(Γt/n) play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime.

Excited-state downfolding using ground-state formalisms

Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H2, Methylene, Formaldehyde, and Nitroxyl.

Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics.

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.

Insulating-to-conducting state transition in the bilayer Hubbard model induced by a perpendicular quench field

A many-body quantum system with varying parameters can exhibit two distinct quantum states within the same energy shell. This allows for a dynamic transition from the ground state of the pre-quench Hamiltonian to a steady state of the post-quench Hamiltonian. We investigate the dynamic response of the ground states in a two-layer half-filled Hubbard model to a perpendicular electric field. We demonstrate that the steady state exhibits conductivity when the field is in resonance with the on-site repulsion, while the initial state is a Mott-insulating state. Additionally, the two layers exhibit identical conducting behavior due to the formation of long-lived dopings, as evidenced by the charge fluctuation. The key factor in achieving this dynamic transition is the cooperative interplay between on-site interactions and the resonant field, rather than the individual roles they play. Our findings offer an alternative mechanism for field-induced conductivity in strongly correlated systems.

Separability criterion using one observable for special states: Entanglement detection via quantum quench

Detecting entanglement in many-body quantum systems is crucial but challenging, typically requiring multiple measurements. Here, we establish a class of states where measuring connected correlations in just basis gives a necessary condition to detect bipartite separability, thus offering a sufficient condition to detect entanglement, provided the appropriate basis and observables are chosen. This methodology leverages prior information about the state, which, although insufficient to reveal the complete state or its entanglement, enables our one basis approach to be effective. We discuss the possibility of one observable entanglement detection in a variety of systems, including those without conserved charges, such as the transverse Ising model, reaching the appropriate basis via quantum quench. This provides a much simpler pathway of detection than previous works. It also shows improved sensitivity from Pearson correlation detection techniques. Published by the American Physical Society 2024

Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit

We present an expression for the spectral gap, opening up new possibilities for performing and accelerating spectral calculations of quantum many-body systems. We develop and demonstrate one such possibility in the context of tensor network simulations. Our approach requires only minor modifications of the widely used simple update method and is computationally lightweight relative to other approaches. We validate it by computing spectral gaps of the 2D and 3D transverse-field Ising models and find strong agreement with previously reported perturbation theory results. Published by the American Physical Society 2024

Entanglement preservation in tripartite quantum systems under dephasing dynamics

Protecting entanglement from decoherence is a critical aspect of quantum information processsing. For many-body quantum systems evolving under decoherence, estimating multipartite entanglement is challenging. This challenge can be met up by considering a distance-based measure such as relative entropy of entanglement which decisively measures entanglement in both pure as well as mixed states. In this work, we investigate the tripartite entanglement dynamics of pure and mixed states in the presence of a structured dephasing environment at finite temperature. We show that the robustness of the quantum system to decoherence is dependent on the distribution of entanglement and its relation to different configurations of the bath. If the bath is structured individually such that each qubit has its own environment, the system has different dynamics compared to when the bath is common to all the three qubits. From the results we conjecture that there is a connection between the distribution of entanglement among the qubits and the distribution of bath degrees of freedom, and the interplay of these two distributions determines the decay rate of the entanglement dynamics. The sustainability of tripartite entanglement is shown to be enhanced significantly in the presence of reservoir memory.

Resilience of quantum spin fluctuations against Dzyaloshinskii-Moriya interaction.

In low-dimensional systems, the lack of structural inversion symmetry combined with the spin-orbit coupling gives rise to an anisotropic antisymmetric superexchange known as the Dzyaloshinskii-Moriya interaction (DMI). Various features have been reported due to the presence of DMIs in quantum systems. We here study the one-dimensional spin-1/2 transverse field XY chains with a DMI at zero temperature. Our focus is on the quantum fluctuations of the spins measured by the spin squeezing and the entanglement entropy. We find that these fluctuations are resistant to the effect of the DMI in the system. This resistance will fail as soon as the system is placed in the chiral phase where its state behaves as a squeezed state, suggesting the merit of the chiral phase to be used for quantum metrology. Remarkably, we prove that the central charge vanishes on the critical lines between gapless chiral and ferromagnetic/paramagnetic phases where there is no critical scaling versus the system size for the spin squeezing parameter. Our phenomenal results provide a further understanding of the effects of the DMIs in the many-body quantum systems which may be testable in experiments.

Information scrambling —A quantum thermodynamic perspective

Recent advances in quantum information science have shed light on the intricate dynamics of quantum many-body systems, for which quantum information scrambling is a perfect example. Motivated by considerations of the thermodynamics of quantum information, this perspective aims at synthesizing key findings from several pivotal studies and exploring various aspects of quantum scrambling. We consider quantifiers such as the out-of-time-ordered correlator (OTOC) and the quantum mutual information, their connections to thermodynamics, and their role in understanding chaotic vs. integrable quantum systems. With a focus on representative examples, we cover a range of topics, including the thermodynamics of quantum information scrambling, and the scrambling dynamics in quantum gravity models such as the Sachdev-Ye-Kitaev (SYK) model. Examining these diverse approaches enables us to highlight the multifaceted nature of quantum information scrambling and its significance in understanding the fundamental aspects of quantum many-body dynamics at the intersection of quantum mechanics and thermodynamics.

Band gap engineering and controlling transport properties of single photons in periodic and disordered Jaynes–Cummings arrays

We theoretically study the single-photon transport properties in periodic and position-disordered Jaynes–Cummings (or JC) arrays of waveguide-coupled microtoroidal ring resonators, each interacting with a single two-level quantum emitter. Employing the real-space formalism of quantum optics, we focus on various parameter regimes of cavity quantum electrodynamics (cQED) to gain better control of single-photon propagation in such a many-body quantum optical setting. As for some of the key findings, we observe that the periodic setting leads to the formation of the band structure in the photon transmission spectra, which is most evident in the strong coupling regime of cQED. However, under resonant conditions with no losses, the application of Bloch’s theorem indicates that the width of forbidden gaps can be altered by tuning the emitter-cavity coupling to small values. Moreover, in the disordered case, we find that the single-photon transmission curves show the disappearance of band formation. However, spectral features originating from cQED interactions observed for the single atom-cavity problem remain robust against weak-disordered conditions. The results of this work may find application in the study of quantum many-body effects in the optical domain as well as in different areas of quantum computation and quantum networking.

Local gate control of Mott metal-insulator transition in a 2D metal-organic framework

Electron-electron interactions in materials lead to exotic many-body quantum phenomena, including Mott metal-insulator transitions (MITs), magnetism, quantum spin liquids, and superconductivity. These phases depend on electronic band occupation and can be controlled via the chemical potential. Flat bands in two-dimensional (2D) and layered materials with a kagome lattice enhance electronic correlations. Although theoretically predicted, correlated-electron Mott insulating phases in monolayer 2D metal-organic frameworks (MOFs) with a kagome structure have not yet been realised experimentally. Here, we synthesise a 2D kagome MOF on a 2D insulator. Scanning tunnelling microscopy (STM) and spectroscopy reveal a MOF electronic energy gap of ∼200 meV, consistent with dynamical mean-field theory predictions of a Mott insulator. Combining template-induced (via work function variations of the substrate) and STM probe-induced gating, we locally tune the electron population of the MOF kagome bands and induce Mott MITs. These findings enable technologies based on electrostatic control of many-body quantum phases in 2D MOFs.

Hayden-Preskill recovery in Hamiltonian systems

Information scrambling refers to the unitary dynamics that quickly spreads and encodes localized quantum information over an entire many-body system and makes the information accessible from any small subsystem. While information scrambling is the key to understanding complex quantum many-body dynamics and is well-understood in random unitary models, it has been hardly explored in Hamiltonian systems. In this Letter, we investigate the information recovery in various time-independent Hamiltonian systems, including chaotic spin chains and Sachdev-Ye-Kitaev models. We show that information recovery is possible in certain, but not all, chaotic models, which highlights the difference between information recovery and quantum chaos based on the energy spectrum or the out-of-time-ordered correlators. We also show that information recovery probes transitions caused by the change of information-theoretic features of the dynamics. Published by the American Physical Society 2024

Entanglement phase transitions in non-Hermitian Floquet systems

The competition between unitary time evolution and quantum measurements could induce phase transitions in the entanglement characteristics of quantum many-body dynamics. In this work, we reveal such entanglement transitions in the context of non-Hermitian Floquet systems. Focusing on noninteracting fermions in a representative bipartite lattice with balanced gain/loss and under time-periodic quenches, we uncover rich patterns of entanglement transitions due to the interplay between driving and non-Hermitian effects. Specially, we find that the monotonic increase of quenched hopping amplitude could flip the system between volume-law and area-law entangled Floquet phases, yielding alternated entanglement transitions. Meanwhile, the increase of gain/loss strength could trigger area-law to volume-law reentrant transitions in the scaling behavior of steady-state entanglement entropy, which are abnormal and highly unexpected in nondriven systems. Connections between entanglement transitions and parity-time-reversal (PT) transitions in Floquet spectra are further established. Our findings not only build a foundation for exploring entanglement phase transitions in Floquet non-Hermitian setups, but also provide efficient means to engineer and control such transitions by driving fields. Published by the American Physical Society 2024