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Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we establish a link between the bound on the growth of the quantum Fisher information and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems. We show that for initial separable states, despite the use of local many-body interactions, the precision cannot surpass the shot noise limit at all times. This conclusion also holds for an initial state that is the nondegenerate ground state of a local and gapped Hamiltonian. These findings strongly hint that when one can only prepare separable initial states, nonlocal and long-range interactions are essential resources for surpassing the shot noise limit. This observation is confirmed through numerical analysis on the long-range Ising model. Our results bridge the field of many-body quantum sensing and operator growth in many-body quantum systems and open the possibility to investigate the interplay between quantum sensing and control, many-body physics and information scrambling.
RESUMEN
Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga-Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology.
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Ultracold atoms confined to periodic potentials have proven to be a powerful tool for quantum simulation of complex many-body systems. We confine fermions to one dimension to realize the Tomonaga-Luttinger liquid model, which describes the highly collective nature of their low-energy excitations. We use Bragg spectroscopy to directly excite either the spin or charge waves for various strengths of repulsive interaction. We observe that the velocity of the spin and charge excitations shift in opposite directions with increasing interaction, a hallmark of spin-charge separation. The excitation spectra are in quantitative agreement with the exact solution of the Yang-Gaudin model and the Tomonaga-Luttinger liquid theory. Furthermore, we identify effects of nonlinear corrections to this theory that arise from band curvature and back-scattering.
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Recent experiments on quantum walks (QWs) demonstrated a full control over the statistics-dependent walks of single particles and two particles in one-dimensional lattices. However, little is known about the general characterization of QWs at the many-body level. Here, we rigorously study QWs, Bloch oscillations, and the quantum Fisher information for three indistinguishable bosons and fermions in one-dimensional lattices using a time-evolving block decimation algorithm and many-body perturbation theory. We show that such strongly correlated QWs not only give rise to statistics-and-interaction-dependent ballistic transports of scattering states and of two- and three-body bound states but also allow a quantum enhanced precision measurement of the gravitational force. In contrast to the QWs of the fermions, the QWs of three bosons exhibit strongly correlated Bloch oscillations, which present a surprising time scaling t^{3} of the Fisher information below a characteristic time t_{0} and saturate to the fundamental limit of t^{2} for t>t_{0}.
RESUMEN
At low temperature, collective excitations of one-dimensional (1D) interacting fermions exhibit spin-charge separation, a unique feature predicted by the Tomonaga-Luttinger liquid (TLL) theory, but a rigorous understanding remains challenging. Using the thermodynamic Bethe ansatz (TBA) formalism, we analytically derive universal properties of a 1D repulsive spin-1/2 Fermi gas with arbitrary interaction strength. We show how spin-charge separation emerges from the exact TBA formalism, and how it is disrupted by the interplay between the two degrees of freedom that brings us beyond the TLL paradigm. Based on the exact low-lying excitation spectra, we further evaluate the spin and charge dynamical structure factors (DSFs). The peaks of the DSFs exhibit distinguishable propagating velocities of spin and charge as functions of interaction strength, which can be observed by Bragg spectroscopy with ultracold atoms.
RESUMEN
A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases, respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation and discuss the phase transitions between the two SPT phases and their experimental signatures.
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We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL.
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We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.
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We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy, and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds. Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds (5IAP)2CuBr4.2H(2)O, Cu2(C5H12N2)2Cl4, etc.