Quantum Limit Research Articles

High pressure ferroelectric-like semi-metallic state in Eu-doped BaTiO3.

We have conducted a detailed high-pressure (HP) investigation on Eu-doped BaTiO3 using angle-resolved x-ray diffraction, Raman spectroscopy, and dielectric permittivity measurements. The x-ray diffraction data analysis shows a pressure-induced structural phase transition from the ambient tetragonal to the mixed cubic and tetragonal phases above 1.4GPa. The tetragonality of the sample due to the internal deformation of the TiO6 octahedra caused by the charge difference from Eu doping cannot be lifted by pressure. Softening, weakening, and disappearance of low-frequency Raman modes indicate ferroelectric tetragonal to the paraelectric cubic phase transition. However, the pressure-induced increase in the intensity of [E(LO), A1(LO)] and the octahedral breathing modes indicate that the local structural inhomogeneity remains in the crystal and is responsible for spontaneous polarization in the sample. The low-frequency electronic scattering response suggests pressure-induced carrier delocalization, leading to a semi-metallic state in the system. Our HP dielectric constant data can be explained by the presence of pressure-induced localized clusters of microscopic ferroelectric ordering. Our results suggest that the HP phase coexistence leads to a ferroelectric-like semi-metallic state in Eu-doped BaTiO3 under extreme quantum limits.

Harnessing graph state resources for robust quantum magnetometry under noise

Precise measurement of magnetic fields is essential for various applications, such as fundamental physics, space exploration, and biophysics. Although recent progress in quantum engineering has assisted in creating advanced quantum magnetometers, there are still ongoing challenges in improving their efficiency and noise resistance. This study focuses on using symmetric graph state resources for quantum magnetometry to enhance measurement precision by analyzing the estimation theory under time-homogeneous and time-inhomogeneous noise models. The results show a significant improvement in estimating both single and multiple Larmor frequencies. In single Larmor frequency estimation, the quantum Fisher information spans a spectrum from the standard quantum limit to the Heisenberg limit within a periodic range of the Larmor frequency, and in the case of multiple Larmor frequencies, it can exceed the standard quantum limit for both noisy cases. This study highlights the potential of graph state-based methods for improving magnetic field measurements under noisy environments.

A quantum-enhanced magnetometer using a single high-spin nucleus in silicon

Abstract Quantum enhanced metrology has the potential to go beyond the standard quantum limit and eventually to the ultimate Heisenberg bound. In particular, quantum probes prepared in nonclassical coherent states have recently been recognized as a useful resource for metrology. Hence, there has been considerable interest in constructing magnetic quantum sensors that combine high resolution and high sensitivity. Here, we explore a nanoscale magnetometer with quantum-enhanced sensitivity, based on 123Sb (I = 7/2) nuclear spin doped in silicon, that takes advantage of techniques of spin-squeezing and coherent control. With the optimal squeezed initial state, the magnetic field sensitivity may be expected to approach 6 aT⋅Hz−1/2⋅cm−3/2 and 603 nT⋅Hz−1/2 at the single-spin level. This magnetic sensor may provide a novel sensitive and high-resolution route to microscopic mapping of magnetic fields as well as other applications.

On-chip quantum NOON state sensing for temperature and humidity

Abstract A maximal photon number entangled state, namely NOON state, can be adopted for sensing with a quantum enhanced precision. In this work, we designed silicon quantum photonic chips containing two types of Mach–Zehnder interferometers wherein the two-photon NOON state, sensing element for temperature or humidity, is generated. Compared with classical light or single photon case, two-photon NOON state sensing shows a solid enhancement in the sensing resolution and precision. As the first demonstration of on-chip quantum photonic sensing, it reveals the advantages of photonic chips for high integration density, small-size, stability for multiple-parameter sensing serviceability. A higher sensing precision is expected to beat the standard quantum limit with a higher photon number NOON state.

Quantum limits of perturbed sub-Riemannian contact Laplacians in dimension 3

Quantum limits of perturbed sub-Riemannian contact Laplacians in dimension 3

Bistability-assisted mechanical squeezing and entanglement

Based on a scheme proposed to experience the dynamical Casimir effect in optomechanical systems, we show how to squeeze mechanical motion and entangle the optical field with mechanical motion in an optomechanical system containing a parametric amplification. The scheme is based on optical bistability which emerges in the system for a strong enough driving field. By considering the steady state’s lower branch of the bistability, the system shows weak entanglement and almost no mechanical squeezing. When the steady state is on the upper branch of the bistable shape, both squeezing and entanglement are greatly enhanced. Specifically, the entanglement shows three degrees of magnitude enhancement. However, this giant entanglement is fragile against decoherence and thermal fluctuation. Regarding the mechanical squeezing, it reaches the standard quantum limit (SQL) in the upper branch of the bistability. Our proposal provides a way to improve quantum effects in optomechanical systems by taking advantage of nonlinearities. This scheme can be realized in similar systems such as superconducting microwave, and hybrid optomechanical systems.

Control-enhanced non-Markovian quantum metrology

Quantum metrology promises unprecedented precision of parameter estimation, but it is often vulnerable to noise. While significant efforts have been devoted to improving the metrology performance in Markovian environments, practical control schemes specifically designed for non-Markovian noises are much less investigated. Here, we propose two control-enhanced quantum metrology schemes that are suitable for tackling general non-Markovian noises described by noise channels or noise spectra. We conduct experiments to verify the efficacy of these schemes on a nuclear magnetic resonance system. The experimental results involving multiqubit probes show that the parameter estimation precision can be greatly improved, significantly surpassing the standard quantum limit, with our schemes. At present, non-Markovian noises are widely encountered on diverse quantum devices, the proposed schemes are relevant for realistic metrology applications on these platforms.

Atomic and Electronic Structure of Defects in hBN: Enhancing Single-Defect Functionalities.

Defect centers in insulators play a critical role in creating important functionalities in materials: prototype qubits, single-photon sources, magnetic field probes, and pressure sensors. These functionalities are highly dependent on their midgap electronic structure and orbital/spin wave function contributions. However, in most cases, these fundamental properties remain unknown or speculative due to the defects being deeply embedded beneath the surface of highly resistive host crystals, thus impeding access through surface probes. Here, we directly inspected the atomic and electronic structures of defects in thin carbon-doped hexagonal boron nitride (hBN:C) by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Such investigation adds direct information about the electronic midgap states to the well-established photoluminescence response (including single-photon emission) of intentionally created carbon defects in the most commonly investigated van der Waals insulator. Our joint atomic-scale experimental and theoretical investigations reveal two main categories of defects: (1) single-site defects manifesting as donor-like states with atomically resolved structures observable via STM and (2) multisite defect complexes exhibiting a ladder of empty and occupied midgap states characterized by distinct spatial geometries. Combining direct probing of midgap states through tunneling spectroscopy with the inspection of the optical response of insulators hosting specific defect structures holds promise for creating and enhancing functionalities realized with individual defects in the quantum limit. These findings underscore not only the versatility of hBN:C as a platform for quantum defect engineering but also its potential to drive advancements in atomic-scale optoelectronics.

Single-photon induced instabilities in a cavity electromechanical device

Cavity-electromechanical systems are extensively used for sensing and controlling the vibrations of mechanical resonators down to their quantum limit. The nonlinear radiation-pressure interaction in these systems could result in an unstable response of the mechanical resonator showing features such as frequency-combs, period-doubling bifurcations and chaos. However, due to weak light-matter interaction, typically these effects appear at very high driving strengths. By using polariton modes formed by a strongly coupled flux-tunable transmon and a microwave cavity, here we demonstrate an electromechanical device and achieve a single-photon coupling rate g0/2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left({g}_{0}/2\\pi \\right)$$\\end{document} of 160 kHz, which is nearly 4% of the mechanical frequency ωm. Due to large g0/ωm ratio, the device shows an unstable mechanical response resulting in frequency combs in sub-single photon limit. We systematically investigate the boundary of the unstable response and identify two important regimes governed by the optomechanical backaction and the nonlinearity of the electromagnetic mode. Such an improvement in the single-photon coupling rate and the observations of microwave frequency combs at single-photon levels may have applications in the quantum control of the motional states and critical parametric sensing. Our experiments strongly suggest the requirement of newer approaches to understand instabilities.

Trade-offs between unitary and measurement induced spin squeezing in cavity QED

We study the combined effects of measurements and unitary evolution on the preparation of spin squeezing in an ensemble of atoms interacting with a single electromagnetic field mode inside a cavity. We derive simple criteria that determine the conditions at which measurement based entanglement generation overperforms unitary protocols. We include all relevant sources of decoherence and study both their effect on the optimal spin squeezing and the overall size of the measurement noise, which limits the dynamical range of quantum-enhanced phase measurements. Our conclusions are relevant for state-of-the-art atomic clocks that aim to operate below the standard quantum limit. Published by the American Physical Society 2024

Effective and robust quantum state tomography of electron-nuclear spins in diamond by time-resolved fluorescence

Quantum state tomography (QST) of electron-nuclear spins of nitrogen-vacancy (NV) center in diamond commonly requires a sequence of population flipping operations and frequent calibration of basis states by fluorescence photon-counting. Here, we realize an effective and robust quantum state tomography of electron-nuclear spins based on time-resolved fluorescence, which can enhance the signal-to-noise ratio between different basis states up to 29.6% compared to the photon-counting method. Meanwhile, our method can directly obtain the population of four basis states with only one measurement, which significantly improves the efficiency of tomography. Furthermore, the photon count rate fluctuation of time-resolved fluorescence can be reduced to the standard quantum limit by normalization operation, indicating that the time-resolved method is calibration-free. This method could be easily applied to multi-nuclear spins of NV center in diamond and extended to other solid-state spin systems.

Neural quantum embedding: Pushing the limits of quantum supervised learning

Neural quantum embedding: Pushing the limits of quantum supervised learning

Electron-proton relaxation in hot-dense plasmas with a screened quantum statistical potential.

Modeling the nonequilibrium process between ions and electrons is of great importance in laboratory fusion ignition, laser-plasma interaction, and astrophysics. For hot and dense plasmas, theoretical descriptions of Coulomb collisions remain complicated due to quantum effect at short distances and screening effect at long distances. In this paper, we propose an analytical screened quantum statistical potential that takes into account both the short-range quantum diffraction effect and the long-range screening effect. By implementing the newly developed potential into the binary scattering framework, the electron-proton temperature relaxation in hot-dense hydrogen plasmas is investigated. In both the classical and quantum limits, analytical expressions for the Coulomb logarithm have been obtained, which are generally embedded in an asymptotic matching formula. Quantitative comparisons with molecular dynamics simulations and recent OMEGA experiments demonstrate that the present modeling is well suited to describe the temperature relaxation process between electrons and ions in hot-dense plasmas.

Surpassing the Quantum Limit in Bosonic Loss Estimation without Quantum Probes.

Bosonic loss estimation has an important role in quantum metrology. It was once believed that the ultimate precision of this task is restricted to the standard quantum limit if no quantum probe is involved. Nevertheless, a recent proposal showed that this limit can be surpassed by utilizing ring resonators with coherent state probe. Here, we experimentally realize the resonator-based bosonic loss estimation and verify the resonant enhancement effect. This Letter explores the advantages of resonator-based metrology and sheds light on the development of high-precision miniature sensors.

Quantum linewidth limitation of a laser stabilized with a nonlinear microcavity.

We show that the linewidth of a laser locked to an optical cavity characterized with nonzero optical cubic nonlinearity is restricted by the value of the nonlinear frequency shift of the cavity mode per single photon localized in the mode. This effect is masked by the fundamental thermodynamic noise in monolithic microcavities. The quantum limit of the linewidth can be measured using two independent lasers separately locked to spatially overlapping modes of the nonlinear resonator.

Intensity-Product-Based Optical Sensing to Beat the Diffraction Limit in an Interferometer.

The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.

Squeezing-enhanced quantum sensing with quadratic optomechanics

Cavity optomechanical (COM) sensors, enhanced by quantum squeezing or entanglement, have become powerful tools for measuring ultra-weak forces with high precision and sensitivity. However, these sensors usually rely on linear COM couplings, a fundamental limitation when measurements of the mechanical energy are desired. Very recently, a giant enhancement of the signal-to-noise ratio was predicted in a quadratic COM system. Here we show that the performance of such a system can be further improved surpassing the standard quantum limit by using quantum squeezed light. Our approach is compatible with available engineering techniques of advanced COM sensors and provides new opportunities for using COM sensors in tests of fundamental laws of physics and quantum metrology applications.

Quantum advantage of one-way squeezing in weak-force sensing

Cavity optomechanical (COM) sensors, featuring efficient light–motion couplings, have been widely used for ultrasensitive measurements of various physical quantities ranging from displacements to accelerations or weak forces. Previous works, however, have mainly focused on reciprocal COM systems. Here, we propose how to further improve the performance of quantum COM sensors by breaking reciprocal symmetry in purely quantum regime. Specifically, we consider a spinning COM resonator and show that by selectively driving it in opposite directions, highly nonreciprocal optical squeezing can emerge, which in turn provides an efficient way to surpass the standard quantum limit which is otherwise unattainable for the corresponding reciprocal devices. Our work confirms that breaking reciprocal symmetry, already achieved in diverse systems well beyond spinning systems, can serve as a new strategy to further enhance the abilities of advanced quantum sensors, for applications ranging from testing fundamental physical laws to practical quantum metrology.

Estimation of Hamiltonian Parameters from Thermal States.

We upper bound and lower bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term's degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/sqrt[n], beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g., a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

Phase estimation via coherent and photon-catalyzed squeezed vacuum states.

The research focused on enhancing the measurement accuracy through the use of non-Gaussian states has garnered increasing attention. In this study, we propose a scheme to input the coherent state mixed with a photon-catalyzed squeezed vacuum state into the Mach-Zender interferometer to enhance phase measurement accuracy. The findings demonstrate that photon catalysis, particularly multi-photon catalysis, can effectively improve the phase sensitivity of parity detection and the quantum Fisher information. Moreover, the situation of photon losses in practical measurement was studied. The results indicate that external dissipation has a greater influence on phase sensitivity than the internal dissipation. Compared to input coherent state mixed with squeezed vacuum state, the utilization of coherent state mixed photon-catalyzed squeezed vacuum state, particularly the mixed multi-photon catalyzed squeezed vacuum state as input, can enhance the phase sensitivity and quantum Fisher information. Furthermore, the phase measurement accuracy can exceed the standard quantum limit, and even surpass the Heisenberg limit. This research is expected to significantly contribute to quantum precision measurement.