Weak Measurements Research Articles

Relative pressure functions and their equilibrium states

AbstractFor a subshift $(X, \sigma _{X})$ and a subadditive sequence ${\mathcal F}=\{\log f_{n}\}_{n=1}^{\infty }$ on X, we study equivalent conditions for the existence of $h\in C(X)$ such that $\lim _{n\rightarrow \infty }(1/{n})\int \log f_{n}\, d\kern-1pt\mu =\int h \,d\kern-1pt\mu $ for every invariant measure $\mu $ on X. For this purpose, we first we study necessary and sufficient conditions for ${\mathcal F}$ to be an asymptotically additive sequence in terms of certain properties for periodic points. For a factor map $\pi : X\rightarrow Y$ , where $(X, \sigma _{X})$ is an irreducible shift of finite type and $(Y, \sigma _{Y})$ is a subshift, applying our results and the results obtained by Cuneo [Additive, almost additive and asymptotically additive potential sequences are equivalent. Comm. Math. Phys.37 (3) (2020), 2579–2595] on asymptotically additive sequences, we study the existence of h with regard to a subadditive sequence associated to a relative pressure function. This leads to a characterization of the existence of a certain type of continuous compensation function for a factor map between subshifts. As an application, we study the projection $\pi \mu $ of an invariant weak Gibbs measure $\mu $ for a continuous function on an irreducible shift of finite type.

A Testable Theory for the Emergence of the Classical World.

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.

Why are we still using 3D masses for cluster cosmology?

ABSTRACT The abundance of clusters of galaxies is highly sensitive to the late-time evolution of the matter distribution, since clusters form at the highest density peaks. However, the 3D cluster mass cannot be inferred without deprojecting the observations, introducing model-dependent biases and uncertainties due to the mismatch between the assumed and the true cluster density profile and the neglected matter along the sightline. Since projected aperture masses can be measured directly in simulations and observationally through weak lensing, we argue that they are better suited for cluster cosmology. Using the Mira–Titan suite of gravity-only simulations, we show that aperture masses correlate strongly with 3D halo masses, albeit with large intrinsic scatter due to the varying matter distribution along the sightline. Nonetheless, aperture masses can be measured ≈2–3 times more precisely from observations, since they do not require assumptions about the density profile and are only affected by the shape noise in the weak lensing measurements. We emulate the cosmology dependence of the aperture mass function directly with a Gaussian process. Comparing the cosmology sensitivity of the aperture mass function and the 3D halo mass function for a fixed survey solid angle and redshift interval, we find the aperture mass sensitivity is higher for Ωm and $w_a$, similar for σ8, ns, and $w_0$, and slightly lower for h. With a carefully calibrated aperture mass function emulator, cluster cosmology analyses can use cluster aperture masses directly, reducing the sensitivity to model-dependent mass calibration biases and uncertainties.

Signature of the photonic spin Hall effect in monolayer MoS2 via weak measurement

We report the direct experimental evidence of the photonic spin Hall shift (PSHS) in monolayer M o S 2 for a fundamental Gaussian beam via a weak measurement scheme involving definite preselection and postselection spin states. We find that the PSHS is largely dependent on the angle of incidence, postselection angles, and polarization states along with specific ways of interaction of the light with the M o S 2 surface. Our findings reveal a unique signature linking angular positions at which the spin Hall shifts (SHS) (zero crossing) with the discontinuity in the phase difference ( ϕ P − ϕ S ) of the reflection coefficients further establishing the connection of the PSHS to the geometric phases of the light. An effective theoretical model is applied to confirm the experimental measurements. This paper, thus, deepens our understanding of the tiny spin-dependent splitting in monolayer M o S 2 , opening a new, to the best of our knowledge, avenue for the practical applications of the PSHSs.

Fundamental physics with ESPRESSO: Constraints on Bekenstein and dark energy models from astrophysical and local probes

Dynamical scalar fields in an effective four-dimensional field theory are naturally expected to couple to the rest of the theory's degrees of freedom, unless some new symmetry is postulated to suppress these couplings. In particular, a coupling to the electromagnetic sector will lead to spacetime variations of the fine-structure constant, $\alpha$. Astrophysical tests of the space-time stability of $\alpha$ are therefore a powerful probe of new physics. Here we use ESPRESSO and other contemporary measurements of $\alpha$, together with background cosmology data, local laboratory atomic clock and Weak Equivalence Principle measurements, to place stringent constraints on the simplest examples of the two broad classes of varying $\alpha$ models: Bekenstein models and quintessence-type dark energy models, both of which are parametric extensions of the canonical $\Lambda$CDM model. In both cases, previously reported constraints are improved by more than a factor of ten. This improvement is largely due to the very strong local constraints, but astrophysical measurements can help to break degeneracies between cosmology and fundamental physics parameters.

Implementation of the quantum three box paradox through atomic internal states

Quantum three box paradox is one of the key dynamical mysteries of the quantum evolution explored through Two-State Vector Formalism (TSVF) of the quantum theory in conjunction with the weak measurements. The paradox further deepens the notation of quantum reality while highlighting the strange and counterintutive traits of the quantum unitary evolution in-between two strong measurements. We present an experimentally feasible protocol for implementing the paradox through internal states of a three-level ladder atomic system. The techniques invoked here are all state of the art cavity QED tools and the suggested schematics can be executed practically with good overall results.

Observing a topological transition in weak-measurement-induced geometric phases

Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable various levels of coherent control. The latter ranges from observing quantum trajectories to state dragging and steering. Furthermore, just like the adiabatic evolution of quantum states that is known to induce the Berry phase, sequential weak measurements may lead to path-dependent geometric phases. Here we measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. This connection between weak measurement induced quantum dynamics and topological transitions reveals subtle topological features in measurement-based manipulation of quantum systems. Our protocol could be implemented for classes of operations (e.g. braiding) which are topological in nature. Furthermore, our results open new horizons for measurement-enabled quantum control of many-body topological states.

Protecting genuine tripartite nonlocality by weak measurement and quantum measurement reversal

Protecting genuine tripartite nonlocality by weak measurement and quantum measurement reversal

The dark matter halo masses of elliptical galaxies as a function of observationally robust quantities

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can therefore help to understand their evolution. Aims. We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on the following galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods. We selected 2409 central massive elliptical galaxies (log M*/M⊙ ≳ 11.4) from the Sloan Digital Sky Survey spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sérsic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame r-band luminosity, half-light radius, and rest-frame u − g colour, using KiDS weak lensing measurements and a Bayesian hierarchical approach. For the sake of robustness with respect to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing the total luminosity and half-light radius with the luminosity within a 10 kpc aperture, Lr, 10, and the light-weighted surface brightness slope, Γ10. Results. We did not detect any correlation between the halo mass and either the half-light radius or colour at fixed redshift and luminosity. Using the robust surface brightness parameterisation, we found that the halo mass correlates weakly with Lr, 10 and anti-correlates with Γ10. At fixed redshift, Lr, 10 and Γ10, the difference in the average halo mass between galaxies at the 84th percentile and 16th percentile of the colour distribution is 0.00 ± 0.11 dex. Conclusion. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than the halo mass.

Enhancing quantum teleportation fidelity under decoherence via weak measurement with flips

Noiseless quantum channels are critical to share a pure maximally entangled state for performing an ideal teleportation protocol. However, in reality the shared entanglement severely degraded due to decoherence. In this paper, we propose a quantum teleportation channel protection scheme to enhance the teleportation fidelity in presence of decoherence. Before the entangled pair enters the decoherence channel, the weak measurement and flip operations are applied to transfer the qubit to a more robust state to the effects of the noise. After the decoherence channel the reversed flip operations and weak measurement reversal are applied to recover the initial state. We illustrate our protected teleportation scheme and compare it with a protocol based on weak measurement reversal. The numerical results show that the average teleportation fidelity of our proposed scheme can be significantly improved. Although the proposed entanglement protection scheme is probabilistic, after a successful entanglement transmission, we use the standard teleportation protocol which has probability one.

Proposal to observe path superpositions in a double-slit setup

The interference pattern produced by a quantum particle in Young's double-slit setup is attributed to the particle's wave function having gone through both slits. In the path integral formulation, this interference involves a superposition of paths, going through either slit, linking the source to the detection point. We show how these paths superpositions can in principle be observed by implementing a series of minimally perturbing weak measurements between the slits and the detection plane. We further propose a simplified protocol in order to observe these ``weak trajectories'' with single photons.

Demonstration of a New Characterization Method for Weak Measurement.

In this work, the difference between the weak measurement method and the weak value amplification process and the classical measurement process is thoroughly discussed, and the transition conditions of the weak value enhancement are obtained. A transition mode of the weak measurement and the classical measurement is proposed for the first time, and a better fitting model of the measurement results is found by performing a systematic analysis. On top of that, the importance of the new fitting method for the application of the weak measurement system is verified during the industrial production of organic molecular -nucleic acid, protein, polysaccharide-hydrolysis or synthesis. At the same time, a variety of spectral characterization methods are proposed and the advantages and disadvantages of the different characterization methods are analyzed through carrying out experiments. Consequently, the wide implementation of weak measurement-based detection technology is attained.

Past of a Quantum particle: An atom interferometric based study

The past of a Quantum particle and the investigations of the particle’s unitary evolution in between two strong measurements have generated a heated debate recently in quantum foundational context mainly studied earlier through photonics techniques. We, however, here propose an atom interferometric exploration based on the time tested tools of Atomic Bragg Diffraction to study the past of an atom, more akin to a real, concrete particle as compared with its counterpart i.e. photon. Two-State Vector Formalism (TSVF) along with the methodology of weak measurement have been invoked for the analysis of the past of an atom traversing a Mach–Zehnder Bragg atom interferometer and the results obtained are quite interesting. It is also being demonstrated explicitly that the suggested schematics are inherently deterministic and the proposal can be experimentally executed with high enough fidelity under the prevailing atom-field interaction based laboratory tools.

Real-time monitoring the hydrolysis of chiral molecules by optical weak measurement

As one of important optical properties of chiral molecules, the real-time monitoring of the optical rotation is of great significance to study the reaction characteristics of chiral molecules. In this study, we have built an optical frequency domain weak measurement system with linear common-path method for chiral sensing, in which the response between optical rotation and central wavelength shift can reach more than 1200 nm/rad. The high-precision measurement of the optical rotation of chiral molecules and the high-sensitivity real-time monitoring of the decomposition rate in the acidic hydrolysis of sucrose under different concentrations of catalysts are realized using this system. The experimental results are basically consistent with the theoretical prediction. This study shows that optical weak measurement chiral sensing can monitor the hydrolysis degree of chiral molecules in real time without separating and labeling molecules. It has great application potential in the production and research of chiral compounds, especially chiral medicine.

Toward practical weak measurement wavefront sensing: spatial resolution and achromatism.

The weak measurement wavefront sensor detects the phase gradient of light like the Shack-Hartmann sensor does. However, the use of one thin birefringent crystal to displace light beams results in a wavelength-dependent phase difference between the two polarization components, which limits the practical application. Use of a Savart plate, which consists of two such crystals, can compensate for the phase difference and realize achromatic wavefront sensing when combined with an achromatic retarder. We discuss the spatial resolution of the sensor and experimentally reconstruct a wavefront modulated by a pattern. Then we obtain the Zernike coefficients with three different wavelengths before and after modulation. Our work makes this new wavefront sensor more applicable to actual tasks like biomedical imaging.

Protecting unknown qubit states from decoherence of qubit channels by weak measurement

The problem of combating de-coherence by weak measurements has already been studied for the amplitude damping channel and for specific input states. We generalize this to a large four-parameter family of qubit channels and for the average fidelity over all pure states. As a by-product we classify all the qubit channels which have one invariant pure state and show that the parameter manifold of these channels is isomorphic to S 2 × S 1 × S 1 and contains many interesting sub-classes of channels. By tuning the parameter of the weak measurement, we show that it is possible to increase the average input–output fidelity without blocking too many particles to pass through the channel. Quantitative analysis reveals that the increase of average fidelity can be up to 0.3, by blocking less than half of the particles.

The laws of physics do not prohibit counterfactual communication

It has been conjectured that counterfactual communication is impossible, even for post-selected quantum particles. We strongly challenge this by proposing precisely such a counterfactual scheme where—unambiguously—none of Alice’s photons that correctly contribute to her information about Bob’s message have been to Bob. We demonstrate counterfactuality experimentally by means of weak measurements, and conceptually using consistent histories—thus simultaneously satisfying both criteria without loopholes. Importantly, the fidelity of Alice learning Bob’s bit can be made arbitrarily close to unity.

Incorporating the weak mixing angle dependence to reconcile the neutron skin measurement on Pb208 by PREX-II

The only available electroweak measurement of the $^{208}\mathrm{Pb}$ neutron skin $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{np}}$, performed by the PREX-II Collaboration through polarized electron-lead scattering, shows a mild tension with respect to both the theoretical nuclear-model predictions and a host of measurements. However, the dependence on the weak mixing angle should be incorporated in the calculation, since its low-energy value is experimentally poorly known. We first repeat the PREX-II analysis confirming their measurement by fixing the weak mixing angle to its standard model value. Then, we show the explicit dependence of the PREX-II measurement on the weak mixing angle, obtaining that it is fully degenerate with the neutron skin. To break this degeneracy, we exploit the weak mixing angle measurement from atomic parity violation on lead, obtaining a slightly thinner neutron skin but with about doubled uncertainties, possibly easing the PREX tension. Relying on the theoretical prediction, $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{np}}^{\mathrm{th}}\ensuremath{\approx}0.13\text{--}0.19\phantom{\rule{4pt}{0ex}}\mathrm{fm}$, and using it as a prior in the fit, we find a weak mixing angle value about $1.2\ensuremath{\sigma}$ smaller than the standard model prediction. Thus, we suggest a possible solution of the PREX-II tension by showing that, considering its underlying dependence on the weak mixing angle, the PREX-II neutron skin determination could be in agreement with the other available measurements and predictions if the weak mixing angle at the proper energy scale is smaller than the standard model prediction.

Swept-wavelength null polarimeter for high-speed weak anisotropy measurements.

Null-polarimeters provide the best sensitivity to anisotropy measurements and so far have been developed for the detection of small optical activities. This paper revisits null polarimetry through an original configuration based on the concept of spectrally encoded light polarization, in order to measure, with unprecedented speed, either linear or circular retardance with the same degree of sensitivity . Using passive polarization optics and a high speed wavelength swept laser source, the achieved single-pass sensitivity was 55nrad/Hz and 45nrad/Hz for respectively linear and circular retardance considering a minimum acquisition time of 10 µs. Due to its compactness and rapidity, the method could be further implemented in laser scanning microscopes, which should be of great interest for revealing very low anisotropies in biological tissues.

Activation of magnetic moments by annealing in chemical vapor deposited graphene

The effects of annealing on chemical vapor deposited graphene are investigated via a weak localization magnetoresistance measurement. Annealing at $300{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ in inert gases, a common cleaning procedure for graphene devices, is found to raise the dephasing rate significantly above the rate from electron-electron interactions, which would otherwise be expected to dominate dephasing at 4 K and below. This extra dephasing is apparently induced by local magnetic moments activated by the annealing process, and depends strongly on the backgate voltage applied.