Weak values of a quantum observable and the cross-Wigner distribution

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor here is the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future.     

Comment on “Non-representative Quantum Mechanical Weak Values”

Svensson (Found Phys 45: 1645, 2015) argued that the concept of the weak value of an observable of a pre- and post-selected quantum system cannot be applied when the expectation value of the observable in the initial state vanishes. Svensson’s argument is analyzed and shown to be inconsistent using several examples.     

How Much Time Does a Measurement Take?

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.     

Hidden supersymmetry

Inspired by the concept of complementarity, we present a illustrative model for the weak interactions with unbroken gauge symmetry and unbroken supersymmetry. The observable particles are bound states of some more fundamental particles. Supersymmetry is broken at the macroscopic scale of the observable particles by a discrete symmetry but remains exact at the scale of the fundamental particle and is thus hidden. This provides a link between theories at very high energies and the observed particle physics. Supersymmetric particles are confined in usual matter.     

Bell’s theory with no locality assumption

We prove versions of the Bell and the GHZ theorems that do not assume locality but only the effect after cause principle (EACP) according to which for any Lorentz observer the value of an observable cannot change because of an event that happens after the observable is measured. We show that the EACP is strictly weaker than locality. As a consequence of our results, locality cannot be considered as the common cause of the contradictions obtained in all versions of Bell’s theory. All versions of Bell’s theorem assume weak realism according to which the value of an observable is well defined whenever the measurement could be made and some measurement is made. As a consequence of our results, weak realism becomes the only hypothesis common to the contradictions obtained in all versions of Bell’s theory. Usually, one avoids these contradictions by assuming non-locality; this would not help in our case since we do not assume locality. This work indicates that it is weak realism, not locality, that needs to be negated to avoid contradictions in microscopic physics, at least if one refuses as false the de Broglie-Bohm hidden variable theory because of its essential violation of Lorentz invariance.     

Monte Carlo estimate of the background field coupling renormalization in the Heisenberg model

We relate the difference between the bare and renormalized coupling constant in the O(n) σ-model to the expectation value of one simple observable. For n = 3 numerical results are obtained on the lattice. At weak coupling they agree with perturbation theory, while at intermediate coupling consistency is found with results from Monte Carlo renormalizationgroup calculations     

What Is a Quantum-Mechanical “Weak Value” the Value of?

A so called “weak value” of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three-Box Paradox and Hardy’s Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.     

The weak coupling limit as a quantum functional central limit

We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Ito correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.     

Conditional expectation values in quantum mechanics

The general question of defining the expectation value of an operator for a fixed value of another noncommuting observable is considered and explicit expressions are derived. Due to the noncommutivity of operators a unique definition is not possible, and we consider different possible expressions. Special cases which have previously been considered in the literature are shown to be derivable from the methods presented.In honor of Ilya Prigogine on the occasion of his 70th birthday.     

Scheme to measure the expectation value of a physical quantity in weak coupling regime

In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, ifthe coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointercan not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, whichmakes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurementmethod in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement,our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped40Ca+ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.     

Strong entanglement criterion involving momentum weak values

In recent years weak values have been used to explore interesting quantum features in novel ways. In particular, the real part of the weak value of the momentum operator has been widely studied, mainly in connection with Bohmian trajectories. Here we focus on the imaginary part and its role in relation with the entanglement of a bipartite system. We establish an entanglement criterion based on weak momentum correlations, that allows to discern whether the entanglement is encoded in the amplitude and/or in the phase of the wave function. Our results throw light on the physical role of the real and imaginary parts of the weak values, and stress the relevance of the latter in the multi-particle scenario.     

Strong coupling between single photons in semiconductor microcavities

We discuss the observability of strong coupling between single photons in semiconductor microcavities coupled by a chi2 nonlinearity. We present two schemes and analyze the feasibility of their practical implementation in three systems: photonic crystal defects, micropillars, and microdisks, fabricated out of GaAs. We show that, if a weak coherent state is used to enhance the chi2 interaction, the strong coupling regime between two modes at different frequencies occupied by a single photon is within reach of current technology. The unstimulated strong coupling of a single photon and a photon pair is very challenging and will require an improvement in mirocavity quality factors of 2-4 orders of magnitude to be observable.     

Renormalization of the Strongly Attractive Inverse Square Potential: Taming the Singularity

Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle’s state as it approaches the origin when the attractive coupling parameter is greater than the critical value of 1/4. Due to this unphysical divergence in oscillations, we are proposing that the interaction gets screened at short distances making the coupling parameter acquire an effective (renormalized) value that falls within the weak range 0–1/4. This prevents the oscillations form growing without limit giving a lower bound to the energy spectrum and forcing the Hamiltonian of the system to be self-adjoint. Technically, this translates into a regularization scheme whereby the inverse square potential is replaced near the origin by another that has the same singularity but with a weak coupling strength. Here, we take the Eckart as the regularizing potential and obtain the corresponding solutions (discrete bound states and continuum scattering states).     

Rotational tunnelling splitting of a chain of four coupled methyl groups

It is our goal to obtain a reliable prediction of the rotational tunnelling spectrum to be expected for a long chain of coupled one-dimensional quantum rotors. The problem is intractable by the simple methods used so far for up to three coupled methyl groups. Therefore, an efficient, nevertheless sufficiently precise method for solving the stationary Schrödinger equation of interacting methyl groups is developed first; it proves to be valid for a broad range of not too weak potential strengths. Then, three scenarios are investigated: they differ with respect to the relative strength of the single-rotor potential and the interaction potential. For each scenario, we illustrate the dependence of the energy level scheme on the number of coupled groups. For strong coupling and weak single-particle potential, the characteristic features of the energy level scheme of interacting methyls are most clearly observable: For as few as four coupled methyl groups we predict tunnelling spectra which are hardly distinguishable from single-methyl spectra. However, the collective behaviour is still important for the value of the tunnelling splitting. Therefore, the interpretation of such a spectrum in terms of single-methyl tunnelling is obvious but misleading with respect to the potential seen by a methyl group in the crystal.     

Phase modulation in dipolar-coupled A2 spin systems: effect of maximum state mixing in 1H NMR in vivo

Coupling constants of nuclear spin systems can be determined from phase modulation of multiplet resonances. Strongly coupled systems such as citrate in prostatic tissue exhibit a more complex modulation than AX connectivities, because of substantial mixing of quantum states. An extreme limit is the coupling of n isochronous spins (An system). It is observable only for directly connected spins like the methylene protons of creatine and phosphocreatine which experience residual dipolar coupling in intact muscle tissue in vivo. We will demonstrate that phase modulation of this "pseudo-strong" system is quite simple compared to those of AB systems. Theory predicts that the spin-echo experiment yields conditions as in the case of weak interactions, in particular, the phase modulation depends linearly on the line splitting and the echo time.     

Photoemission studies of TCNQ compounds

The densities of occupied states of a series of TNCQ compounds have been determined by u.v. photoemission. A clear difference between TCNQ weak charge transfer complexes and anion radical salts including TTF-TCNQ is found. Due to strong electron-molecule coupling narrow delocalized electron bands are not observable.     

Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex core energy

In layered superconductors (SC) with small interlayer Josephson coupling vortex-antivortex phase fluctuations characteristic of quasi two-dimensional (2D) Kosterlitz-Thouless behavior are expected to be observable at some energy scale T(d). While in the 2D case T(d) is uniquely identified by the KT temperature T(KT) where the universal value of the superfluid density is reached, we show that in a generic anisotropic 3D system T(d) is controlled by the vortex-core energy, and can be significantly larger than the 2D scale T(KT). These results are discussed in relation to recent experiments in cuprates, which represent a typical experimental realization of layered anisotropic SC.     

强偶合系统的弱偶合方法处理

本文提出了强偶合系统的弱偶合方法处理。利用么正变换,把强偶合系统的哈密顿变成弱偶合系统哈密顿的形式,射频脉冲也作相同的变换,这样强偶合系统的多脉冲实验就能在弱偶合空间{φ}中计算。以AB体系的COSY和2D-J谱为例作了计算和讨论。     

Dynamics of entanglement under decoherence in noninertial frames

In this paper,we investigate the entanglement dynamics of a two-qubit entangled state coupled with its noisy environment,and plan to utilize weak measurement and quantum reversal measurement to study the entanglement dynamics under different decoherence channels in noninertial frames.Through the calculations and analyses,it is shown that the weak measurement can prevent entanglement from coupling to the amplitude damping channel,while the system is under the phase damping and flip channels.This protection protocol cannot prevent entanglement but will accelerate the death of entanglement.In addition,if the system is in the noninertial reference frame,then the effect of weak measurement will be weakened for the amplitude damping channel.Nevertheless,for other decoherence channels,the Unruh effect does not affect the quantum weak measurement,the only exception is that the maximum value of entanglement is reduced to√2/2of the original value in the inertial frames.     

Weak values of electron spin in a double quantum dot

We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure.