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It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations in this process are also presented.
For a function given by contour integral the two types (conventions) of asymptotic representations are considered: the usual representation by asymptotic series in inverse powers of large parameters and the special division of contour integral in contributions of high and low saddle points. It is shown that the width of the recessive term formation zone (Stokes strip) in the second convention is determined by uncertainty relation and is much less than the zone width in the first convention. The reasons of such a difference is clarified. The results of the work are useful for understanding of formation region of the exponentially small process arising on the background of the strong one.
A Lorentz-covariant localization for light waves is presented. The unitary representation for the electromagnetic four-potential is constructed for a monochromatic light wave. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta-t)(Delta-omega) = about 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.
Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At the microscale, another distinct possibility becomes more likely: processes where no entropy is produced overall. In this work, we explore the constraints imposed by such null-entropy events on the fluctuations of thermodynamic currents. By incorporating the probability of null-entropy events, we obtain tighter bounds on finite-time thermodynamic uncertainty relations derived from fluctuation theorems. We validate this framework using an example of a qudit SWAP engine.
The proceedings from the workshop are presented, and the focus was on the application of squeezed states. There are many who say that the potential for industrial applications is enormous, as the history of the conventional laser suggests. All those who worked so hard to produce squeezed states of light are continuing their efforts to construct more efficient squeezed-state lasers. Quite naturally, they are looking for new experiments using these lasers. The physical basis of squeezed states is the uncertainty relation in Fock space, which is also the basis for the creation and annihilation of particles in quantum field theory. Indeed, squeezed states provide a unique opportunity for field theoreticians to develop a measurement theory for quantum field theory.
Two illustrative examples are given for Feynman's rest of the universe. The first example is the two-mode squeezed state of light where no measurement is taken for one of the modes. The second example is the relativistic quark model where no measurement is possible for the time-like separation fo quarks confined in a hadron. It is possible to illustrate these examples using the covariant oscillator formalism. It is shown that the lack of symmetry between the position-momentum and time-energy uncertainty relations leads to an increase in entropy when the system is different Lorentz frames.
A generalization of the entropic formulation of the Uncertainty Principle of Quantum Mechanics is considered with the introduction of the q-entropies recently proposed by Tsallis. The concomitant generalized measure is illustrated for the case of phase and number operators in quantum optics. Interesting results are obtained when making use of q-entropies as the basis for constructing generalized entropic uncertainty measures.
Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.
Forward GEOS-5 AGCM simulations of CO2, with transport constrained by analyzed meteorology for 2009-2010, are examined. The CO2 distributions are evaluated using AIRS upper tropospheric CO2 and ACOS-GOSAT total column CO2 observations. Different combinations of surface C02 fluxes are used to generate ensembles of runs that span some uncertainty in surface emissions and uptake. The fluxes are specified in GEOS-5 from different inventories (fossil and biofuel), different data-constrained estimates of land biological emissions, and different data-constrained ocean-biology estimates. One set of fluxes is based on the established "Transcom" database and others are constructed using contemporary satellite observations to constrain land and ocean process models. Likewise, different approximations to sub-grid transport are employed, to construct an ensemble of CO2 distributions related to transport variability. This work is part of NASA's "Carbon Monitoring System Flux Pilot Project,"
We discussed how much information is lost when a particle is in equilibrium with the thermal reservoir of temperature T = 1/beta. The universal temperature correction to the r.h.s. of U(X,P:psi) greater than or = 1 + ln(pi) is determined. For this purpose, it is convenient to employ the framework of thermo-field dynamics (TFD). This formulation of finite-temperature (T not = 0) quantum theory utilizes the doubled Hilbert space, the normal operator (A) acting on the objective space, and its corresponding tildian operator on the fictitious space. The physical probability density associated with the measurement of the normal operator, A, is given, and the information entropy at T not = 0 is defined. The results describe how the thermal disturbance effects in S sub X or S sub P (delta X or delta P) can be suppressed by squeezing with keeping U = S sub X + S sub P (delta X x delta P) its minimum value.
The notion of squeezing in spin systems is clarified, and the principle for spin squeezing is shown. Two twisting schemes are proposed as building blocks for spin squeezing and are shown to reduce the standard quantum noise, s/2, of the coherent S-spin state down to the order of S(sup 1/3) and 1/2. Applications to partition noise suppression are briefly discussed.
Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have.
The purpose of these workshops is to bring together an international selection of scientists to discuss the latest developments in Squeezed States in various branches of physics, and in the understanding of the foundations of quantum mechanics. At the third workshop, special attention was given to the influence that quantum optics is having on our understanding of quantum measurement theory. The fourth meeting in this series will be held in the People's Republic of China.
This paper explores the challenges in neutrino detection and emphasizes the importance of understanding the ICARUS neutrino detector. It delves into the use of cosmic rays to bridge the gap between experimental and theoretical data, offering insights into the behavior of different components of neutrino detectors. This procedure sheds light on the intricate aspects of cosmic ray detection in ICARUS, contributing to an increased understanding of how this detector's uncertainties operate. More can be learned about neutrino physics in future experiments through this understanding.
This paper explores the challenges in neutrino detection and emphasizes the importance of understanding the ICARUS neutrino detector. It delves into the use of cosmic rays to bridge the gap between experimental and theoretical data, offering insights into the behavior of different components of neutrino detectors. This procedure sheds light on the intricate aspects of cosmic ray detection in ICARUS, contributing to an increased understanding of how this detector's uncertainties operate. More can be learned about neutrino physics in future experiments through this understanding.
Relative error is discussed in light of a proposed orbiter mission to Venus. It is hypothesized that the relative (position) error of the orbiting spacecraft between disjoint data sets will be large because of residual uncertainties of the absolute estimates and their decorrelation caused by succeeding estimates. A method is proposed to limit relative error by inducing correlations between the estimates on successive data arcs. These correlations are induced by overlapping the data arcs. Covariance analyses of the data sets are undertaken at two distinct mapping times, yielding the relative error between those mapping times. The technique is applied to a mosaicking problem on a specific day in the mission.
Nomographs were developed for relating uncertainty in temperature T to uncertainty in the observed height profiles of both pressure p and density rho. The relative uncertainty delta T/T is seen to depend not only upon the relative uncertainties delta P/P or delta rho/rho, and to a small extent upon the value of T or H, but primarily upon the sampling-height increment Delta h, the height increment between successive observations of p or delta. For a fixed value of delta p/p, the value of delta T/T varies inversely with Delta h. No limit exists in the fineness of usable height resolution of T which may be derived from densities, while a fine height resolution in pressure-height data leads to temperatures with unacceptably large uncertainties.
A graph was developed for relating delta T/T, the relative uncertainty in atmospheric temperature T, to delta p/p, the relative uncertainty in the atmospheric pressure p, for situations, when T is derived from the slope of the pressure-height profile. A similar graph relates delta T/T to delta roh/rho, the relative uncertainty in the atmospheric density rho, for those cases when T is derived from the downward integration of the density-height profile. A comparison of these two graphs shows that for equal uncertainties in the respective basic parameters, p or rho, smaller uncertainties in the derived temperatures are associated with density-height rather than with pressure-height data. The value of delta T/T is seen to depend not only upon delta p or delta rho, and to a small extent upon the value of T or the related scale height H, but also upon the inverse of delta h, the height increment between successive observations of p or rho. In the case of pressure-height data, delta T/T is dominated by 1/delta h for all values of delta h; for density-height data, delta T/T is dominated by delta rho/rho for delta h smaller than about 5 km. In the case of T derived from density-height data, this inverse relationship between delta T/T and delta h applies only for large values of delta h, that is, for delta h 35 km. No limit exists in the fineness of usable height resolution of T which may be derived from densities, while a fine height resolution in pressure-height data leads to temperature with unacceptably large uncertainties.