Coherent Phenomena in Systems Interacting With Resonant Radiation

Novikov, L. N.; Pokazan'ev, V. G.; Skrotskiǐ, G. V.

doi:10.1070/pu1970v013n03abeh004259

Cited by 15 publications

(5 citation statements)

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“…For both magnetometer cells only B 1 -field strength and laser detuning play remarkable roles. This resonance broadening by the B 1 field is well known [16,33,46,47]. The weighting of the laser detuning is stronger for the medium-pressure cell, what once again reflects the more pronounced influence of the single absorption lines in this case.…”

Section: Complete Lsd-mz Parameter Characterizationsupporting

confidence: 56%

An Optically Pumped Magnetometer Working in the Light-Shift Dispersed Mz Mode

Schultze

Schillig

IJsselsteijn³

et al. 2017

Sensors

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We present an optically pumped magnetometer working in a new operational mode—the light-shift dispersed Mz (LSD-Mz) mode. It is realized combining various features; (1) high power off-resonant optical pumping; (2) Mz configuration, where pumping light and magnetic field of interest are oriented parallel to each other; (3) use of small alkali metal vapor cells of identical properties in integrated array structures, where two such cells are pumped by circularly polarized light of opposite helicity; and (4) subtraction of the Mz signals of these two cells. The LSD-Mz magnetometer’s performance depends on the inherent and very complex interplay of input parameters. In order to find the configuration of optimal magnetometer resolution, a sensitivity analysis of the input parameters by means of Latin Hypercube Sampling was carried out. The resulting datasets of the multi-dimensional parameter space exploration were assessed by a subsequent physically reasonable interpretation. Finally, the best shot-noise limited magnetic field resolution was determined within that parameter space. As the result, using two 50 mm3 integrated vapor cells a magnetic field resolution below 10 fT/√Hz at Earth’s magnetic field strength is possible.

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Section: Complete Lsd-mz Parameter Characterizationsupporting

confidence: 56%

An Optically Pumped Magnetometer Working in the Light-Shift Dispersed Mz Mode

Schultze

Schillig

IJsselsteijn³

et al. 2017

Sensors

View full text Add to dashboard Cite

show abstract

“…As a consequence of the used methodology, it turns out that the collapse problem comes with a mathematically convergent description, thereby establishing a new class of exact analytical solutions for the cosmological fluid equations. Generally, exact analytical solutions to the fluid equations are a very rare-case scenario; so far the only known exact solutions are those for one-dimensional (Novikov 1970;Zel'dovich 1970) and quasi-one-dimensional collapse (Rampf & Frisch 2017).…”

Section: Introductionmentioning

confidence: 99%

Quasi-spherical collapse of matter in ΛCDM

Rampf

2019

Monthly Notices of the Royal Astronomical Society

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We report the findings of new exact analytical solutions to the cosmological fluid equations, namely for the case where the initial conditions are perturbatively close to a spherical tophat profile. To do so we enable a fluid description in a Lagrangian-coordinates approach, and prove the convergence of the Taylor-series representation of the Lagrangian displacement field until the time of collapse ("shell-crossing"). This allows the determination of the time for quasi-spherical collapse, which is shown to happen generically earlier than in the spherical case. For pedagogical reasons, calculations are first given for a spatially flat universe that is only filled with a non-relativistic component of cold dark matter (CDM). Then, the methodology is updated to a ΛCDM Universe, with the inclusion of a cosmological constant Λ > 0.

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“…To lowest (zeroth) order in ǫ, the problem is exactly onedimensional and has the initial condition ϕ (init) g (q1, q2, q3) = − cos q1. In this instance, as is well known, the Zel'dovich approximation is exact until shell-crossing (Novikov 1970;Zel'dovich 1970). In Lagrangian coordinates, this is particularly obvious.…”

Section: Lagrangian Equations To Zeroth Order In ǫmentioning

confidence: 86%

“…When the problem is exactly 1D, the fluid equations become linear when expressed in Lagrangian coordinates. As a consequence, the linear Lagrangian solution solves the fully non-linear problem in 1D (Novikov 1970;Zentsova & Chernin 1980). Expressed in comoving coordinates and enabling the linear growth time τ (see below for details), the resulting Lagrangian map is in one spatial dimension exactly…”

Section: Introductionmentioning

confidence: 99%

Shell-crossing in quasi-one-dimensional flow

Rampf

Frisch

2017

Monthly Notices of the Royal Astronomical Society

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Blow-up of solutions for the cosmological fluid equations, often dubbed shell-crossing or orbit crossing, denotes the breakdown of the single-stream regime of the cold-dark-matter fluid. At this instant, the velocity becomes multi-valued and the density singular. Shell-crossing is well understood in one dimension (1D), but not in higher dimensions. This paper is about quasione-dimensional (Q1D) flow that depends on all three coordinates but differs only slightly from a strictly 1D flow, thereby allowing a perturbative treatment of shell-crossing using the Euler-Poisson equations written in Lagrangian coordinates. The signature of shell-crossing is then just the vanishing of the Jacobian of the Lagrangian map, a regular perturbation problem. In essence the problem of the first shell-crossing, which is highly singular in Eulerian coordinates, has been desingularized by switching to Lagrangian coordinates, and can then be handled by perturbation theory. Here, all-order recursion relations are obtained for the time-Taylor coefficients of the displacement field, and it is shown that the Taylor series has an infinite radius of convergence. This allows the determination of the time and location of the first shell-crossing, which is generically shown to be taking place earlier than for the unperturbed 1D flow.The time variable used for these statements is not the cosmic time t but the linear growth time τ ∼ t 2/3 . For simplicity, calculations are restricted to an Einstein-de Sitter universe in the Newtonian approximation, and tailored initial data are used. However it is straightforward to relax these limitations, if needed.

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Coherent Phenomena in Systems Interacting With Resonant Radiation

Cited by 15 publications

References 1 publication

An Optically Pumped Magnetometer Working in the Light-Shift Dispersed Mz Mode

An Optically Pumped Magnetometer Working in the Light-Shift Dispersed Mz Mode

Quasi-spherical collapse of matter in ΛCDM

Shell-crossing in quasi-one-dimensional flow

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