Strong coupling between whispering gallery modes and chromium ions in ruby

Farr, Warrick G.; Goryachev, Maxim; Creedon, Daniel L.; Tobar, Michael E.

doi:10.1103/physrevb.90.054409

Cited by 24 publications

(25 citation statements)

References 17 publications

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“…It has been shown previously [5] that a standard model of two interacting harmonic oscillators can accurately determine the coupling values from such avoided crossings. However, we observe strong distortion around 0 T, and also an asymmetry of the mode splittings about the central magnon resonances due to the ultrastrong coupling of the photon modes to the magnon modes, as was observed previously in Ruby [29]. There-Frequency (GHz) Magnetic Field (T) 3 4 5 6 7…”

Section: Experimental Observationssupporting

confidence: 76%

“…In order to investigate this regime we use common microwave spectroscopy techniques [5,23,[25][26][27][28] to directly observe the mode splitting caused by the magnon interaction to determine the coupling values. Similar systems have been extensively utilised not only in the field of spintronics to investigate the interaction between microwave photons and paramagnetic spin ensembles [25][26][27][28][29], but also to realise optical comb generation [30], ultra-low threshold lasing [31] measurement of optomechanical systems [32,33], and extremely stable cryogenic sapphire oscillator clock technology [34,35]. To date, exciting internal, highly-confined photonic modes in a YIG sphere has only recently been demonstrated in the optical regime using Whispering Gallery Modes (WGM) [10,11] but has never before been achieved in the microwave domain.…”

Section: Introductionmentioning

confidence: 99%

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Ultrahigh cooperativity interactions between magnons and resonant photons in a YIG sphere

et al. 2016

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Resonant photon modes of a 5mm diameter YIG sphere loaded in a cylindrical cavity in the 10-30GHz frequency range are characterised as a function of applied DC magnetic field at millikelvin temperatures. The photon modes are confined mainly to the sphere, and exhibited large mode filling factors in comparison to previous experiments, allowing ultrastrong coupling with the magnon spin wave resonances. The largest observed coupling between photons and magnons is 2g/2π = 7.11 GHz for a 15.5 GHz mode, corresponding to a cooperativity of C = 1.51±0.47×10 7 . Complex modifications beyond a simple multi-oscillator model, of the photon mode frequencies were observed between 0 and 0.1 Tesla. Between 0.4 to 1 Tesla, degenerate resonant photon modes were observed to interact with magnon spin wave resonances with different couplings strengths, indicating time reversal symmetry breaking due to the gyrotropic permeability of YIG. Bare dielectric resonator mode frequencies were determined by detuning magnon modes to significantly higher frequencies with strong magnetic fields. By comparing measured mode frequencies at 7 Tesla with Finite Element modelling, a bare dielectric permittivity of 15.96 ± 0.02 of the YIG crystal has been determined at about 20mK.

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Section: Experimental Observationssupporting

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Ultrahigh cooperativity interactions between magnons and resonant photons in a YIG sphere

et al. 2016

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“…We sample in the system frame (Farr et al 2014b), where the binary is parametrised by the masses and spin magnitudes of the two component BHs {mi} and {χi}, the spin misalignment angles {θi}, the angle ∆Φ between the projections of the two spins on the orbital plane, and the angle β between the total and orbital angular momentum vectors. We find, in agreement with similar studies such as Littenberg et al (2015) and , that there is a strong preference for detecting GWs from nearly faceon binaries, since GW emission is strongest perpendicular to the orbital plane.…”

Section: Signal Analysis and Inferencementioning

confidence: 99%

Hierarchical analysis of gravitational-wave measurements of binary black hole spin–orbit misalignments

Stevenson

Berry

Mandel

2017

Monthly Notices of the Royal Astronomical Society

215

205

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Binary black holes may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the black hole spins and the orbital angular momentum. Gravitational waves from these systems directly encode information about the spin-orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution. We simulate a mixed population of binary black holes with spin-orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. Assuming a population with dimensionless spin magnitudes of χ = 0.7, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With 100 observations it will be possible to infer the relative fraction of coalescing binary black holes with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of ∼ 40%. Meanwhile, only ∼ 5 observations are sufficient to distinguish between extreme models-all binary black holes either having exactly aligned spins or isotropic spin directions.

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“…This is E-mail: c.matthews@uchicago.edu particularly true when the low-probability tails of the distribution contribute significantly to the integral of eq. 1 and when π(x) is multi-modal, as is often the case in astrophysical applications in multi-dimensional spaces (e.g., Farr et al 2014). For example, in sampling a Bayesian posterior in a statistical analysis, one may be interested in robust determination of credible regions up to highlevels (e.g., 99.99%) to evaluate the level of discrepancy with theoretical prediction or with another measurement.…”

Section: Introductionmentioning

confidence: 99%

Umbrella sampling: a powerful method to sample tails of distributions

Matthews

Weare

Kravtsov

et al. 2018

Monthly Notices of the Royal Astronomical Society

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We present the umbrella sampling (US) technique and show that it can be used to sample extremely low probability areas of the posterior distribution that may be required in statistical analyses of data. In this approach sampling of the target likelihood is split into sampling of multiple biased likelihoods confined within individual umbrella windows. We show that the US algorithm is efficient and highly parallel and that it can be easily used with other existing MCMC samplers. The method allows the user to capitalize on their intuition and define umbrella windows and increase sampling accuracy along specific directions in the parameter space. Alternatively, one can define umbrella windows using an approach similar to parallel tempering. We provide a public code that implements umbrella sampling as a standalone python package. We present a number of tests illustrating the power of the US method in sampling low probability areas of the posterior and show that this ability allows a considerably more robust sampling of multi-modal distributions compared to the standard sampling methods. We also present an application of the method in a real world example of deriving cosmological constraints using the supernova type Ia data. We show that umbrella sampling can sample the posterior accurately down to the ≈ 15σ credible region in the Ω m − Ω Λ plane, while for the same computational work the affine-invariant MCMC sampling implemented in the emcee code samples the posterior reliably only to ≈ 3σ.

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Strong coupling between whispering gallery modes and chromium ions in ruby

Cited by 24 publications

References 17 publications

Ultrahigh cooperativity interactions between magnons and resonant photons in a YIG sphere

Ultrahigh cooperativity interactions between magnons and resonant photons in a YIG sphere

Hierarchical analysis of gravitational-wave measurements of binary black hole spin–orbit misalignments

Umbrella sampling: a powerful method to sample tails of distributions

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