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Atacama Cosmology Telescope: DR6 gravitational lensing and SDSS BOSS cross-correlation measurement and constraints on gravity with the 𝐸 𝐺 statistic

We derive new constraints on the 𝐸 𝐺 statistic as a test of gravity, combining the cosmic microwave background (CMB) lensing map estimated from Data Release 6 (DR6) of the Atacama Cosmology Telescope with Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (SDSS BOSS) CMASS and LOWZ galaxy data. We develop an analysis pipeline to measure the cross-correlation between CMB lensing maps and galaxy data, following a blinding policy and testing the approach through null and consistency checks. By testing the equivalence of the spatial and temporal gravitational potentials, the 𝐸 𝐺 statistic can distinguish Λ⁢ CDM from alternative models of gravity. We find 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢1$^{+0.06}_{−0.05}$ for Atacama Cosmology Telescope (ACT) and CMASS data at 68.28% confidence level, and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢9$^{+0.14}_{−0.11}$ for the ACT and LOWZ. Systematic errors are estimated to be 3% and 4%, respectively. Including CMB lensing information from Planck PR4 results in 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢4$^{+0.05}_{−0.05}$ with CMASS and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢3$^{+0.11}_{−0.09}$ with LOWZ. These are consistent with predictions for the Λ⁢ CDM model that best fits the Planck CMB anisotropy and SDSS BOSS baryon acoustic oscillations (BAO), where 𝐸$^{GR}_{𝐺⁡}$(𝑧 eff =0.555) =0.401 ± 0.005 for CMB lensing combined with CMASS and 𝐸$^{GR}_{𝐺}$⁡(𝑧 eff = 0.316) = 0.452 ± 0.005 combined with LOWZ. We also find 𝐸 𝐺 to be scale independent, with probability to exceed >5%, as predicted by general relativity. The methods developed in this work are also applicable to improved future analyses with upcoming spectroscopic galaxy samples and CMB lensing measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

BICEP/ Keck XVIII: Measurement of BICEP3 polarization angles and consequences for constraining cosmic birefringence and inflation

We use a custom-made calibrator to measure individual detectors’ polarization angles of BICEP3, a small aperture telescope observing the cosmic microwave background (CMB) at 95 GHz from the South Pole. We describe our calibration strategy and the statistical and systematic uncertainties associated with the measurement. We reach an unprecedented precision for such measurement on a CMB experiment, with a repeatability for each detector pair of 0.02°. Here, we show that the relative angles measured using this method are in excellent agreement with those extracted from CMB data. Because the absolute measurement is currently limited by a systematic uncertainty, we do not derive cosmic birefringence constraints from BICEP3 data in this work. Rather, we forecast the sensitivity of BICEP3 sky maps for such analysis. We investigate the relative contributions of instrument noise, lensing, and dust, as well as astrophysical and instrumental systematics. We also explore the constraining power of different angle estimators, depending on analysis choices. We establish that the BICEP3 2-year dataset (2017–2018) has an on-sky sensitivity to the cosmic birefringence angle of 𝜎 𝛼 = 0.07⁢8°, which could be improved to 𝜎 𝛼 = 0.05⁢5° by adding all of the existing BICEP3 data (through 2023). Furthermore, we emphasize the possibility of using the BICEP3 sky patch as a polarization calibration source for CMB experiments, which with the present data could reach a precision of 0.035°. Finally, in the context of inflation searches, we investigate the impact of detector-to-detector variations in polarization angles as they may bias the tensor-to-scalar ratio 𝑟. We show that while the effect is expected to remain subdominant to other sources of systematic uncertainty, it can be reliably calibrated using polarization angle measurements such as the ones we present in this paper.

Cosmic microwave background↗

Multiprobe cosmology from the abundance of SPT clusters and DES galaxy clustering and weak lensing

Cosmic shear, galaxy clustering, and the abundance of massive halos each probe the large-scale structure of the Universe in complementary ways. We present cosmological constraints from the joint analysis of the three probes, building on the latest analyses of the lensing-informed abundance of clusters identified by the South Pole Telescope (SPT) and of the auto- and cross-correlation of galaxy position and weak lensing measurements (3 × 2 ⁢pt) in the Dark Energy Survey (DES). We consider the cosmological correlation between the different tracers and we account for the systematic uncertainties that are shared between the large-scale lensing correlation functions and the small-scale lensing-based cluster mass calibration. Marginalized over the remaining Λ cold dark matter (Λ ⁢CDM) parameters (including the sum of neutrino masses) and 52 astrophysical modeling parameters, we measure Ω m = 0.300 ± 0.017 and 𝜎 8 = 0.797 ± 0.026. Compared to constraints from Planck primary cosmic microwave background (CMB) anisotropies, our constraints are only 15% wider with a probability to exceed of 0.22 (1.2⁢𝜎) for the two-parameter difference. We further obtain 𝑆 8 ≡𝜎 8 ⁢(Ω m /0.3) 0.5 = 0.796 ± 0.013 which is lower than the Planck measurement at the 1.6⁢𝜎 level. The combined SPT cluster, DES 3 ×2 ⁢pt, and Planck datasets mildly prefer a nonzero positive neutrino mass, with a 95% upper limit ∑ 𝑚 𝜈 < 0.25 eV on the sum of neutrino masses. Assuming a 𝑤⁢CDM model, we constrain the dark energy equation of state parameter 𝑤 = −1.1⁢5$^{+0.23}_{−0.17}$ and when combining with Planck primary CMB anisotropies, we recover 𝑤 = −1.2⁢0$^{+0.15}_{−0.09}$, a 1.7⁢𝜎 difference with a cosmological constant. The precision of our results highlights the benefits of multiwavelength multiprobe cosmology and our analysis paves the way for upcoming joint analyses of next-generation datasets.

79 ASTRONOMY AND ASTROPHYSICS↗

Atacama Cosmology Telescope: Multiprobe cosmology with unWISE galaxies and ACT DR6 CMB lensing

We present a joint analysis of the cosmic microwave background (CMB) lensing power spectra measured from the Data Release 6 of the Atacama Cosmology Telescope (ACT) and Planck PR4, cross-correlations between the ACT and Planck lensing reconstruction and galaxy clustering from unWISE, and the unWISE clustering auto-spectrum. We obtain 1.5% constraints on the matter density fluctuations at late times parametrized by the best constrained parameter combination 𝑆$^{3⁢x⁢2⁢pt}_{8}$ ≡ 𝜎 8 ⁢(Ω 𝑚 /0.3) 0.4 = 0.815 ± 0.012. The commonly used 𝑆 8 ≡ 𝜎 8⁢ (Ω 𝑚 /0.3) 0.5 parameter is constrained to 𝑆 8 = 0.816 ± 0.015. In combination with baryon acoustic oscillation (BAO) measurements we find 𝜎 8 = 0.815 ± 0.012. We also present sound-horizon-independent estimates of the present day Hubble rate of 𝐻 0 = 66.4$^{+3.2}_{−3.7}$ km s −1 Mpc −1 from our large scale structure data alone and 𝐻 0 = 64.3$^{+2.1}_{−2.4}$ km s −1 Mpc −1 in combination with uncalibrated supernovae from Pantheon+. Using parametric estimates of the evolution of matter density fluctuations, we place constraints on cosmic structure in a range of high redshifts typically inaccessible with cross-correlation analyses. Combining lensing cross- and autocorrelations, we derive a 3.3% constraint on the integrated matter density fluctuations above 𝑧 = 2.4, one of the tightest constraints in this redshift range and fully consistent with a Λ cold dark matter (Λ⁢CDM) model fit to the primary CMB from Planck. Finally, combining with primary CMB observations and using the extended low redshift coverage of these combined datasets we derive constraints on a variety of extensions to the Λ⁢CDM model including massive neutrinos, spatial curvature, and dark energy. We find in flat Λ⁢CDM⁢ ∑𝑚 𝜈 < 0.12 eV at 95% confidence using the large scale structure data, BAO measurements from Sloan Digital Sky Survey, and primary CMB observations.

79 ASTRONOMY AND ASTROPHYSICS↗

Atacama Cosmology Telescope DR6 and DESI: Structure growth measurements from the cross-correlation of DESI legacy imaging galaxies and CMB lensing from ACT DR6 and 𝑃⁢𝑙⁢𝑎⁢𝑛⁢𝑐⁢𝑘 PR4

We measure the growth of cosmic density fluctuations on large scales and across the redshift range 0.3 < 𝑧 < 0.8 through galaxy clustering and the cross-correlation of the ACT data release 6 cosmic microwave background (CMB) lensing map and galaxies from the Dark Energy Spectroscopic Instrument Legacy Survey, using three galaxy samples spanning the redshifts of 0.3 ≲ 𝑧 ≲ 0.45, 0.45 ≲ 𝑧 ≲ 0.6, 0.6 ≲ 𝑧 ≲ 0.8. We adopt a scale cut where nonlinear effects are negligible, so that the cosmological constraints are derived from the linear regime. We determine the amplitude of matter fluctuations over all three redshift bins using Atacama Cosmology Telescope (ACT) data alone to be 𝑆 8 ≡ 𝜎 8 ⁢(Ω 𝑚 /0.3) 0.5 =0.772 ± 0.040 in a joint analysis combining the three redshift bins and ACT lensing alone. Using a combination of ACT and Planck data we obtain 𝑆 8 = 0.765 ± 0.032. The lowest redshift bin used is the least constraining and exhibits a ∼2⁢𝜎 tension with the other redshift bins; thus we also report constraints excluding the first redshift bin, giving 𝑆 8 = 0.785 ± 0.033 for the combination of ACT and Planck. This result is in excellent agreement at the 0.3⁢𝜎 level with measurements from galaxy lensing, but is 1.8⁢𝜎 lower than predictions based on Planck primary CMB data. Understanding whether this hint of discrepancy in the growth of structure at low redshifts arises from a fluctuation, from systematics in data, or from new physics is a high priority for forthcoming CMB lensing and galaxy cross-correlation analyses.

cosmic microwave background↗

Tuning of strong nonlinearity in radio-frequency superconducting-quantum-interference-device meta-atoms

Strong nonlinearity of a self-resonant radio-frequency (rf) superconducting-quantum-interference-device (SQUID) meta-atom is explored via intermodulation (IM) measurements. Previous work in zero dc magnetic flux showed a sharp onset of IM response as the frequency sweeps through the resonance. A second onset at higher frequency was also observed, creating a prominent gap in the IM response. By extending those measurements to nonzero dc flux, different dynamics are revealed, including dc flux tunability of the aforementioned gaps and enhanced IM response near geometric resonance of the rf SQUID. These features observed experimentally are understood and analyzed theoretically through a combination of a steady-state analytical modeling and a full numerical treatment of the rf SQUID dynamics. The latter in addition predicts the presence of chaos in narrow parameter regimes. Here, the understanding of intermodulation in rf SQUID metamaterials is important for producing low-noise amplification of microwave signals and tunable filters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Dark Photon Oscillations in Our Inhomogeneous Universe

A dark photon kinetically mixing with the ordinary photon represents one of the simplest viable extensions to the standard model, and would induce oscillations with observable imprints on cosmology. Oscillations are resonantly enhanced if the dark photon mass equals the ordinary photon plasma mass, which tracks the free electron number density. Previous studies have assumed a homogeneous Universe; in this Letter, we introduce for the first time an analytic formalism for treating resonant oscillations in the presence of inhomogeneities of the photon plasma mass. We apply our formalism to determine constraints from cosmic microwave background photons oscillating into dark photons, and from heating of the primordial plasma due to dark photon dark matter converting into low-energy photons. Including the effect of inhomogeneities demonstrates that prior homogeneous constraints are not conservative, and simultaneously extends current experimental limits into a vast new parameter space.

79 ASTRONOMY AND ASTROPHYSICS↗

Photon-Instanton Collider Implemented by a Superconducting Circuit

Instantons, spacetime-localized quantum field tunneling events, are ubiquitous in correlated condensed matter and high-energy systems. However, their direct observation through collisions with conventional particles has not been considered possible. We show how recent advances in circuit quantum electrodynamics, specifically, the realization of galvanic coupling of a transmon qubit to a high-impedance transmission line, allows the observation of inelastic collisions of single microwave photons with instantons (phase slips). We develop a formalism for calculating the photon-instanton cross section, which should be useful in other quantum field theoretical contexts. In particular, we show that the inelastic scattering probability can significantly exceed the effect of conventional Josephson quartic anharmonicity and reach order-unity values.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Inelastic Scattering of a Photon by a Quantum Phase Slip

Spontaneous decay of a single photon is a notoriously inefficient process in nature irrespective of the frequency range. We report that a quantum phase-slip fluctuation in high-impedance superconducting waveguides can split a single incident microwave photon into a large number of lower-energy photons with a near unit probability. The underlying inelastic photon-photon interaction has no analogs in non-linear optics. Instead, the measured decay rates are explained without adjustable parameters in the framework of a new model of a quantum impurity in a Luttinger liquid. Our result connects circuit quantum electrodynamics to critical phenomena in two-dimensional boundary quantum field theories, important in the physics of strongly-correlated systems. Here, the photon lifetime data represents a rare example of verified and useful quantum many-body simulation.

1-dimensional systems↗

Symmetry of Cosmological Observables, a Mirror World Dark Sector, and the Hubble Constant

We find that a uniform scaling of the gravitational free-fall rates and photon-electron scattering rate leaves most dimensionless cosmological observables nearly invariant. This result opens up a new approach to reconciling cosmic microwave background and large-scale structure observations with high values of the Hubble constant H0: Find a cosmological model in which the scaling transformation can be realized without violating any measurements of quantities not protected by the symmetry. A “mirror world” dark sector allows for effective scaling of the gravitational free-fall rates while respecting the measured mean photon density today. Further model building might bring consistency with the two constraints not yet satisfied: the inferred primordial abundances of deuterium and helium.

79 ASTRONOMY AND ASTROPHYSICS↗

Evidence for Suppression of Structure Growth in the Concordance Cosmological Model

We present evidence for a suppressed growth rate of large-scale structure during the dark-energy dominated era. Modeling the growth rate of perturbations with the ``growth index'' γ, we find that current cosmological data strongly prefer a higher growth index than the value γ=0.55 predicted by general relativity in a flat ΛCDM cosmology. Both the cosmic microwave background data from Planck and the large-scale structure data from weak lensing, galaxy clustering, and cosmic velocities separately favor growth suppression. When combined, they yield γ = 0.633$^{+0.025}_{–0.024}$, excluding γ = 0.55 at a statistical significance of 3.7σ. The combination of fσ8 and Planck measurements prefers an even higher growth index of γ = 0.639$^{+0.024}_{–0.025}$, corresponding to a 4.2σ-tension with the concordance model. In Planck data, the suppressed growth rate offsets the preference for nonzero curvature and fits the data equally well as the latter model. Furthermore, a higher γ leads to a higher matter fluctuation amplitude S 8 inferred from galaxy clustering and weak lensing measurements, and a lower S 8 from Planck data, effectively resolving the S 8 tension.

79 ASTRONOMY AND ASTROPHYSICS↗

New Probe of the High- z Baryon Acoustic Oscillation Scale: BAO Tomography with CMB × LIM -Nulling Convergence

Standard rulers such as the baryon acoustic oscillation (BAO) scale serve as workhorses for precision tests of cosmology, enabling distance measurements that probe the geometry and expansion history of our Universe. Aside from BAO measurements from the cosmic microwave background (CMB), most standard ruler techniques operate at relatively low redshifts and depend on biased tracers of the matter density field. In a companion paper, we explored the scientific reach of nulling estimators, where CMB lensing convergence maps are cross-correlated with linear combinations of similar maps from line intensity mapping (LIM) to precisely null out the low-redshift contributions to CMB lensing. We showed that nulling estimators can be used to constrain the high redshift matter power spectrum and showed that this spectrum exhibits discernible BAO features. Here we propose using these features as a standard ruler at high redshifts that does not rely on biased tracers. Forecasting such a measurement at z ~ 5, we find that next-generation instruments will be able to constrain the BAO scale to 7.2% precision, while our futuristic observing scenario can constrain the BAO scale to 4% precision. In conclusion, this constitutes a fundamentally new kind of BAO measurement during early epochs in our cosmic history.

79 ASTRONOMY AND ASTROPHYSICS↗

Finite Bubble Statistics Constrain Late Cosmological Phase Transitions

We consider first order cosmological phase transitions (PTs) happening at late times below standard model temperatures T PT ≲ GeV. The inherently stochastic nature of bubble nucleation and the finite number of bubbles associated with a late-time PT lead to superhorizon fluctuations in the PT completion time. We compute how such fluctuations eventually source curvature fluctuations with universal properties, independent of the microphysics of the PT dynamics. Using cosmic microwave background (CMB) and large scale structure measurements, we constrain the energy released in a dark-sector PT. For 0.1 eV ≲ T PT ≲ keV this constraint is stronger than both the current bound from additional neutrino species Δ⁢N eff , and in some cases, even CMB-S4 projections. Future measurements of CMB spectral distortions and pulsar timing arrays will also provide competitive sensitivity for keV ≲ T PT ≲ GeV.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraints on Local Primordial Non-Gaussianity with 3D Velocity Reconstruction from the Kinetic Sunyaev-Zeldovich Effect

The cosmic velocity field is an unbiased probe of the total matter distribution but is challenging to measure directly at intermediate and high redshifts. The large-scale velocity field imprints a signal in the cosmic microwave background (CMB) through the kinetic Sunyaev-Zeldovich (kSZ) effect. We perform the first 3D reconstruction of the large-scale velocity field from the kSZ effect by applying a quadratic estimator to CMB temperature maps and the 3D positions of galaxies. We do so by combining CMB data from the fifth data release of the Atacama Cosmology Telescope (in combination with Planck) and a spectroscopic galaxy sample from the Sloan Digital Sky Survey. We then measure the galaxy-velocity cross-power spectrum and detect the presence of the kSZ signal at a signal-to-noise ratio of 7.2⁢𝜎. Using this galaxy-velocity cross-correlation alone, we constrain the amplitude of local primordial non-Gaussianity finding 𝑓 NL =−9⁢0$^{+210}_{−350}$. In conclusion, this pathfinder measurement sets the stage for joint galaxy-CMB kSZ constraints to significantly enhance the 𝑓 NL information obtained from galaxy surveys through sample variance cancellation.

79 ASTRONOMY AND ASTROPHYSICS↗

Introducing a multiscale feature integration network for inpainting with applications to enhanced CMB map reconstruction

We introduce a novel neural network, SkyReconNet, which combines the expanded receptive fields of dilated convolutional layers along with standard convolutions, to capture both the global and local features for reconstructing the missing information in an image. We implement our network to inpaint the masked regions in a full-sky cosmic microwave background (CMB) map. Inpainting CMB maps is a particularly formidable challenge when dealing with extensive and irregular masks, such as galactic masks which can obscure substantial fractions of the sky. The hybrid design of SkyReconNet leverages the strengths of standard and dilated convolutions to accurately predict CMB fluctuations in the masked regions by effectively utilizing the information from surrounding unmasked areas. During training, the network optimizes its weights by minimizing a composite loss function that combines the structural similarity index measure (SSIM) and mean squared error (MSE). SSIM preserves the essential structural features of the CMB, ensuring an accurate and coherent reconstruction of the missing CMB fluctuations, while MSE minimizes the pixelwise deviations, thus enhancing the overall accuracy of the predictions. The predicted CMB maps and their corresponding angular power spectra align closely with the targets, achieving the performance limited only by the fundamental uncertainty of cosmic variance. The network’s generic architecture enables application to other physics-based challenges involving data with missing or defective pixels, systematic artifacts, etc. In conclusion, our results demonstrate its effectiveness in addressing the challenges posed by large irregular masks, offering a significant inpainting tool not only for CMB analyses but also for image-based experiments across disciplines where such data imperfections are prevalent.

Cosmic microwave background↗

Test of the Gravitational Force Law on Cosmological Scales Using the Kinematic Sunyaev-Zeldovich Effect

The mean pairwise velocity of massive halos reflects the gravitational force law on cosmic scales. For this work, we combine cosmic microwave background intensity maps from the Atacama Cosmology Telescope and a galaxy catalog from the Sloan Digital Sky Survey to estimate the mean pairwise velocity using the kinematic Sunyaev-Zeldovich (kSZ) effect. On scales from 30 to 230 megaparsecs, we constrain the gravitational acceleration between pairs of halos at separation 𝑟 to be 𝑔 ∝ 1/𝑟 𝑛 with 𝑛 = 2.1 ± 0.3, which is consistent with Newtonian gravity in an expanding spacetime (i.e., the standard Λ⁢ CDM model). This constraint shows agreement with an inverse quadratic radial dependence over the large distances separating galaxy halos, as expected in standard cosmology. Upcoming surveys have the potential to rule out 𝑛 = 1 at 10⁢𝜎 significance. Our results establish the kSZ effect as a powerful tool for testing gravity on cosmological scales.

alternative gravity theories↗

Multiprobe constraints on early and late time dark energy

We perform a multiprobe analysis combining cosmic microwave background (CMB) data from Planck and the Atacama Cosmology Telescope (ACT), ACT CMB lensing, and large-scale structure (LSS) measurements from the Dark Energy Spectroscopic Instrument (DESI), including DESI Legacy Imaging Survey (LS) galaxies and baryon acoustic oscillations (BAOs). We present the first 5×2 pt analysis of ACT DR6 lensing, DESI LS, and Planck Integrated Sachs-Wolfe (ISW). Within Λ⁢CDM, this yields 𝑆 8 =𝜎 8 ⁢(Ω 𝑚 /0.3) 0.5 =0.819 ±0.016, in good agreement with primary CMB inferences and provides a sound-horizon-free Hubble constant constraint of 𝐻 0 =70.0±4.4 km s −1 Mpc −1 . Then, combining with CMB primary and BAO, we reconfirm a CMB–BAO discrepancy in the Ω 𝑚 –$\frac{𝐷𝑣}{𝑟𝑑}$ plane, which is heightened when combining BAO with the 5 ×2 pt data vector. We explore two dark-energy extensions that may reconcile this: an early-time modification, early dark energy (EDE), and late-time dynamical dark energy (DDE) parametrized by 𝑤 0 ⁢𝑤 𝑎 . For CMB primary +BAO +5 ×2 pt, we find a 3.3⁢𝜎 preference for DDE over Λ⁢CDM, while EDE is modestly favored at 2.3⁢𝜎. The models address different shortcomings of Λ⁢CDM: DDE relaxes the neutrino mass bound (𝑀 𝜈 <0.17 eV vs <0.050 eV under Λ⁢CDM), making it compatible with neutrino oscillation measurements, while EDE raises the Hubble constant to 𝐻 0 =70.5±1.2 km s −1 Mpc −1 , easing the discrepancy with SH0ES. However, neither model resolves both issues simultaneously. Our analysis indicates that both DDE and EDE remain viable extensions of Λ⁢CDM within current uncertainties and demonstrates the capacity of combined probes to place increasingly stringent constraints on cosmological parameters.

79 ASTRONOMY AND ASTROPHYSICS↗

Nonequilibrium dynamics of two-level systems directly after cryogenic alternating bias

Two-level systems (TLSs) are a dominant decoherence mechanism in superconducting qubits, microwave kinetic inductance detectors, and quantum dots. TLSs are tunneling states commonly found in amorphous materials and interfaces, which interact electromechanically, leading to energy loss. Fluctuations in the frequency of the TLSs are a significant problem for qubit operation and force recalibration every few hours. In this study, we probe the effect of alternating bias at cryogenic temperatures on TLSs in a purpose-built LC oscillator. When an in situ alternating bias is applied, the steady-state spectra of the TLSs disappear. Spectroscopy reveals transient behavior, in which the TLS frequency fluctuates on the order of minutes. Thermal cycling above 10 K reverses these effects, restoring the TLS spectrum to its original state. Importantly, the intrinsic loss tangent of the LC oscillator remains unchanged before and after the application of the alternating bias. We propose that the disappearance of the steady-state spectrum is caused by nonequilibrium energy buildup from strain in the oxide film introduced by the pulsed voltage-bias sequence. Understanding this nonequilibrium energy could shed light on TLS fluctuations and reduce the calibration requirements for qubits.

general physics↗