Frequency Omega Research Articles

Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator

We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator (lambda /4 CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency omega _{textrm{cutoff}} for the coupling between the FQ and the modes in the CPWR, where the coupling grows as sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}ll 1 and decreases as 1/sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}gg 1. Here omega _n is the frequency of the nth mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above omega _{textrm{cutoff}} at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3% and the total Lamb shift from all the modes is 96.5%. This result illustrates that the coupling to the large number of modes in a CPWR yields an extremely large Lamb shift but does not suppress the qubit energy to zero, which would happen in the absence of a high-frequency cut-off.

Thermal stability with emission energy and Joule–Thomson expansion of regular BTZ-like black hole

We investigate the thermodynamic properties and Joule–Thomson expansion for conical or BTZ-like black holes. To analyze the thermal stability, we discuss the temperature and thermal stability relative to the horizon radius for different values of model parameters beta _0 and alpha _2. Moreover, we analyze thermodynamical geometries like Ruppeiner, Weinhold and Hendi Panahiyah Eslam Momennia formulation and calculate respective scalar curvatures for BTZ-like black holes. Interestingly, the black holes have no singularity in some cases, i.e., completely regular. We obtain the inversion temperatures and inversion curves and investigate the similarities and differences between van der Waals and charged fluids. To discuss this expansion, we use a BTZ-like black hole. Further, we establish the position of the inversion point versus different values of mass mu , and the parameters beta _0 and alpha _2 for such a BTZ-like black hole. The Joule–Thomson coefficient mu at this point disappears. A crucial trait upon which we relied to inspect the sign of quantity mu to get the cooling-heating areas. We also investigate the energy emission depending upon the frequency omega .

Vortex Shedding from a Microsphere Oscillating in Superfluid ^4He at mK Temperatures and from a Laser Beam Moving in a Bose–Einstein Condensate

Turbulent drag of an oscillating microsphere that is levitating in superfluid ^4He at mK temperatures, is unstable slightly above a critical velocity amplitude v_c. The lifetime tau of the turbulent state is determined by the number n of vortices shed per half-period. It is found that this number is identical to the superfluid Reynolds number. The possibility of moving a levitating sphere through superfluid ^3He at microkelvin temperatures is considered. A laser beam moving through a Bose–Einstein condensate (BEC) (as observed by other authors) also produces vortices in the BEC. In particular, in either case, a linear dependence of the shedding frequency f_v on Delta v = v - v_c is observed, where v is the velocity amplitude of the sphere or the constant velocity of the laser beam above v_c for the onset of turbulent flow: f_v = a ,Delta v, where the coefficient a is proportional to the oscillation frequency omega above some characteristic frequency omega _k and assumes a finite value for steady motion omega rightarrow 0. A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.

The investigation of low-frequency dilaton generation

The electromagnetic source of dilaton radiation is a first invariant of the electromagnetic field tensor. For electromagnetic waves, this invariant can be nonzero only in the near zone. Pulsars and magnetars are natural sources of this type. We calculated the generation of dilatons by a coherent electromagnetic field of rotating magnetic dipole moments of pulsars and magnetars. It was shown that the radiation of dilaton waves occurs at two frequencies: the rotation frequency omega of the magnetic dipole moment of the neutron star, and twice that frequency. The generation of dilatons at frequency omega is maximal when the angle between the magnetic dipole moment and the axis of its rotation is pi /4. If this angle is pi /2, then dilaton radiation at frequency omega does not occur. The generation of dilatons at frequency 2omega is maximal when the angle between the magnetic dipole and the axis of its rotation is pi /2. The angular distribution of radiation of dilatons having a frequency of omega is maximal along the conic surfaces theta =pi /4 and theta =3pi /4. The angular distribution of radiation of dilatons having a frequency of 2omega is maximal in the plane perpendicular to the axis of rotation (theta =pi /2).

Boson stars with negative Gauss–Bonnet coupling

In this paper, we discuss asymptotically flat and anti-de Sitter (AdS) boson star in (4+1)-dimensional Gauss–Bonnet gravity. We describe the dependence of the mass, the charge and the radius of the boson star on the model parameters, such as Gauss–Bonnet coupling alpha , cosmological constant Lambda and gravitational constant kappa . The basic properties of the solutions of boson stars have been studied for the different negative values of Gauss–Bonnet coupling. We found that when kappa is large and alpha is negative enough, the spiral shrinks and pulls back to the larger internal frequency omega , and there is only one branch exists. We have also observed that when kappa is small enough and if alpha is close to zero, the spiral will unfold.

Analogue of the pole-skipping phenomenon in acoustic black holes

The pole-skipping phenomenon is a special property of the retarded Green’s function of black hole perturbations. We turn to its analog in acoustic black holes, which may relate to experiments. The frequencies of these special points are located at negative integer (imaginary) Matsubara frequencies omega =-i2pi Tn, which are consistent with the imaginary frequencies of quasinormal modes (QNMs). This implies that the lower-half plane pole-skipping phenomena have the same physical meaning as the imaginary part of QNMs, which represents the dissipation of perturbation of acoustic black holes and is related to the instability time scale of perturbation.

Probing the current-phase relation in Josephson point-contact junctions between hbox {Pb}_{0.6}In_{0.4} and hbox {Ba}_{0.6}K_{0.4}(FeAs)_2 superconductors

The Josephson effect in point contacts between an “ordinary” superconductor hbox {Pb}_{0.6}In_{0.4} (T_c approx 6.6 , {mathrm {K}}) and single crystals of the Fe-based superconductor Ba_{0.6}K_{0.4}(FeAs)_2 (T_c approx 38.5 , {mathrm {K}}), was investigated. In order to shed light on the order parameter symmetry of Ba_{0.6}K_{0.4}(FeAs)_2, the dependence of the Josephson supercurrent I_s on the temperature and on sin (dvarphi ) with d = 1, 2 was studied. The dependencies of the critical current on temperature I_c (T) and of the amplitudes of the first current steps of the current–voltage characteristic i_n^{exp} (sqrt{P})(n = 0, 1, 2) on the power of microwave radiation with frequency f = (1.5 div 8), {mathrm {GHz}} were measured. It is shown that the dependencies I_c (T) are close to the well-known Ambegaokar–Baratoff (AB) dependence for tunnel contacts between “ordinary” superconductors and to the dependence calculated by Burmistrova et al. (Phys Rev B 91, 214501 (2015)) for microshorts between an “ordinary” superconductor and a two-band superconductor with s pm order parameter symmetry at certain values of the transparency of boundaries and thickness of the transition layer. It is found that the dependencies i_n^{exp} (sqrt{P}) cannot be approximated within the resistively shunted model using the normalized microwave frequencies Omega = 2 pi f / (2eV_c / hbar ) with characteristic voltages V_c = I_c R_N, (R_N—normal resistance of the contact) found from the low-voltage parts of the current–voltage characteristics. The reasons for this failure are discussed and a method is proposed for accurately determining the value of Omega, which takes into account all the features of the point contact affecting the period of the dependence i_n^{exp} (sqrt{P}). An analysis of the I_c (T) and i_n^{exp} (sqrt{P}) dependencies shows that the superconducting current of the Josephson contacts under investigation is proportional to the sin of the phase difference varphi, I_s = I_c sin(varphi ). The implications of these results on the symmetry of the order parameter are also discussed.

On the ridge of instability in ferrofluidic Couette flow via alternating magnetic field

There is a huge number of natural and industrial flows, which are subjected to time-dependent boundary conditions. The flow of a magnetic fluid under the influence of temporal modulations is such an example. Here, we perform numerical simulations of ferrofluidic Couette flow subject to time-periodic modulation (with frequency Omega _H) in a spatially homogeneous magnetic field and report how such a modulation can lead to a significant Reynolds number Re enhancement. Consider a modified Niklas approximation we explain the relation between modulation amplitude, driving frequency and stabilization effect. From this, we describe the system response around the primary instability to be sensitive/critical by an alternating field. We detected that such an alternating field provides an easy and in particular accurate controllable key parameter to trigger the system to change from subcritical to supercritical and vice versa. Our findings provide a framework to study other types of magnetic flows driven by time-dependent forcing.

Mass-selective removal of ions from Paul traps using parametric excitation

We study a method for mass-selective removal of ions from a Paul trap by parametric excitation. This can be achieved by applying an oscillating electric quadrupole field at twice the secular frequency omega _{text {sec}} using pairs of opposing electrodes. While excitation near the resonance with the secular frequency omega _{text {sec}} only leads to a linear increase of the amplitude with excitation duration, parametric excitation near 2, omega _{text {sec}} results in an exponential increase of the amplitude. This enables efficient removal of ions from the trap with modest excitation voltages and narrow bandwidth, therefore, substantially reducing the disturbance of ions with other charge-to-mass ratios. We numerically study and compare the mass selectivity of the two methods. In addition, we experimentally show that the barium isotopes with 136 and 137 nucleons can be removed from small ion crystals and ejected out of the trap while keeping ^{138}text {Ba}^{+} ions Doppler cooled, corresponding to a mass selectivity of better than Delta m / m = 1/138. This method can be widely applied to ion trapping experiments without major modifications since it only requires modulating the potential of the ion trap.

Improved opacity expansion at NNLO for medium induced gluon radiation

When an energetic parton propagates in a hot and dense QCD medium it loses energy by elastic scatterings or by medium-induced gluon radiation. The gluon radiation spectrum is suppressed at high frequency due to the LPM effect and encompasses two regimes that are known analytically: at high frequencies omega >{omega}_c=hat{q}{L}^2 , where hat{q} is the jet quenching transport coefficient and L the length of the medium, the spectrum is dominated by a single hard scattering, whereas the regime ω < ωc is dominated by multiple low momentum transfers. In this paper, we extend a recent approach (dubbed the Improved Opacity Expansion (IOE)), which allows an analytic (and systematic) treatment beyond the multiple soft scattering approximation, matching this result with the single hard emission spectrum. We calculate in particular the NNLO correction analytically and numerically and show that it is strongly suppressed compared to the NLO indicating a fast convergence of the IOE scheme and thus, we conclude that it is sufficient to truncate the series at NLO. We also propose a prescription to compare the GW and the HTL potentials and relate their parameters for future phenomenological works.

Standing waves of the quintic NLS equation on the tadpole graph

The tadpole graph consists of a circle and a half-line attached at a vertex. We analyze standing waves of the nonlinear Schrödinger equation with quintic power nonlinearity equipped with the Neumann–Kirchhoff boundary conditions at the vertex. The profile of the standing wave with the frequency omega in (-infty ,0) is characterized as a global minimizer of the quadratic part of energy constrained to the unit sphere in L^6. The set of standing waves includes the set of ground states, which are the global minimizers of the energy at constant mass (L^2-norm), but it is actually wider. While ground states exist only for a certain interval of masses, the standing waves exist for every omega in (-infty ,0) and correspond to a bigger interval of masses. It is proven that there exist critical frequencies omega _1 and omega _0 with -infty< omega _1< omega _0 < 0 such that the standing waves are the ground state for omega in [omega _0,0), local constrained minima of the energy for omega in (omega _1,omega _0) and saddle points of the energy at constant mass for omega in (-infty ,omega _1). Proofs make use of the variational methods and the analytical theory for differential equations.

Invariant tori of full dimension for higher-dimensional beam equations with almost-periodic forcing

In this paper, we focus on the class of almost-periodically forced higher-dimensional beam equations utt+(−Δ+μ)2u+ψ(ωt)u=0,μ>0,t∈R,x∈Rd,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ u_{tt}+(-\\Delta +\\mu )^{2}u+\\psi (\\omega t)u=0,\\quad \\mu >0, t \\in \\mathbb{R}, x\\in \\mathbb{R}^{d}, $$\\end{document} subject to periodic boundary conditions, where psi (omega t) is real analytic and almost-periodic in t. We show the existence of almost-periodic solutions for this equation under some suitable hypotheses. In the proof, we improve the KAM iteration to deal with the infinite-dimensional frequency omega =(omega _{1},omega _{2},ldots).

Identification and correction of Sagnac frequency variations: an implementation for the GINGERINO data analysis

Ring laser gyroscopes are top sensitivity inertial sensors used in the measurement of angular rotation. It is well known that the response of such remarkable instruments can in principle access the very low frequency band, but the occurrence of nonlinear effects in the laser dynamics imposes severe limitations in terms of sensitivity and stability. We report here general relationships aimed at evaluating corrections able to effectively account for nonlinear laser dynamics. The so-derived corrections are applied to analyse thirty days of continuous operation of the large area ring laser gyroscope GINGERINO leading to duly reconstruct the Sagnac frequency omega _s. The analysis shows that the evaluated corrections affect the measurement of the Earth rotation rate varOmega _{oplus } at the level of 1 part in 1.5times 10^{3}. The null shift term omega _{ns} plays a non negligible role. It turns out proportional to the optical losses mu of the ring cavity, which are changing in time at the level of 10% within the considered period of thirty days. The Allan deviation of estimated varOmega _{oplus } shows a remarkable long term stability, leading to a sensitivity better than 10^{-10} rad/s with more than 10 s of integration time, and approaching (8.5pm 0.5)times 10^{-12} rad/s with 4.5times 10^{5} s of integration time.

A Scattering Theory for Linear Waves on the Interior of Reissner\u2013Nordstr\xf6m Black Holes

We develop a scattering theory for the linear wave equation Box _g psi = 0 on the interior of Reissner–Nordström black holes, connecting the fixed frequency picture to the physical space picture. Our main result gives the existence, uniqueness and asymptotic completeness of finite energy scattering states. The past and future scattering states are represented as suitable traces of the solution psi on the bifurcate event and Cauchy horizons. The heart of the proof is to show that after separation of variables one has uniform boundedness of the reflection and transmission coefficients of the resulting radial o.d.e. over all frequencies omega and ell . This is non-trivial because the natural T conservation law is sign-indefinite in the black hole interior. In the physical space picture, our results imply that the Cauchy evolution from the event horizon to the Cauchy horizon is a Hilbert space isomorphism, where the past (resp. future) Hilbert space is defined by the finiteness of the degenerate T energy fluxes on both components of the event (resp. Cauchy) horizon. Finally, we prove that, in contrast to the above, for a generic set of cosmological constants Lambda , there is no analogous finite T energy scattering theory for either the linear wave equation or the Klein–Gordon equation with conformal mass on the (anti-) de Sitter–Reissner–Nordström interior.

Sound Speed Dependence of Alignment in Accretion Disks Subjected to Lense–Thirring Torques

We present a series of simulations in both pure hydrodynamics (HD) and magnetohydrodynamics (MHD) exploring the degree to which alignment of disks subjected to external precessional torques (e.g., as in the `Bardeen-Petterson' effect) is dependent upon the disk sound speed c_s. Across the range of sound speeds examined, we find that the influence of the sound speed can be encapsulated in a simple "lumped-parameter" model proposed by Sorathia et al. (2013a). In this model, alignment fronts propagate outward at a speed ~0.2 rOmega_precess(r), where Omega_precess is the local test-particle precession frequency. Meanwhile, transonic radial motions transport angular momentum both inward and outward at a rate that may be described roughly in terms of an orientation diffusion model with diffusion coefficient ~2c_s^2/Omega, for local orbital frequency Omega. The competition between the two leads, in isothermal disks, to a stationary position for the alignment front at a radius proportional to c_s^(-4/5). For alignment to happen at all, the disk must either be turbulent due to the magnetorotational instability in MHD, or, in HD, it must be cool enough for the bending waves driven by disk warp to be nonlinear at their launch point. Contrary to long-standing predictions, warp propagation in MHD disks is diffusive independent of the parameter c_s/(alpha v_orb$, for orbital speed v_orb and ratio of stress to pressure of alpha. In purely HD disks, i.e., those with no internal stresses other than bulk viscosity, warmer disks align weakly or not at all; cooler disks align qualitatively similarly to MHD disks.

Quantum friction between oscillating crystal slabs: Graphene monolayers on dielectric substrates

We present a theoretical description of energy transfer processes between two noncontact quasi- twodimensional crystals separated by distance a, oscillating with frequency omega0 and amplitude rho0 , and compare it with the case of two quasi-twodimensional crystals in uniform parallel motion. We apply the theory to calculate van der Waals energy and dissipated energy in two oscillating slabs where each slab consists of a graphene monolayer deposited on SiO2 substrate. The graphene dielectric response is determined from first principles, and SiO2 surface response is described using empirical local dielectric function. We studied the modification of vdW attraction as function of the driving frequency and graphene doping. We propose the idea of controlling the sticking and unsticking of slabs by tuning the graphene dopings EF i and driving frequency omega0 . We found simple rho02 dependence of vdW and dissipated energy. As the Dirac plasmons are the dominant channels through which the energy between slabs can be transferred, the dissipated power in equally doped EF1 = EF2 = 0 graphenes shows strong omega0 = 2omegap peak. This peak is substantially reduceed when graphenes are deposited on SiO2 substrate. If only one graphene is pristine (EFi = 0) the 2omegap peak disappears. For larger separations a the phononic losses also become important and the doping causes shifts, appearance and disappearance of many peaks originating from resonant coupling between hybridized electronic-phononic excitations in graphene-substrate slabs.

The origin of the Gaia phase-plane spiral

A simple model is presented of the formation of the spiral the (z,v_z) phase plane of solar-neighbourhood stars that was recently discovered in Gaia data. The key is that the frequency Omega_z at which stars oscillate vertically depends on angular momentum about the z axis in addition to the amplitude of the star's vertical oscillations. Spirals should form in both <v_phi> and <v_R> whenever a massive substructure, such as the Sgr dwarf galaxy, passes through the Galactic plane. The model yields similar spirals to those observed in both <v_phi> and <v_R>. The primary driver is the component of the tidal force that lies in the plane. We investigate the longevity of the spirals and the mass of the substructure, but the approximations inherent in the model make quantitative results unreliable. The work relies heavily on a self-consistent, multi-component model of our Galaxy produced by the AGAMA package for f(J) modelling.

Muonic molecular ionsppμandpdμdriven by superintense VUV laser pulses: Postexcitation muonic and nuclear oscillations and high-order harmonic generation

The non-Born-Oppenheimer quantum dynamics of pp mu and pd mu molecular ions excited by ultrashort, superintense VUV laser pulses polarized along the molecular axis (z) is studied by the numerical solution of the time-dependent Schrodinger equation within a three-dimensional (3D) model, including the internuclear distance R and muon coordinates z and rho, a transversal degree of freedom. It is shown that in both pp mu and pd mu, muons approximately follow the applied laser field out of phase. After the end of the laser pulse, expectation values , , and demonstrate oscillations in both pp mu and pd mu. In the case of pd mu, the post-laser-pulse oscillations of and appear as shaped echo pulses. Power spectra, which are related to high-order harmonic generation (HHG), generated due to muonic and nuclear motion are calculated in the acceleration form. For pd mu it is found that there exists a unique characteristic frequency omega(pd mu)(osc) representing both frequencies of post-laser-pulse muonic oscillations and the frequency of nuclear vibrations, which manifest themselves by very sharp maxima in the corresponding power spectra of pd mu. The homonuclear pp p. ion does not possess such a unique characteristic frequency. The exact dynamics and power, and HHG spectra of the 3D model are compared with a Born-Oppenheimer, fixed-nuclei model featuring interesting differences: postpulse oscillations are absent and HHG spectra are affected indirectly or directly by nuclear motion.

Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars

It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these horizonless compact objects cannot support spatially regular static matter configurations made of scalar (spin-0) fields, vector (spin-1) fields and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support stationary (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein–Gordon wave equation for a linearized scalar field of mass mu and proper frequency omega in the curved background of a spherically symmetric compact reflecting star of mass M and radius R_{text {s}}. It is proved that the regime of existence of these stationary composed star–field configurations is characterized by the simple inequalities 1-2M/R_{text {s}}<(omega /mu )^2<1. Interestingly, in the regime M/R_{text {s}}ll 1 of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum {omega (M,R_{text {s}},mu )}^{n=infty }_{n=1} of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star–linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star–field configurations with direct numerical computations.

Error analysis of the extended Filon-type method for highly oscillatory integrals

We investigate the impact of adding inner nodes for a Filon-type method for highly oscillatory quadrature. The error of Filon-type method is composed of asymptotic and interpolation errors, and the interplay between the two varies for different frequencies. We are particularly concerned with two strategies for the choice of inner nodes: Clenshaw–Curtis points and zeros of an appropriate Jacobi polynomial. Once the frequency omega is large, the asymptotic error dominates, but the situation is altogether different when omega ge 0 is small. In the first regime, our optimal error bounds indicate that Clenshaw–Curtis points are always marginally better, but this is reversed for small omega ; then, Jacobi points enjoy an advantage. The main tool in our analysis is the Peano Kernel theorem. While the main part of the paper addresses integrals without stationary points, we indicate how to extend this work to the case when stationary points are present. Numerical experiments are provided to illustrate theoretical analysis.