In recent work we formulated a new set of electrodynamic equations for superconductors as an alternative to the conventional London equations, compatible with the prediction of the theory of hole superconductivity that superconductors expel negative charge from the interior towards the surface. Charge expulsion results in a macroscopically inhomogeneous charge distribution and an electric field in the interior, and because of this a spin current is expected to exist. Furthermore, we have recently shown that a dynamical explanation of the Meissner effect in superconductors leads to the prediction that a spontaneous spin current exists near the surface of superconductors. In this paper we extend the electrodynamic equations proposed earlier for the charge density and charge current to describe also the space and time dependence of the spin density and spin current. This allows us to determine the magnitude of the expelled negative charge and interior electric field as well as of the spin current in terms of other measurable properties of superconductors. We also provide a 'geometric' interpretation of the difference between type I and type II superconductors, discuss the relationship between our model and Slater's seminal work on superconductivity, and discuss the magnitude of the expected novel effects for elemental and other superconductors.
We report the first optical study of CaAlSi, a superconductor which displays both the crystal structure of MgB2 and the electronic band structure of intercalated graphites. The reflectivity of a CaAlSi single crystal was measured down to sub-THz frequencies and to 3.3 K, with the use of Coherent Synchrotron Radiation. A superconducting gap in the hexagonal planes, two gaps along the c axis were found and measured, as expected from the structure of the CaAlSi Fermi surface. The anisotropic optical parameters of the normal state were also determined.
A fully consistent model to study electrodynamics for superconductors in the stationary and non-stationary regime has been developed based on Proca equations and a massive photon. In particular, this approach has been applied to study the electric field penetration depth in superconductors. The model shows a deviation from the charge contribution to an internal electric field compared to previous approaches.
An alternative form of London's electrodynamic theory of superconductors predicts that the electrostatic screening length is the same as the magnetic penetration depth. We argue that experiments performed to date do not rule out this alternative formulation and propose an experiment to test it. Experimental evidence in its favor would have fundamental implications for the understanding of superconductivity.
The pairing state symmetry of the electron-doped cuprate superconductors is thought to be s-wave in nature, in contrast with their hole-doped counterparts which exhibit a d-wave symmetry. We re-examine this issue based on recent improvements in our electron-doped materials and our measurement techniques. We report microwave cavity perturbation measurements of the temperature dependence of the penetration depth of Pr_(2-x)Ce_(x)CuO_(4-y) and Nd_(2-x)Ce_(x)CuO_(4-y) crystals. Our data strongly suggest that the pairing symmetry in these materials is not s-wave.
In previous works, axion electrodynamics in three dimensional $p+is$ superconductors is discussed by borrowing the results from superconducting Dirac systems. However, in this work, based on a systematic path integral approach, we show that the axion electrodynamics in $p+is$ superconductors exhibits a nonrelativistic form, which is different from the superconducting Dirac and Weyl systems. More precisely, the induced electric field does not enter into the axion action, and gauge invariance is ensured by the combination of the electric potential and the Nambu-Goldstone phase mode. Furthermore,…
Electrodynamics of superconductors is primarily the electrodynamics of the Meissner state, a state characterized by zero magnetic induction of a superconducting fraction of conduction electrons. Simultaneously, the Meissner state is characterized by zero resistivity and zero entropy of these electrons. The latter means that the temperature of an ensemble of superconducting electrons is zero as well. Understanding properties of the Meissner state provides a key to understand and predict these and other equilibrium and non-equilibrium properties of superconductors, e.g., properties of the interm…
The electric losses in a bulk or film superconductor exposed to a parallel radio-frequency magnetic field may have three origins: In homogeneous vortex-free superconductors losses proportional to the frequency squared originate from the oscillating normal-conducting component of the charge carriers which is always present at temperatures $T>0$. With increasing field amplitude the induced supercurrents approach the depairing current at which superconductivity breaks down. And finally, if magnetic vortices can penetrate the superconductor they typically cause large losses since they move driven …
We report microwave cavity perturbation measurements of the temperature dependence of the penetration depth, lambda(T), and conductivity, sigma(T) of Pr_{2-x}Ce_{x}CuO_{4-delta} (PCCO) crystals, as well as parallel-plate resonator measurements of lambda(T) in PCCO thin films. Penetration depth measurements are also presented for a Nd_{2-x}Ce_{x}CuO_{4-delta} (NCCO) crystal. We find that delta-lambda(T) has a power-law behavior for T<T_c/3, and conclude that the electron-doped cuprate superconductors have nodes in the superconducting gap. Furthermore, using the surface impedance, we have derive…
We consider the Maxwell-London electrodynamics of three dimensional superconductors in p-wave pairing states with nodal points or lines in the energy gap. The current-velocity relation is then nonlinear in the applied field, cubic for point nodes and quadratic for lines. We obtain explicit angular and depth dependent expressions for measurable quantities such as the transverse magnetic moment, and associated torque. These dependences are different for point and line nodes and can be used to distinguish between different order parameters. We discuss the experimental feasibility of this method, …
In this paper we give a derivation of a system of equations to describe the electrodynamics of s-wave superconductors. First, we consider a relativistically covariant theory in terms of gauge four-vector electromagnetic potential and scalar complex field. We use the first-order formalism to obtain the supplemented Maxwell equations for gauge invariant electric, magnetic, four-vector fields and the modulus of the superconducting order parameter. The new four-vector field appears in some of the equations as a gauge invariant super-current and in other ones, while gauge invariant, as a four-vecto…
We show that the Higgs mode of a superconductor, which is usually challenging to observe by far-field optics, can be made clearly visible using near-field optics by harnessing ultraconfined graphene plasmons. As near-field sources we investigate two examples: graphene plasmons and quantum emitters. In both cases the coupling to the Higgs mode is clearly visible. In the case of the graphene plasmons, the coupling is signaled by a clear anticrossing stemming from the interaction of graphene plasmons with the Higgs mode of the superconductor. In the case of the quantum emitters, the Higgs mode is…
The model for high frequency electrodynamics in anisotropic type-II superconductors in the vortex state is studied considering arbitrary orientations between the applied field, the applied current and the anisotropy axis. An anisotropic treatment is provided for the vortex dynamics, taking into account all the phenomena relevant at high frequency, which include flux flow, pinning and creep. The coupling between vortex motion and high frequency currents is included, providing an entirely tensor model of the electromagnetic response to high frequency fields. Examples of data analysis of angular …
We investigate the holographic superconductors in Gauss-Bonnet gravity with Born-Infeld electrodynamics. We find that the Gauss-Bonnet constant, the model parameters and the Born-Infeld coupling parameter will affect the formation of the scalar hair, the transition point of the phase transition from the second order to the first order, and the relation connecting the gap frequency in conductivity with the critical temperature. The combination of the Gauss-Bonnet gravity and the Born-Infeld electrodynamics provides richer physics in the phase transition and the condensation of the scalar hair.
We probe the effects of strong disorder (2.4 < kFl < 8.6) on superconductivity in thin films of niobium titanium nitride and titanium nitride by measuring the microwave electrodynamics in coplanar waveguide resonators. We find a gradual evolution of the electromagnetic response with disorder, deviating from Mattis-Bardeen theory, for both materials. This result can be understood as due to changes in the quasiparticle density of states, induced by the short elastic scattering length. The observations are consistent with a model using an effective pair breaker, dependent on the level of disorder…
In close analogy to quantum electrodynamics, we derive a quantum field theory of Josephson plasma waves (JPWs) in layered superconductors (LSCs), which describes two types of interacting JPW bosonic quanta: one massive and the other almost-massless. We also calculate the amplitude of their decay and scattering. We propose a mechanism of enhancement of macroscopic quantum tunneling (MQT) in stacks of intrinsic Josephson-junctions (SIJJs). Due to the long-range interactions between many junctions in the LSCs, the calculated MQT escape rate $Γ$ has a very nonlinear dependence on the number of jun…
Although cuprate superconductors have been intensively studied for the past decades, there is no consensus regarding the microscopic origin of their superconductivity. In this work, we measure the low-energy electrodynamic response of slightly underdoped and overdoped La$_{2-x}$Ce$_x$CuO$_4$ thin films using time-domain terahertz (THz) spectroscopy to determine the temperature and field dependence of the superfluid spectral weight. We show that the temperature dependence obeys the relation \textit{n$_s$} $\propto$ $1-(T/T_c)^2$, typical for dirty limit BCS-like $d$-wave superconductors. Furthe…
We perform an experiment to test between two theories of the electrodynamics of superconductors: the standard London theory and an alternative proposed by J. E. Hirsch [Phys. Rev. B 69, 214515 (2004)]. The two alternatives give different predictions with respect to the screening of an electric field by a superconductor, and we try to detect this effect using atomic force microscopy on a niobium sample. We also perform the reverse experiment, where we demonstrate a superconductive tip mounted on a qPlus force sensor. Due to limited accuracy, we are able neither to prove nor to disprove Hirsch's…
We report here the frequency-dependent optical response of a nearly ferroelectric superconductor (NFE-SC), like Na$_{x}$WO$_3$, or n-SrTiO$_3$. From $ω=0$, up to a critical frequency $ ω_{c1}$, Meissner-like field extinction occurs as in a usual superconductor. In the "anomalous" region $ω_{c1}<ω<ω_{TO}$ (the TO frequency of the NFE) the field propagates as in a dielectric. For $ω>ω_{TO}$ Meissner damping recurrs, then at higher $ω$, dielectriclike propagation is found. New optical anomalies (peaks in transmission) are predicted for a film of NFE-SC below the soft mode frequency $ω_{TO}$. Thes…
The temperature dependence of the microwave surface impedance and conductivity are used to study the pairing symmetry and properties of cuprate superconductors. However, the superconducting properties can be hidden by the effects of paramagnetism and antiferromagnetic long-range order in the cuprates. To address this issue we have investigated the microwave electrodynamics of GdBa_2Cu_3O_{7-δ}, a rare-earth cuprate superconductor which shows long-range ordered antiferromagnetism below T_N=2.2 K, the Neel temperature of the Gd ion subsystem. We measured the temperature dependence of the surface…
The vortex dynamics of uniaxial anisotropic superconductors in magnetic fields applied with arbitrary orientation is theoretically studied. Focus is on the model for electrical transport experiments in the linear regime. Relevant vortex parameters, like the viscous drag, the vortex mobility and pinning constant (with point pins), together with the flux flow and Campbell resistivities, are derived in tensor form, in the very different free flux flow and pinned Campbell regimes. The applicability to the various tensor quantities of the well-known scaling laws for the angular dependence on the fi…
We report the structure of the magnetic field and secular current in a Nearly Ferroelectric Superconducting (NFE-SC) thin film. It was shown that unlike in conventional superconducting films, the external radiation causes alternating pattern of current strips. The strength of the innermost current torrents is governed by the laser field intensity as well as resonance with the ferroelectric component. The latter is modeled by secular reflection and random scattering in the Pippard non-local limit. Our calculations suggest that corresponding magnetic field pattern affects vortex formation in suc…
We report the low-energy electrodynamics of a moderately clean A15 superconductor (SC) following ultrafast excitation to understand and manipulate terahertz (THz) quasi--particle (QP) transport by tuning pump photoexcitation of from competing orders. Using 35-fs optical pulses, we observe a non-thermal enhancement in the low frequency conductivity, opposite to that observed for THz pump, which persists up to an additional critical temperature, above the SC one, from an electronic order in the Martensitic normal state. In the SC state, the fluence dependence of pair breaking kinetics together w…
We derive general frequency dependencies of the surface impedance modulus for conductors without the dc dissipation, i. e. for superconductors or perfect conductors. The frequency-dependent surface impedance was applied for the solutions corresponding to the spatially dispersive eigenvalues of the permittivity operator for conductors. We demonstrate that appropriately taken into account effects of the spatial dispersion can give the general frequency dependence of the surface impedance for the obtained solutions including that for superconductor. It is shown that an incorporation of the spatia…
Effective magnetic penetration depth and microwave surface impedance are derived for anisotropic layered superconductors in the shape of spheres and long cylinders, where the external magnetic field is applied in the plane of the highly conducting layers to induce out-of-plane screening currents. The results are extended by analytic continuation to highly anisotropic conductors and to lossy superconductors at high frequency. The electrodynamics for the general case of a superconductor or metal with arbitrary anisotropy are presented. The treatment is then specialized to layered materials with …
A microwave cavity perturbation technique is used to probe the interlayer electrodynamics within the vortex state of the organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2. A Josephson plasma mode is observed which is extremely sensitive to correlations in the locations of vortices in adjacent layers and may, therefore, be used to gauge collective effects between vortices and crystal pinning sites in the title compound. Our previous investigations [M. M. Mola et al., Phys. Rev. B 62 (2000) 5965] revealed a transformation from a correlated quasi-two-dimensional pinned vortex phase, to either a de…
I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ago. However their basic properties and stability in these systems remains an outstandingly difficult question both for analytical and numerical treatment. Here I propose a new perturbative approach to treat self-consistently all the degrees of freedom in the problem. I show that there exists a length scale for a Hopfion texture where the electrodynamics of a two-component superconductor is dominate…
We report on a detailed study of the optical response and $T_c-ρ$ phase diagram ($T_c$ being the superconducting critical temperature and $ρ$ the normal state resistivity of the film) of granular aluminum, combining transport measurements and a high resolution optical spectroscopy technique. The $T_c-ρ$ phase diagram is discussed as resulting from an interplay between the phase stiffness, the Coulomb repulsion and the superconducting gap $Δ$. We provide a direct evidence for two different types of well resolved sub-gap absorptions, at $ω_1\simeqΔ$ and at $Δ\lesssimω_2\lesssim2Δ$ (decreasing wi…
The electrodynamic properties of Ba(Fe$_{0.92}$Co$_{0.08})_2$As$_{2}$ and Ba(Fe$_{0.95}$Ni$_{0.05})_As$_{2}$ single crystals have been investigated by reflectivity measurements in a wide frequency range. In the metallic state, the optical conductivity consists of a broad incoherent background and a narrow Drude-like component which determines the transport properties; only the latter contribution strongly depends on the composition and temperature. This subsystem reveals a $T^2$ behavior in the dc resistivity and scattering rate disclosing a hidden Fermi-liquid behavior in the 122 iron-pnictid…
We performed resonant microwave measurements on superconducting titanium (Ti) down to temperatures of 40~mK, well below its critical temperature $T_\mathrm{c} \approx 0.5$~K. Our wide frequency range 3.3-40~GHz contains the zero-temperature energy gap $2Δ_0$ and allows us to probe the full electrodynamics of the superconducting state, including excitations across the gap and the low-frequency responses of superfluid condensate and thermal quasiparticles. The observed behavior follows the predictions of the BCS-based Mattis-Bardeen formalism, which implies that superconducting Ti is in the dirt…
Our objective is to study the extreme and local electrodynamic properties of Niobium (Nb), and to relate these properties to specific defects that limit the ultimate RF performance of superconducting radio frequency (SRF) cavities made from Nb. Specifically, we wish to develop a microscopic measure of the response of Nb to RF magnetic fields up to the critical field (Hc) at microwave frequencies (few GHz), and at temperatures down to 4.2 K. In order to image the local electromagnetic response in the GHz frequency regime, a magnetic writer from a commercial hard drive is integrated into the nea…
Based on an analytic scheme and neglecting the back reaction effect several crucial properties of holographic $ s $- wave superconductors have been investigated in the presence of an external magnetic field in the background of a $ D $ dimensional Schwarzschild AdS space time. Inspired by low energy limit of heterotic string theory, in the present paper we replace the conventional Maxwell action by a Power Maxwell action. Immersing the holographic superconductors in an external static magnetic field the spatially dependent condensate solutions have been obtained analytically. Interestingly eno…
It is argued that experiments on rotating superconductors provide evidence for the existence of macroscopic spin currents in superconductors in the absence of applied external fields. Furthermore it is shown that the model of hole superconductivity predicts the existence of such currents in all superconductors. In addition it is pointed out that spin currents are required within a related macroscopic (London-like) electrodynamic description of superconductors recently proposed. The spin current arises through an intrinsic spin Hall effect when negative charge is expelled from the interior of t…
The vortex-state electrodynamics of s-wave superconductors has been studied by infrared spectroscopy. Far-infrared transmission and reflection spectra of superconducting NbTiN and NbN thin films were measured in a magnetic field perpendicular to the film surface, and the optical conductivity was extracted. The data show clear reduction of superconducting signature. We consider the vortex state as a two-component effective medium of normal cores embedded in a BCS superconductor. The spectral features are well explained by the Maxwell-Garnett theory. Our analysis supports the presence of magneti…
The linear and nonlinear response to a microwave electromagnetic field of two c-axis oriented polycrystalline samples of the newly discovered superconductor CaC6 (Tc = 11.5 K) is studied in the superconducting state down to 2 K. The surface resistance Rs and the third order intermodulation distortion, arising from a two-tone excitation, have been measured as a function of temperature and microwave circulating power. Experiments are carried out using a dielectrically loaded copper cavity operating at 7 GHz in a "hot finger" configuration. The results confirm recent experimental findings that Ca…
A chain of Josephson junctions implements one of the simplest many-body models undergoing a superconductor-insulator (SI) quantum phase transition between states with zero and infinite resistance. Apart from zero resistance, the superconducting state is necessarily accompanied by a sound-like mode due to collective oscillations of the phase of the complex-valued order parameter. Exciting this phase mode results in transverse photons propagating along the chain. Surprisingly little is known about the fate of this mode upon entering the insulating state, where the order parameter's amplitude rem…
Terahertz Electrodynamics and Kinetic Inductance of Disordered Titanium-Vanadium Alloy Thin Films
Free Electron Laser Utilization Laboratory, Raja Ramanna Center for Advanced Technology（自由电子激光利用实验室，拉贾·拉曼纳先进技术中心）；Homi Bhabha National Institute（霍米·巴哈国家研究所）
We present exact numerical calculations of supercurrent density, inductance, and impurity-induced flux noise of cylindrical superconducting wires in the nonlocal Pippard regime, which occurs when the Pippard coherence length is larger than the London penetration depth. In this regime the supercurrent density displays a peak away from the surface, and changes sign inside the superconductor, signalling a breakdown of the usual approximation of local London electrodynamics with a renormalized penetration depth. Our calculations show that the internal inductance and the bulk flux noise power is en…
Resolving unconventional gap structure in kagome superconductors with hybrid microwave circuits
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体和化学物理研究所）；Institute of Solid State and Material Physics, Technische Universität Dresden（德累斯顿工业大学固态与材料物理研究所）；Institute of Applied Physics, Technische Universität Dresden（德累斯顿工业大学应用物理研究所）；Leibniz Institute for Solid State and Materials Research Dresden（德累斯顿莱布尼茨固体与材料研究所）；Department of Physics, University of Naples Federico II（那不勒斯费德里科二世大学物理系）；Department of Electrical Engineering and Information Technology, University of Naples Federico II（那不勒斯费德里科二世大学电气与信息工程系）
From the outset of superconductivity research it was assumed that no electrostatic fields could exist inside superconductors, and this assumption was incorporated into conventional London electrodynamics. Yet the London brothers themselves initially (in 1935) had proposed an electrodynamic theory of superconductors that allowed for static electric fields in their interior, which they unfortunately discarded a year later. I argue that the Meissner effect in superconductors necessitates the existence of an electrostatic field in their interior, originating in the expulsion of negative charge fro…
The continuous development of superconducting electronics is encouraging several studies on hybrid Josephson junctions (JJs) based on superconductor/ferromagnet/superconductor (SFS) heterostructures, as either spintronic devices or switchable elements in quantum and classical circuits. Recent experimental evidence of macroscopic quantum tunneling and of an incomplete 0-pi transition in tunnel-ferromagnetic spin-filter JJs could enhance the capabilities of SFS JJs also as active elements. Here, we provide a self-consistent electrodynamic characterization of NbN/GdN/NbN spin-filter JJs as a func…
We studied response of the Josephson vortex lattice in layered superconductors to the high-frequency c-axis electric field. We found a simple relation connecting the dynamic dielectric constant with the perturbation of the superconducting phase, induced by oscillating electric field. Numerically solving equations for the oscillating phases, we computed the frequency dependences of the loss function at different magnetic fields, including regions of both dilute and dense Josephson vortex lattices. The overall behavior is mainly determined by the c-axis and in-plane dissipation parameters, which…
We consider the effective 2+1 dimensional electrodynamics (QED_3) of low-energy quasiparticles coupled to fluctuating vortex loops in the d-wave superconductor, with the velocity anisotropy: v_F not equal to v_Delta. This theory should be relevant to the quantum superconductor-insulator transition in underdoped cuprates. Working in the customary large-N approximation, we find that weak anisotropy is a marginally irrelevant perturbation to the Lorentz invariant QED_3, and that the critical number N_c of Dirac fields below which the theory suffers the antiferromagnetic (chiral) instability stays…
For a single crystal of YNi(2)B(2)C superconductor, the equilibrium magnetization M in the square basal plane has been studied experimentally as a function of temperature and magnetic field. While the magnetization M(H) deviates from conventional London predictions, a recent extension of London theory (to include effects of non-local electrodynamics) describes the experiments accurately. The resulting superconductive parameters are well behaved. These results are compared with corresponding findings for the case with M perpendicular to the basal plane.
Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently difficult to analyze both numerically and analytically. We present a formalism which allows many phenomena related to superconducting and Ohmic films to be modelled and analyzed. The formalism is based on the Maxwell equations, and a material current-voltage characteristics, linear for normal metals, and nonlinear for superconductors, plus a careful account of the …
The introduction of crystalline defects or dopants can give rise to so-called "dirty superconductors", characterized by reduced coherence length and quasiparticle mean free path. In particular, granular superconductors such as Granular Aluminum (GrAl), consisting of remarkably uniform grains connected by Josephson contacts have attracted interest since the sixties thanks to their rich phase diagram and practical advantages, like increased critical temperature, critical field, and kinetic inductance. Here we report the measurement and modeling of circuit quantum electrodynamics properties of Gr…
The most general electrodynamic equations of a perfect conducting state are obtained using a variational principle in a classical framework, following an approach by Pierre-Gilles de Gennes. London equations are derived as the time-independent case of these equations, corresponding to the magnetostatic minimal energy state of the perfect conducting system. For further confirmation, the same equations are also derived in the classical limit of the Coleman-Weinberg model, the most successful quantum macroscopic theory of superconductivity. The magnetic field expulsion is, therefore, a direct con…
We investigate theoretically the shielding of the electromagnetic field fluctuations by s-wave and d-wave superconductors within the framework of macroscopic quantum electrodynamics. The spin flip lifetime is evaluated above a niobium and a bismuth strontium calcium copper oxide (BSCCO) surface, and the screening effect is studied as a function of the thickness of the superconducting layer. Further, we study the different temperature dependence of the atomic spin relaxation above the two superconductors.
We report the numerical solutions of the system of equations, which describes the electrodynamics of s-wave superconductors, for time independent fields and half-plane superconductor geometry. The results are: i)the applied magnetic field increases the Ginzburg-Landau (GL) coherence length and suppresses the superconductivity, ii)the applied electric field decreases GL coherence length and supports the superconductivity, iii) if the applied magnetic field is fixed and the applied electric field increases the London penetration depth of the magnetic field decreases. The main conclusion is that …
The ac response of a slab of material with electrodynamic characteristics $E\sim j^{κ+1}$, $κ\geq0$, is studied numerically. From the solutions of the nonlinear diffusion equation, the fundamental and higher-order components of the harmonic susceptibility are obtained. A large portion of the data for every $κ$ can be scaled by a single parameter, $ξ$ =$t^{1/(κ+2)}\cdot H_0^{κ/(κ+2)}/D$, where $t$ is the period of the ac field at the surface, $H_0$ is its amplitude and $D$ is the slab thickness. This is, however, only an approximate scaling property: The field penetration into a nonlinear mediu…
Most iron-based superconductors are characterized by the s+- symmetry of their order parameter, and are expected to go through a transition to the s++ state if enough disorder is introduced. We previously reported the observation of this transition in Ba(Fe1-xRhx)2As2 through a study of the disorder dependence of the critical temperature and low-temperature London penetration depth. In this paper we report on the analysis of the electrodynamic response of the same sample across the transition and we identify peculiarities in the behaviour of the surface resistance and normal conductivity, that…
We propose to couple an on-chip high finesse superconducting cavity to the lateral-motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15 microseconds, while energy will be coherently exchanged with the cavity photons in less than 10 nanoseconds for charge states and faster than 1 microsecond for spin states, making the system attractive for quantum information processing and cavity quantum electrodynamics experiments. Strong interaction with cavity photons will provide the means for both nondestructive read…
Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding principle. We demonstrate that the relativistic vortex worldsheet in spacetime is the object that naturally conveys all electric and magnetic information, for which we obtain simple and concise equations. Breaking Lorentz invariance leads to down-to-earth Abrikosov vortices, and special limits of these equations include for instance dynamic Meissner screening and the…
Non-linear electrodynamics of a ring-shaped Andreev interferometer (superconductor-normal conductor-superconductor hybrid structure) inductively coupled to a circuit of the dissipative current is investigated. The current-voltage characteristics (CVC) is demonstrated to be a series of loops with several branches intersecting in the CVC origin. The sensitivity of the transport current to a change of the applied external magnetic flux can be comparable to the one of the conventional SQUID's. Spontaneous arising of coupled non-linear oscillations of the transport current, the Josephson current an…
We present cavity QED experiments with an Er:YSO crystal magnetically coupled to a 3D cylindrical sapphire loaded copper resonator. Such waveguide cavities are promising for the realization of a superconducting quantum processor. Here, we demonstrate the coherent integration of a rare-earth spin ensemble with the 3D architecture. The collective coupling strength of the Er$^{3+}$ spins to the 3D cavity is 21 MHz. The cylindrical sapphire loaded resonator allowed us to explore the anisotropic collective coupling between the rare-earth doped crystal and the cavity. This work shows the potential o…
