Josephson Plasma Waves Research Articles

Engineering ultrastrong coupling between Josephson plasmon polaritons and subwavelength microcavity arrays in silicon/van der Waals layered superconductor heterostructure for terahertz hybrid circuit cavity quantum electrodynamics

The realization of the ultrastrong coupling between Josephson plasma waves (JPWs) and terahertz (THz) photons in the subwavelength microcavity array is of interest for manipulating the THz cavity quantum electrodynamics (cQED), ultrahigh-resolution sensing and imaging, and quantum information processing. Here, we describe the engineering of ultrastrong light-matter interactions in a deeply subwavelength microcavity array based on the hybrid silicon and high-temperature superconductor (HTS) ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (BSCCO) van der Waals (vdW) heterostructure. We perform numerical modeling and analytical calculation to describe Josephson THz cQED and the ultrastrong coupling process between THz radiation and the JPWs in Josephson medium which is naturally present in BSCCO vdW. The resonance frequency of microcavities is swept through the Josephson plasma frequency by altering their width. THz reflection demonstrates the anticrossing behavior of ultrastrong coupling with a normalized Rabi frequency (coupling strength) $2{\mathrm{\ensuremath{\Omega}}}_{\mathrm{R}}/{f}_{\mathrm{c}}=0.29$ for the BSCCO thickness $t=200$ nm, which increases to the value of 0.87 for $t=800$ nm. Furthermore, the thermal behavior of coupling strength shows modulation of Rabi splitting $2{\mathrm{\ensuremath{\Omega}}}_{\mathrm{R}}$ with temperature. We show that the normalized Rabi splitting $2{\mathrm{\ensuremath{\Omega}}}_{\mathrm{R}}/{f}_{\mathrm{c}}$ is independent of the temperature in the BSCCO superconducting regime, while a weak coupling can be observed above the superconducting transition temperature. The proposed chip-scale THz photonic integrated circuit with subwavelength microcavity metamaterial array shall guide the effort in the development of power-efficient coherent THz sources, quantum sensors, ultrasensitive detectors, parametric amplifiers and tunable bolometers based on BSCCO HTS quantum material.

Surface Josephson plasma waves in a high-temperature superconductor

Electron density oscillations with acoustic dispersions and sustained at boundaries between different media provide information about surface and interface properties of heterostructures. In ultrathin metallic films these plasmonic excitations are heavily damped. Superconductivity is predicted to reduce dissipation allowing detection of these resonances. Emerging low-loss interface Cooper-pair waves have been studied before, however, the observation of surface-confined Josephson plasmons in highly anisotropic superconductors has remained elusive. Here, we report on generation and coupling to these excitations in an ultrathin single-crystal film of high-temperature superconductor La1.85Sr0.15CuO4. The film becomes brighter than Au below the critical temperature when probed with sub-gap THz photons. We show that the enhanced signal in the superconducting state, which can be visualized with a spatial resolution better than λ/3000, originates from near-field coupling of light to surface Josephson plasmons. Our results open a path towards non-invasive investigation of enhanced superconductivity in artificial multilayers, buried interface states in topological heterostructures, and non-linear phenomena in Josephson devices.

Excitation of Josephson plasma waves in a layered high-temperature superconductor slab embedded in a high refractive index dielectric

The nonlocal optical response of a layered high-temperature superconductor slab embedded in a dielectric medium is theoretically studied. It is assumed that the layers inside the high-temperature superconductor are parallel to the slab surfaces. We calculate its p-polarization optical spectra by using an average permittivity tensor which depends on both the frequency and the wave vector of the electromagnetic wave. Consequently, additional electromagnetic modes just above the characteristic Josephson plasma frequency, being in the terahertz range, are generated. It is shown that the p-polarization reflectivity spectra for a Bi2Sr2CaCu2O8 + δ (Bi2212) superconductor slab, embedded in high refractive index dielectric, exhibit prominent dips breaking the total internal reflection. For very small superconductor slab thicknesses, the optical spectra resonances are associated with Fabry-Perot resonances of the short-wavelength electromagnetic modes. In contrast, the long-wavelength electromagnetic modes, having anomalous dispersion relation, are excited at relatively-large slab thicknesses and manifest themselves as strong resonances in both absorption and transmissivity spectra, suppressing the specular reflectivity.

Effect of a dc magnetic field on the anomalous dispersion of localized Josephson plasma modes in layered superconductors

We study theoretically the propagation of Josephson plasma waves (JPWs) localized on a slab of layered superconductor in the presence of an external dc magnetic field. The slab is sandwiched between two dielectric half-spaces and the wave modes propagate across the layers. We derive analytic expressions for the dispersion relations of the localized JPWs and present the numerical simulation for the effect of the external dc magnetic field on the dispersion. The anomalous dispersion of localized JPWs is predicted for a wide range of frequencies, wave vectors, and dc fields. Also, we discuss the possibility of the internal reflection of the localized modes in the inhomogeneous dc magnetic field. This phenomenon can find application in the terahertz electronics for the control of the localized mode propagation.

Parametric Amplification of a Superconducting Plasma Wave.

Many applications in photonics require all-optical manipulation of plasma waves1, which can concentrate electromagnetic energy on sub-wavelength length scales. This is difficult in metallic plasmas because of their small optical nonlinearities. Some layered superconductors support Josephson plasma waves (JPWs)2,3, involving oscillatory tunneling of the superfluid between capacitively coupled planes. Josephson plasma waves are also highly nonlinear4, and exhibit striking phenomena like cooperative emission of coherent terahertz radiation5,6, superconductor-metal oscillations7 and soliton formation8. We show here that terahertz JPWs can be parametrically amplified through the cubic tunneling nonlinearity in a cuprate superconductor. Parametric amplification is sensitive to the relative phase between pump and seed waves and may be optimized to achieve squeezing of the order parameter phase fluctuations9 or single terahertz-photon devices.

Superposition principle for nonlinear Josephson plasma waves in layered superconductors

We show that a specific superposition principle is valid for \emph{nonlinear} Josephson plasma waves in layered superconductors. We study theoretically the reflection and transmission of terahertz waves through a finite-size superconducting slab placed inside a rectangular waveguide with ideal-metal walls. We assume that the superconducting layers are parallel to the waveguide axis. We show that there exist two specific mutually-orthogonal polarizations for waves which, in spite of the nonlinearity, reflect and transmit through the superconductor \emph{independently}. The wave of the first polarization causes a strong shielding current along the crystallographic \textbf{ab}-plane of the superconductor. Therefore, this wave reflects nearly completely from the superconductor and excites only an evanescent mode inside it. The wave of the other polarization does not contain the electric field component parallel to both the sample surface and the crystallographic \textbf{ab}-plane, and excites much weaker shielding currents. Therefore, it partially reflects and partially transmits through the sample. Moreover, this wave excites the nonlinear mode in the layered superconductor, and the transmission coefficient of the superconductor depends on the amplitude of the incident wave of this polarization.On the basis of the discussed superposition principle, we suggest a new method for solving nonlinear problems of waves interaction in layered superconductors. Namely, it is reasonably to represent incident, reflected, and transmitted waves of any polarizations as superpositions of the modes with the two specific polarizations considered here, and then solve the problem separately for these modes. We apply this method to the case of nonlinear interaction and mutual transformation of the transverse electric and transverse magnetic modes in layered superconductors.

Possibility to enhance teraherz emission from intrinsic Josephson junction by external local heating

We theoretically propose a practical method for realizing intense terahertz (THz) emission from intrinsic Josephson junctions (IJJs) using an external heat source. An artificial inhomogeneous temperature distribution by the local heating strongly excites the Josephson plasma wave inside IJJs and enhances THz emission power. We show optimum heating conditions for achieving high power THz emission. Our result indicates that local heat control is a powerful method to realize practical solid-state THz-emitters utilizing IJJs.

Intense terahertz emission from intrinsic Josephson junctions by external heat control

A practical method for realizing intense terahertz (THz) emission from intrinsic Josephson junctions (IJJs) by utilizing external local-heating is proposed and demonstrated theoretically. An artificial temperature distribution induced by local heating strongly excites Josephson plasma waves inside IJJs. Accordingly, the emission power of the THz wave is enhanced drastically, and it can reach the order of mW. Our result indicates that the use of local heat control is a powerful method to realize practical solid-state THz-emitters based on IJJs.

Josephson surface plasmons in spatially confined cuprate superconductors

In this work, we generalize the theory of localized surface plasmons to the case of high-${T}_{\mathrm{c}}$ cuprate superconductors, spatially confined in the form of small spherical particles. At variance from ordinary metals, cuprate superconductors are characterized by a low-energy bulk excitation known as the Josephson plasma wave (JPW), arising from interlayer tunneling of the condensate along the $c$ axis. The effect of the JPW is revealed in a characteristic spectrum of surface excitations, which we call Josephson surface plasmons. Our results, which apply to any material with a strongly anisotropic electromagnetic response, are worked out in detail for the case of multilayered superconductors supporting both low-frequency (acoustic) and transverse-optical JPW. Spatial confinement of the Josephson plasma waves may represent a new degree of freedom to engineer their frequencies and to explore the link between interlayer tunneling and high-${T}_{\mathrm{c}}$ superconductivity.

Self-induced terahertz-wave transmissivity of waveguides with finite-length layered superconductors

We predict and study theoretically a new nonlinear electromagnetic phenomenon in a sample of layered superconductor of finite length placed in a waveguide with ideal walls. Two geometries are considered here: when the superconducting layers are parallel or perpendicular to the waveguide axis. We show that the transmittance of the superconductor slab can vary over a wide range, from nearly zero to one, when changing the amplitude of the incident wave. Thus, one can induce the total transmission or reflection of the incident wave by just changing its amplitude. Moreover, the dependence of the superconductor transmittance on the incident wave amplitude has a hysteretic behavior with jumps. The considered phenomenon of self-induced transparency can be observed even at small amplitudes, if the wave frequency $\omega$ is close to the cutoff frequency for linear Josephson plasma waves.

An effect of temperature distribution on terahertz phase dynamics in intrinsic Josephson junctions

In this study, we numerically calculate the temperature distribution and the THz phase dynamics in the mesa-structured intrinsic Josephson junctions (IJJs) using the thermal diffusion equation and the Sine–Gordon equation. We observe that the temperature distribution has a broad peak around the center region of the IJJ mesa. Under a high external current, a “hot spot” where the temperature is locally higher than the superconducting critical temperature appears around this region. The transverse Josephson plasma wave is strongly excited by the inhomogeneous temperature distribution in the mesa. This gives rise to intense THz emission.

Optical excitation of Josephson plasma solitons in a cuprate superconductor

Josephson plasma waves are linear electromagnetic modes that propagate along the planes of cuprate superconductors, sustained by interlayer tunnelling supercurrents. For strong electromagnetic fields, as the supercurrents approach the critical value, the electrodynamics become highly nonlinear. Josephson plasma solitons (JPSs) are breather excitations predicted in this regime, bound vortex-antivortex pairs that propagate coherently without dispersion. We experimentally demonstrate the excitation of a JPS in La1.84Sr0.16CuO4, using intense narrowband radiation from an infrared free-electron laser tuned to the 2-THz Josephson plasma resonance. The JPS becomes observable as it causes a transparency window in the opaque spectral region immediately below the plasma resonance. Optical control of magnetic-flux-carrying solitons may lead to new applications in terahertz-frequency plasmonics, in information storage and transport and in the manipulation of high-Tc superconductivity.

Oblique surface Josephson plasma waves in layered superconductors

We have theoretically studied oblique surface waves (OSWs) which propagate along the interface between a dielectric and a layered superconductor. We assume that this interface is perpendicular to the superconducting layers, and OSWs at the interface can propagate at an arbitrary angle with respect to them. The electromagnetic field of the OSWs in a layered superconductor is a superposition of an ordinary wave (with its electric field parallel to the layers) and an extraordinary wave (with its magnetic field parallel to the layers). We have derived the dispersion equation for the OSWs and shown that the dispersion curves have end points where the extraordinary mode transforms from evanescent wave to bulk wave, propagating deep into the superconductor. In addition, we have analytically solved the problem of the resonance excitation of the OSWs by the attenuated-total-reflection method using an additional dielectric prism. Due to the strong current anisotropy in the boundary of the superconductor, the excitation of the OSWs is accompanied by an additional important phenomenon: The electromagnetic field component with the orthogonal polarization appears in the wave reflected from the bottom of the prism. We show that, for definite optimal combinations of the problem parameters (the wave frequency, the direction of the incident wave vector, the thickness of the gap between dielectric prism and superconductor, etc.), there is a complete suppression of the reflected wave with its polarization coinciding with the polarization of the incident wave. Contrary to the isotropic case, this phenomenon can be observed even in the dissipationless limit. In such a regime, the complete transformation of the incident wave into a reflected wave with orthogonal polarization can be observed.

OBLIQUE SURFACE JOSEPHSON PLASMA WAVES IN LAYERED SUPERCONDUCTORS

In this paper the theoretical analysis of the oblique surface Josephson plasma waves propagating along a dielectric‐layered superconductor interface is first represented. The case when the superconductor layers are perpendicular to the interface is considered. The oblique surface Josephson plasma waves are the surface electromagnetic waves propagating in the interface plane at an arbitrary angle to the superconductor layers. The electromagnetic field of the waves is the superposition of ordinary and extraordinary surface electromagnetic waves. The dispersion equation of the oblique surface Josephson plasma waves has been derived. This equation is the most general dispersion equation of the surface Josephson plasma waves in the case under study. The problem on the excitation of oblique surface Josephson plasma waves by means of the attenuated total reflection method is solved. It has been established that the process of the excitation of oblique surface Josephson plasma waves is accompanied by the onset of an additional reflected wave in the prism with the polarization, being orthogonal to the polarization of the incident wave. It has been found that the reflection coefficient of the exciting wave in the prism can vanish for some optimal parameters of the structure.

Synchronization of Josephson oscillations in a mesa array of Bi2Sr2CaCu2O8+δ through the Josephson plasma waves in the base crystal

Using mesa array fabricated at the top of Bi2Sr2CaCu2O8 single crystal was demonstrated recently as a promising route to enhance the radiation power generated by the Josephson oscillations in mesas. We study the synchronization in such an array via the plasma waves in the base crystal. First, we analyze plasma oscillations inside the base crystal generated by the synchronized mesa array and the associated dissipation. We then solve the dynamic equation for the superconducting phase numerically to find conditions for synchronization and to check the stability of the synchronized state. We find that the mesas are synchronized when the cavity resonance of mesas matches with that of the base crystal. An optimal configuration of the mesa arrays is also obtained.

Transformation of the polarization of THz waves by their reflection and transmission through a finite layered superconductor

The reflection and transmission of terahertz electromagnetic waves propagating in a waveguide through the sample of a layered superconductor of finite length are studied theoretically. The excitation of the two types of Josephson plasma waves, ordinary and extraordinary, in the sample leads to a partial or a complete transformation of the incident wave polarization. The conditions for the complete transformation of polarization are found.

Josephson plasma oscillations in confined layered superconductors

Intrinsic electromagnetic oscillations were investigated in layered superconductors of finite dimensions, filling a rectangular resonator. Spectra of both ordinary and extraordinary eigenmodes were obtained. A nonlinear effect of decreasing eigenfrequencies of extraordinary modes was analyzed and generation of the third harmonic of oscillations was studied. A nonlinearity of the system is related to a nonlinear dependence of the Josephson current density across superconducting layers on interlayer phase difference of the order parameter. Josephson plasma waves running along a waveguide filled with a layered superconductor were investigated as well as nonlinear effects appearing during propagations of these waves. In addition, in the work, an effect of the slowing down of terahertz waves in waveguides, which is caused by a mutual effect of nonlinearity and damping of waves is predicted.

Surface and waveguide Josephson plasma waves in slabs of layered superconductors

We discuss the propagation of symmetric and antisymmetric Josephson plasma waves in a slab of layered superconductor clad between two identical dielectrics. We predict two branches of surface waves in the terahertz frequency range, one above and another below the Josephson plasma frequency. Apart from this, there exists a discrete set of waveguide modes with electromagnetic fields oscillating across the slab thickness and decaying exponentially away from the slab. We consider the excitation of the predicted waves by means of the attenuated-total-reflection method. It is shown that for a specific set of the parameters of the structure, the excitation of the waveguide modes is accompanied by the total suppression of specular reflection.

Interaction of Josephson and magnetic oscillations in Josephson tunnel junctions with a ferromagnetic layer

We study the dynamics of Josephson junctions with a thin ferromagnetic layer F [superconductor-ferromagnet-insulator-ferromagnet-superconductor (SFIFS) junctions]. In such junctions, the phase difference $\phi$ of the superconductors and magnetization $M$ in the F layer are two dynamic parameters coupled to each other. We derive equations describing the dynamics of these two parameters and formulate the conditions of validity. The coupled Josephson plasma waves and oscillations of the magnetization $M$ affect the form of the current-voltage ($I$-$V$) characteristics in the presence of a weak magnetic field (Fiske steps). We calculate the modified Fiske steps and show that the magnetic degree of freedom not only changes the form of the Fiske steps but also the overall view of the $I$-$V$ curve (new peaks related to the magnetic resonance appear). The $I$-$V$ characteristics are shown for different lengths of the junction including those which correspond to the current experimental situation. We also calculate the power $P$ absorbed in the system if a microwave radiation with an ac in-plane magnetic field is applied (magnetic resonance). The derived formula for the power $P$ essentially differs from the one which describes the power absorption in an isolated ferromagnetic film. In particular, this formula describes the peaks related to the excitation of standing plasma waves as well as the peak associated with the magnetic resonance.

Electromagnetic waves in a randomly inhomogeneous Josephson junction

Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of averaged waves, as well as position νm and peak width Δν of the Fourier transform imaginary part of the averaged Green function, are determined as functions of wavevector k. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively agrees with the νm behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on k changes to the inversely proportional one, and damping tends to zero as k → 0, while Δν at small k attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping and Δν are found to be similar functions of k. The results are compared to the numerical calculation data.