Quasiparticle Distribution Function Research Articles

Field, frequency, and temperature dependencies of the surface resistance of nitrogen diffused niobium superconducting radio frequency cavities

We investigate the rf performance of several single-cell superconducting radio-frequency cavities subjected to low temperature heat treatment in nitrogen environment. The cavities were treated at temperature 120–165 °C for an extended period of time (24–48 h) either in high vacuum or in a low partial pressure of ultrapure nitrogen. The improvement in Q0 with a Q rise was observed when nitrogen gas was injected at ∼300 °C during the cavity cooldown from 800 °C and held at 165 °C, without any degradation in accelerating gradient over the baseline performance. The treatment was applied to several elliptical cavities with frequency ranging from 0.75 to 3.0 GHz, showing an improved quality factor as a result of low temperature nitrogen treatments. The Q rise feature is similar to that achieved by nitrogen alloying Nb cavities at higher temperature, followed by material removal by electropolishing. The surface modification was confirmed by the change in electronic mean free path and tuned with the temperature and duration of heat treatment. The decrease of the temperature-dependent surface resistance with increasing rf field, resulting in a Q rise, becomes stronger with increasing frequency and decreasing temperature. The data suggest a crossover frequency of ∼0.95 GHz above that the Q rise phenomenon occurs at 2 K. Some of these results can be explained qualitatively with an existing model of intrinsic field-dependence of the surface resistance with both equilibrium and nonequilibrium quasiparticle distribution functions. The change in the Q slope below 0.95 GHz may result from masking contribution of trapped magnetic flux to the residual surface resistance. Published by the American Physical Society 2024

Nonequilibrium Quasiparticle Distribution in Superconducting Resonators: An Analytical Approach

In the superconducting state, the presence of a finite gap in the excitation spectrum implies that the number of excitations (quasiparticles) is exponentially small at temperatures well below the critical one. Conversely, minute perturbations can significantly impact both the distribution in energy and number of quasiparticles. Typically, the interaction with the electromagnetic environment is the main perturbation source driving quasiparticles out of thermal equilibrium, while a phonon bath is responsible for restoration of equilibrium. Here we derive approximate analytical solutions for the quasiparticle distribution function in superconducting resonators and explore the impact of nonequilibrium on two measurable quantities: the resonator's quality factor and its resonant frequency. Applying our results to experimental data, we conclude that while at intermediate temperatures there is clear evidence for the nonequilibrium effects due to heating of the quasiparticles by photons, the low-temperature measurements are not explained by this mechanism.

Solution of the BEC to BCS Quench in One Dimension.

A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average interparticle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value. Namely, we study a BEC-to-BCS quench. By exploiting a suitable continuum limit of recently discovered solvable quenches in the Hubbard model, we show that the local stationary state reached at large times after the quench can be determined exactly by means of the quench action approach. We provide an experimentally accessible characterization of the stationary state by computing local pair correlation function as well as the quasiparticle distribution functions. We find that the steady state is increasingly dominated by two-particle spin singlet bound states for stronger interaction strength, but that bound state formation is inhibited at larger BEC density. The bound state rapidity distribution displays quartic power-law decay suggesting a violation of Tan's contact relations.

Universal Prethermal Dynamics in Heisenberg Ferromagnets.

We study the far from equilibrium prethermal dynamics of magnons in Heisenberg ferromagnets. We show that such systems exhibit universal self-similar scaling in momentum and time of the quasiparticle distribution function, with the scaling exponents independent of microscopic details or initial conditions. We argue that the SU(2) symmetry of the Hamiltonian, which leads to a strong momentum-dependent magnon-magnon scattering amplitude, gives rise to qualitatively distinct prethermal dynamics from that recently observed in Bose gases. We compute the scaling exponents using the Boltzmann kinetic equation and incoherent initial conditions that can be realized with microwave pumping of magnons. We also compare our numerical results with analytic estimates of the scaling exponents and demonstrate the robustness of the scaling to variations in the initial conditions. Our predictions can be tested in quench experiments of spin systems in optical lattices and pump-probe experiments in ferromagnetic insulators such as yttrium iron garnet.

Stages of the Excitation Relaxation in a Superconductor after the Impact of a Femtosecond Laser Pulse Taking into Account the Momentum Distribution of Quasiparticles

A theoretical model is formulated for the description of the nonequilibrium state of a superconductor on the basis of the nonequilibrium distribution function of phonons and quasiparticles on a finite momentum lattice convenient for numerical simulation. The simulation is performed under conditions of pulsed optical impact demonstrating the role of excess quasiparticles in suppressing the order parameter and the main stages of the relaxation process in the absence of electric current.

Collective modes in pumped unconventional superconductors with competing ground states

Motivated by the recent development of terahertz pump-probe experiments, we investigate the short-time dynamics in superconductors with multiple attractive pairing channels. Studying a single-band square lattice model with spin-spin interaction as an example, we find the signatures of collective excitations of the pairing symmetries (known as Bardasis-Schrieffer modes) as well as the order parameter amplitude (Higgs mode) in the short-time dynamics of the spectral gap and quasiparticle distribution after an excitation by a pump pulse. We show that the polarization and intensity of the pulse can be used to control the symmetry of the non-equilibrium state as well as frequencies and relative intensities of the contributions of different collective modes. We find particularly strong signatures of the Bardasis-Schrieffer mode in the dynamics of the quasiparticle distribution function. Our work shows the potential of modern ultrafast experiments to address the collective excitations in unconventional superconductors and highlights the importance of sub-dominant interactions for the non-equilibrium dynamics in these systems.

Integrable quenches in nested spin chains I: the exact steady states

We consider quantum quenches in the integrable -invariant spin chain (Lai–Sutherland model) which admits a Bethe ansatz description in terms of two different quasiparticle species, providing a prototypical example of a model solvable by nested Bethe ansatz. We identify infinite families of integrable initial states for which analytic results can be obtained. We show that they include special families of two-site product states which can be related to integrable ‘soliton non-preserving’ boundary conditions in an appropriate rotated channel. We present a complete analytical result for the quasiparticle rapidity distribution functions corresponding to the stationary state reached at large times after the quench from the integrable initial states. Our results are obtained within a quantum transfer matrix (QTM) approach, which does not rely on the knowledge of the quasilocal conservation laws or of the overlaps between the initial states and the eigenstates of the Hamiltonian. Furthermore, based on an analogy with previous works, we conjecture analytic expressions for such overlaps: this allows us to employ the quench action method to derive a set of integral equations characterizing the quasi-particle distribution functions of the post-quench steady state. We verify that the solution to the latter coincides with our analytic result found using the QTM approach. Finally, we present a direct physical application of our results by providing predictions for the propagation of entanglement after the quench from such integrable states.

Non-equilibrium quasiparticles in superconducting circuits: photons vs. phonons

We study the effect of non-equilibrium quasiparticles on the operation of a superconducting device (a qubit or a resonator), including heating of the quasiparticles by the device operation. Focusing on the competition between heating via low-frequency photon absorption and cooling via photon and phonon emission, we obtain a remarkably simple non-thermal stationary solution of the kinetic equation for the quasiparticle distribution function. We estimate the influence of quasiparticles on relaxation and excitation rates for transmon qubits, and relate our findings to recent experiments.

Topological interpretation of the Luttinger theorem

Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and noninteracting single-particle Green's functions, is also represented as the winding number of this ratio. The formulation based on the winding number naturally leads to two types of the generalized Luttinger theorem. Exploring two examples of single-band translationally invariant interacting electrons, i.e., simple metal and Mott insulator, we show that the first type falls into the original statement for Fermi liquids given by Luttinger, while the second type corresponds to the extended one for non metallic cases with no Fermi surface generalized by Dzyaloshinskii. This formulation also allows us to derive a sufficient condition for the validity of the Luttinger theorem of the first type by applying the Rouche's theorem in complex analysis as an inequality. Moreover, we can rigorously prove in a non-perturbative manner, without assuming any detail of a microscopic Hamiltonian, that the generalized Luttinger theorem of both types is valid for generic interacting fermions as long as the particle-hole symmetry is preserved. Finally, we show that the winding number of the single-particle Green's function can also be associated with the distribution function of quasiparticles, and therefore the number of quasiparticles is equal to the Luttinger volume.

Departure from equilibrium of the quasiparticle distribution functions in high-energy nuclear collisions

In simulations of high energy heavy ion collisions that employ viscous hydrodynamics, single particle distributions are distorted from their thermal equilibrium form due to gradients in the flow velocity. These are closely related to the formulas for the shear and bulk viscosities in the quasi-particle approximation. Distorted single particle distributions are now commonly used to calculate the emission of photons and dilepton pairs, and in the late stage to calculate the conversion of a continuous fluid to individual particles. We show how distortions of the single particle distribution functions due to both shear and bulk viscous effects can be done rigorously in the quasi-particle approximation and illustrate it with the linear $\sigma$ model at finite temperature.

The non-equilibrium response of a superconductor to pair-breaking radiation measured over a broad frequency band

We have measured the absorption of terahertz radiation in a BCS superconductor over a broad range of frequencies from 200 GHz to 1.1 THz, using a broadband antenna-lens system and a tantalum microwave resonator. From low frequencies, the response of the resonator rises rapidly to a maximum at the gap edge of the superconductor. From there on, the response drops to half the maximum response at twice the pair-breaking energy. At higher frequencies, the response rises again due to trapping of pair-breaking phonons in the superconductor. In practice, this is a measurement of the frequency dependence of the quasiparticle creation efficiency due to pair-breaking in a superconductor. The efficiency, calculated from the different non-equilibrium quasiparticle distribution functions at each frequency, is in agreement with the measurements.

On time-resolved approach for phonon assisted interband transitions

Photoexcited dynamics of electrons and holes in two-band dielectric, with special emphasis on back reaction of phonons are developed by combining the quantum electrodynamics and Baker-Campbell-Hausdorff (BCH) canonical transformation. These methods create an explicit time-domain representation of photoinduced processes and contribute in unifying phonon-assisted description of distribution functions of electron and hole quasiparticles for the description of observable effects of photoinduced processes in dielectrics.

Thermodynamics of the Quark‐Gluon Plasma at Finite Chemical Potential: Color Path Integral Monte Carlo Results

AbstractBased on the constituent quasiparticle model of the quark‐gluon plasma (QGP), color quantum path‐integral Monte‐Carlo (PIMC) calculations of the thermodynamic properties of the QGP are performed. We extend our previous zero chemical potential simulations to the QGP at finite baryon chemical potential. The results indicate that color PIMC can be applied not only above the QCD critical temperature Tc but also below Tc. Besides reproducing the lattice equation of state our approach yields also valuable additional insight into the internal structure of the QGP, via the pair distribution functions of the various quasiparticles. In particular, the pair distribution function of gluons reflects the existence of gluon‐gluon bound states at low temperatures and μ = 175 MeV, i.e. glueballs, while meson‐like bound states are not found. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phonon-assisted kinetics of electron-hole pair in two-band model

Photoexcited kinetics of electrons and holes in two-band dielectric including phonon-assisted generation of the electron-hole pair is modelled by combining the quantum field and solid-state band theory. These methods create an explicit time-domain representation of photoinduced processes without resorting to the perturbation theory for the electromagnetic field. Input entities for the two-band model are dispersion relations for the electron and hole, the band-gap, and the phonon frequencies computed by nonrelativistic methods or found experimentally. The phonon-assisted electron-hole pair kinetics is initiated by the BakerCampbell-Hausdorff canonical transformation accounting for the back reaction of phonons to the electron-hole subsystem. The output is a unifying phonon-assisted description of the distribution function of electron and hole quasiparticles.

Temporary cooling of quasiparticles and delay in voltage response of superconducting bridges after abruptly switching on the supercritical current

We revisit the problem of the dynamic response of a superconducting bridge after abruptly switching on the supercritical current $I>I_c$. In contrast to previous theoretical works we take into account spatial gradients and use both the local temperature approach and the kinetic equation for the distribution function of quasiparticles. In both models the finite delay time $t_d$ in the voltage response is connected with temporary cooling of quasiparticles due to the suppression of the superconducitng order parameter by current. We find that $t_d$ has different values and different temperature dependencies in the considered models. In turns out that the presence of even small inhomogeneities in the bridge or of bulk leads/contacts at the ends of the {\it homogenous} bridge favors a local suppression of the superconducting order parameter $|\Delta|$ during the dynamic response. It results in a decrease of the delay time, in comparison with the spatially uniform model, due to the diffusion of nonequilibrium quasiparticles from the region with locally suppressed $|\Delta|$. In case the current distribution is spatially nonuniform across the bridge the delay time is mainly connected with the time needed for the nucleation of the first vortex at the position where the current density is maximal (at $I\sim I_c$ and for not very wide films). We also find that a short alternating current pulse (sinusoid like) with zero time-average may result in a nonzero time-averaged voltage response where its sign depends on the phase of the ac current.

Nonequilibrium spectroscopy of topological edge liquids

We develop a theory for energy and spatially resolved tunneling spectroscopy of topological quantum spin Hall helical states driven out of equilibrium. When a helical liquid is constrained between two superconducting reservoirs transport at the edge is governed by multiple Andreev reflections. The resulting quasiparticle distribution functions of the edge channels exhibit multiple discontinuities at subgap energies with the periodicity of an applied voltage. The combined effect of interactions, disorder, and normal scattering off the superconducting interface leads to the inelastic processes mixing different helicity modes, thus causing smearing of these singularities. If equilibration is strong, then the distribution functions of the edge channels tend to collapse into a Fermi-like function with an effective temperature determined by the superconducting gap, applied voltage, and intraedge interaction parameter. We conclude that mapping out nonequilibrium distribution functions may help to quantify the relative importance of various relevant perturbations that spoil ideally ballistic edge transport.

PAULI EXCLUSION PRINCIPLE

In terms of an exact equation for the thermodynamic potential due to interaction between two particles and based on Green's function method; we have derived the Landau expansion of the thermodynamic potentials in terms of the variation of the quasiparticle distribution function. We have also derived the expansion of the thermodynamic potential in terms of the variation of an exact single particle (not quasiparticles), this derivations lead to the relationship between the interaction function for two quasiparticles and the interaction energy between two particles as shown. Further, in terms of the four-point vertex part we are led to the Pauli exclusion principle.

Superconductivity in a Fermi liquid from repulsive interactions: The role of electron–phonon interaction

Based on our previously proven theorem that the interaction between a pair of quasiparticles in the normal Fermi liquid has an opposite sign to the interaction between particles, we consider pair correlation between a pair of quasiparticles when the interaction between particles is repulsive. For the convenience of statements, we have presented in this article once again the proof of the theorem in terms of an exact equation for the thermodynamic potential due to interaction between particles and based on the Green’s function method. Further, we have derived the Landau expansion of the thermodynamic potentials in terms of the variation of the quasiparticle distribution function. We have also derived the expansion of the thermodynamic potential in terms of the variation of an exact single particle (not quasiparticles), these derivations lead to the relationship between the interaction function for two quasiparticles and the interaction energy between two particles as shown.According to the proven theorem the interaction between a pair of quasiparticles is attractive in this case, the pairing – Cooper’s pairing between a pair of quasiparticles is possible. We solve the Bethe–Salpeter type equation for paring of two quasiparticles when both interactions – the Coulomb repulsive and electron–phonon interaction are present. We show that the electron–phonon interaction, in fact, leads to the pair breaking effect, in contrast to the common belief that electron–phonon interaction is the main mechanism for Cooper’s pair formation. We have calculated the transition temperature and the isotope effect on the transition temperature in terms of the Bethe–Salpeter equation.

Non-equilibrium superconductivity in quantum-sensing superconducting resonators

Low temperature microwave superconducting resonators (SRs) are attractive candidates for producing quantum-sensitive, arrayable energy or power detectors for astrophysical and other precision measurement applications. Their readout uses a microwave probe signal with quanta of energy well below the threshold for pair-breaking in the superconductor. We have calculated the non-equilibrium quasiparticle and phonon distributions generated by the photons of the probe signal of a resonator operating well below its superconducting transition temperature Tc as the absorbed probe power was changed using the coupled kinetic equations described by Chang and Scalapino. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from their thermal equilibrium value for typical readout powers. From the driven quasiparticle distribution functions, the driven quasiparticle number densities and lifetimes were calculated. An effective temperature to describe the driven quasiparticles was defined. The non-equilibrium lifetimes were compared to the distribution-averaged thermal lifetimes at the effective temperature and good agreement was found typically within a few per cent. We used the non-equilibrium quasiparticle distribution to model a representative SR. The complex conductivity and hence the frequency dependence of the experimentally measured forward scattering parameter S21 of the SR as a function of absorbed power were found. The non-equilibrium S21 cannot be accurately modeled by a thermal distribution even at its own elevated temperature, having a higher quality factor in all cases studied, although for low absorbed powers the two effective temperatures are similar. From the non-equilibrium lifetimes and number densities we determined the achievable noise equivalent power (NEP) of the resonator used as a power detector as a function of absorbed microwave power. Simpler expressions to evaluate the effective quasiparticle temperature as a function of absorbed power have also been derived. We conclude that multiple photon absorption from the microwave probe increases the quasiparticle number above the thermal background and ultimately limits the achievable NEP of the resonator at temperatures well below Tc.

Origin of the hysteresis of the current voltage characteristics of superconducting microbridges near the critical temperature

The current voltage (IV) characteristics of short [with length $L\ensuremath{\lesssim}\ensuremath{\xi}(T)$] and long [$L\ensuremath{\gg}\ensuremath{\xi}(T)$] microbridges are theoretically investigated near the critical temperature of the superconductor. Calculations are made in the nonlocal (local) limit when the inelastic relaxation length due to electron-phonon interactions ${L}_{in}={(D{\ensuremath{\tau}}_{in})}^{1/2}$ is larger (smaller) than the temperature-dependent coherence length $\ensuremath{\xi}(T)$ ($D$ is the diffusion coefficient, ${\ensuremath{\tau}}_{in}$ is the inelastic relaxation time of the quasiparticle distribution function). We find that, in both limits, the origin of the hysteresis in the IV characteristics is mainly connected with the large time scale over which the magnitude of the order parameter varies in comparison with the time-scale variation of the superconducting phase difference across the microbridge in the resistive state. In the nonlocal limit, the time-averaged heating and cooling of quasiparticles are found in different areas of the microbridge, which are driven, respectively, by oscillations of the order parameter and the electric field. We show that, by introducing an additional term in the time-dependent Ginzburg-Landau equation, it is possible to take into account the cooling effect in the local limit too.