Number Of Quasiparticles Research Articles

Fuzzy dark matter dynamics and the quasi-particle hypothesis

ABSTRACT Dark matter may be composed of ultralight bosons whose de Broglie wavelength in galaxies is $\lambda \sim 1\, {\rm kpc}$. The standard model for this fuzzy dark matter (FDM) is a complex scalar field that obeys the Schrödinger–Poisson equations. The wavelike nature of FDM leads to fluctuations in the gravitational field that can pump energy into the stellar components of a galaxy. Heuristic arguments and theoretical analyses suggest that these fluctuations can be modelled by replacing FDM with a system of quasi-particles (QPs). We test this hypothesis by comparing self-consistent simulations of a Schrödinger field with those using a system of QPs in one spatial dimension. Simulations of pure FDM systems allow us to derive a phenomenological relation between the number of QPs that is required to model FDM with a given de Broglie wavelength. We also simulate systems of FDM and stars and find that the FDM pumps energy into the stars whether it is described by QPs or a Schrödinger field with the FDM adiabatically contracting and the stellar system adiabatically expanding. However, we find that QPs overestimate dynamical heating.

Quantum bath suppression in a superconducting circuit by immersion cooling

Quantum circuits interact with the environment via several temperature-dependent degrees of freedom. Multiple experiments to-date have shown that most properties of superconducting devices appear to plateau out at T ≈ 50 mK – far above the refrigerator base temperature. This is for example reflected in the thermal state population of qubits, in excess numbers of quasiparticles, and polarisation of surface spins – factors contributing to reduced coherence. We demonstrate how to remove this thermal constraint by operating a circuit immersed in liquid 3He. This allows to efficiently cool the decohering environment of a superconducting resonator, and we see a continuous change in measured physical quantities down to previously unexplored sub-mK temperatures. The 3He acts as a heat sink which increases the energy relaxation rate of the quantum bath coupled to the circuit a thousand times, yet the suppressed bath does not introduce additional circuit losses or noise. Such quantum bath suppression can reduce decoherence in quantum circuits and opens a route for both thermal and coherence management in quantum processors.

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.

Resolving Power of Visible-To-Near-Infrared Hybrid β−Ta/Nb−Ti−N Kinetic Inductance Detectors

Kinetic inductance detectors (KIDs) are superconducting energy-resolving detectors, sensitive to single photons from the near-infrared to ultraviolet. We study a hybrid KID design consisting of a $\ensuremath{\beta}$-phase tantalum ($\ensuremath{\beta}$-$\mathrm{Ta}$) inductor and a $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{Ti}\text{\ensuremath{-}}\mathrm{N}$ interdigitated capacitor. The devices show an average intrinsic quality factor ${Q}_{i}$ of $4.3\ifmmode\times\else\texttimes\fi{}{10}^{5}\ifmmode\pm\else\textpm\fi{}1.3\ifmmode\times\else\texttimes\fi{}{10}^{5}$. To increase the power captured by the light-sensitive inductor, we 3D print an array of $150\ifmmode\times\else\texttimes\fi{}150\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ resin microlenses on the backside of the sapphire substrate. The shape deviation between design and printed lenses is smaller than $1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$, and the alignment accuracy of this process is ${\ensuremath{\delta}}_{x}=+5.8\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ and ${\ensuremath{\delta}}_{y}=+8.3\ifmmode\pm\else\textpm\fi{}3.3\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$. We measure a resolving power for 1545--402 nm that is limited to 4.9 by saturation in the KID's phase response. We can model the saturation in the phase response with the evolution of the number of quasiparticles generated by a photon event. An alternative coordinate system that has a linear response raises the resolving power to 5.9 at 402 nm. We verify the measured resolving power with a two-line measurement using a laser source and a monochromator. We discuss several improvements that can be made to the devices on a route towards KID arrays with high resolving powers.

Interference Measurements of Non-Abelian e/4 & Abelian e/2 Quasiparticle Braiding

The quantum Hall states at filling factors $\nu=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. The non-Abelian statistics of the latter has been predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of magnetic field in Fabry-P\'erot interferometers using new high purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations at $\nu=7/2$. At both $\nu=5/2$ and $7/2$ we also examine, for the first time, the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near both filling factors, indicating stability of the fermion parity. At both fractions, when phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with either fermion parity change or change in the number of the enclosed $e/4$ quasiparticles. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.

Anomalous Fano factor as a signature of Bogoliubov Fermi surfaces

Bogoliubov Fermi surfaces consist of an extensive number of Bogoliubov quasiparticles and can be created, for example, in semiconductor/superconductor hybrid devices. Noise spectroscopy is proposed to detect the presence of Bogoliubov Fermi surfaces in experiments.

Symmetry resolved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits

The excess entanglement resulting from exciting a finite number of quasiparticles above the ground state of a free integrable quantum field theory has been investigated quite extensively in the literature. It has been found that it takes a very simple form, depending only on the number of excitations and their statistics. There is now mounting evidence that such formulae also apply to interacting and even higher-dimensional quantum theories. In this paper we study the entanglement content of such zero-density excited states focusing on the symmetry resolved entanglement, that is on 1+1D quantum field theories that possess an internal symmetry. The ratio of charged moments between the excited and grounds states, from which the symmetry resolved entanglement entropy can be obtained, takes a very simple and universal form, which in addition to the number and statistics of the excitations, now depends also on the symmetry charge. Using form factor techniques, we obtain both the ratio of moments and the symmetry resolved entanglement entropies in complex free theories which possess U(1) symmetry. The same formulae are found for simple qubit states.

Incoherent excitation of coherent Higgs oscillations in superconductors

We investigate theoretically the excitation of Higgs oscillations of the order parameter in superconductors by incoherent short pulses of light with frequency much larger than the superconducting gap. The excitation amplitude of the Higgs mode is controlled by a single parameter which is determined by the total number of quasiparticles excited by the pulse. This fact can be traced back to the universality of the shape of the light-induced quasiparticle cascade at energy below the Debye frequency and above the gap.

A superconductor free of quasiparticles for seconds

Superconducting devices, based on the Cooper pairing of electrons, play an important role in existing and emergent technologies, ranging from radiation detectors to quantum computers. Their performance is limited by spurious quasiparticle excitations formed from broken Cooper pairs. Efforts to achieve ultra-low quasiparticle densities have reached time-averaged numbers of excitations on the order of one in state-of-the-art devices. However, the dynamics of the quasiparticle population as well as the time scales for adding and removing individual excitations remain largely unexplored. Here, we experimentally demonstrate a superconductor completely free of quasiparticles for periods lasting up to seconds. We monitor the quasiparticle number on a mesoscopic superconductor in real time by measuring the charge tunneling to a normal metal contact. Quiet, excitation-free periods are interrupted by random-in-time Cooper pair breaking events, followed by a burst of charge tunneling within a millisecond. Our results demonstrate the possibility of operating devices without quasiparticles with potentially improved performance. In addition, our experiment probes the origins of nonequilibrium quasiparticles in our device; the decay of the Cooper pair breaking rate over several weeks following the initial cooldown rules out processes arising from cosmic or long-lived radioactive sources.

Strong reduction of quasiparticle fluctuations in a superconductor due to decoupling of the quasiparticle number and lifetime

We measure temperature dependent quasiparticle fluctuations in a small Al volume, embedded in a NbTiN superconducting microwave resonator. The resonator design allows for read-out close to equilibrium. By placing the Al film on a membrane, we enhance the fluctuation level and separate quasiparticle from phonon effects. When lowering the temperature, the recombination time saturates and the fluctuation level reduces a factor $\sim$100. From this we deduce that the number of free quasiparticles is still thermal. Therefore, the theoretical, inverse relation between quasiparticle number and recombination time is invalid in this experiment. This is consistent with quasiparticle trapping, where on-trap recombination limits the observed quasiparticle lifetime.

Continuous real-time detection of quasiparticle trapping in aluminum nanobridge Josephson junctions

Nonequilibrium quasiparticles are ubiquitous in superconducting electronics. These quasiparticles can trap in the internal Andreev bound states of a phase-biased Josephson junction, providing a mechanism for studying their presence and behavior. We characterize a quasiparticle trapping detector device based on a two junction aluminum nanobridge superconducting quantum interference device incorporated into a transmission line resonator. When the device is flux-biased, distinct resonant frequencies develop depending on the trapped quasiparticle number. We demonstrate continuous detection of up to 3 trapped quasiparticles, with detection of a trapped quasiparticle with a signal-to-noise ratio of 27 in 5 μs. We describe initial measurements of quasiparticle behavior and discuss the possible optimization and application of such detector devices.

Time-dependent electric transport in nodal loop semimetals

Close to the Fermi energy, nodal loop semimetals have a torus-shaped, strongly anisotropic Fermi surface which affects their transport properties. Here we investigate the non-equilibrium dynamics of nodal loop semimetals by going beyond linear response and determine the time evolution of the current after switching on a homogeneous electric field. The current grows monotonically with time for electric fields perpendicular to the nodal loop plane however it exhibits non-monotonical behavior for field orientations aligned within the plane. After an initial non-universal growth $\sim Et$, the current first reaches a plateau $\sim E$. Then, for perpendicular directions, it increases while for in-plane directions it decreases with time to another plateau, still $\sim E$. These features arise from interband processes. For long times or strong electric fields, the current grows as $\sim E^{3/2}t$ or $\sim E^3t^2$ for perpendicular or parallel electric fields, respectively. This non-linear response represents an intraband effect where the large number of excited quasiparticles responds to the electric field. Our analytical results are benchmarked by the numerical evaluation of the current from continuum and tight-binding models of nodal loop semimetals.

A method to measure superconducting transition temperature of microwave kinetic inductance detector by changing power of readout microwaves

A microwave kinetic inductance detector (MKID) is a cutting-edge superconducting detector, and its principle is based on a superconducting resonator circuit. The superconducting transition temperature (Tc) of the MKID is an important parameter because various MKID characterization parameters depend on it. In this paper, we propose a method to measure the Tc of the MKID by changing the applied power of the readout microwaves. A small fraction of the readout power is deposited on the MKID, and the number of quasiparticles in the MKID increases with this power. Furthermore, the quasiparticle lifetime decreases with the number of quasiparticles. Therefore, we can measure the relation between the quasiparticle lifetime and the detector response by rapidly varying the readout power. From this relation, we evaluate the intrinsic quasiparticle lifetime. This lifetime is theoretically modeled by Tc, the physical temperature of the MKID device, and other known parameters. We obtain Tc by comparing the measured lifetime with that acquired using the theoretical model. Using an MKID fabricated with aluminum, we demonstrate this method at a 0.3 K operation. The results are consistent with those obtained by Tc measured by monitoring the transmittance of the readout microwaves with the variation in the device temperature. The method proposed in this paper is applicable to other types, such as a hybrid-type MKID.

Observation of quantum Hall interferometer phase jumps due to a change in the number of bulk quasiparticles

We measure the magneto-conductance through a micron-sized quantum dot hosting about 500 electrons in the quantum Hall regime. In the Coulomb blockade, when the island is weakly coupled to source and drain contacts, edge reconstruction at filling factors between one and two in the dot leads to the formation of two compressible regions tunnel coupled via an incompressible region of filling factor $\nu=1$. We interpret the resulting conductance pattern in terms of a phase diagram of stable charge in the two compressible regions. Increasing the coupling of the dot to source and drain, we realize a Fabry-P\'{e}rot quantum Hall interferometer, which shows an interference pattern strikingly similar to the phase diagram in the Coulomb blockade regime. We interpret this experimental finding using an empirical model adapted from the Coulomb blockaded to the interferometer case. The model allows us to relate the observed abrupt jumps of the Fabry-P\'{e}rot interferometer phase to a change in the number of bulk quasiparticles. This opens up an avenue for the investigation of phase shifts due to (fractional) charge redistributions in future experiments on similar devices.

DEMETRA: Suppression of the Relaxation Induced by Radioactivity in Superconducting Qubits

Non-equilibrium quasiparticles can deteriorate the performance of superconducting qubits by reducing their coherence. We are investigating a source of quasiparticles that has been too long neglected, namely radioactivity: cosmic rays, environmental radioactivity and contaminants in the materials can all generate phonons of energy sufficient to break Cooper pairs and thus increase the number of quasiparticles. In this contribution, we describe the status of the project and its perspectives.

Projected shell model analysis of structural evolution and chaoticity in fast-rotating nuclei

Rotationally-induced chaotic motion in fast-rotating nuclei is investigated using the projected shell model with an aggressively extended multi-quasiparticle configuration space. The two-body Hamiltonian in separable forms with quadrupole–quadrupole plus pairing forces is diagonalized in superimposed states with more than 2000 angular momentum projected configurations. By taking 164Yb as an example, it is shown that the experimental energies and moment of inertia (MoI) for the yrast band can be clearly described. The variations in MoI are explained in terms of band crossings among the 2-quasiparticle (qp), 4-qp, 6-qp, and 8-qp bands, corresponding to successive pair-breakings caused by rotation. Moreover, the chaotic motion in different spin and excitation regions is studied by quantitatively analyzing the branching number. It is found that the degree of chaoticity increases monotonically with spin and excitation energy. At the highest spins, bands built by different numbers of quasiparticles, with their own characteristic rotational behavior originally at low spins, tend to rotate uniformly with the same rotational frequency, indicating an emergent nuclear collectivity appearing from an extremely chaotic system. The important role played by nucleon pairing in increasing the chaoticity is emphasized.

Characteristics of Very High Q Nb Superconducting Resonators for Microwave Kinetic Inductance Detectors

We have prepared superconducting resonators using high-quality Nb thin films with RRR = 48 and studied their resonance characteristics in detail. It was observed that the measured internal quality factor Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> reached as high as 4×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> , which might be the highest value obtained among the Nb thin film superconducting resonators ever reported. It is demonstrated that the temperature dependence of the internal quality factors can be well explained by considering the temperature dependence of the residual resistance due to phonon scattering, electron-electron scattering, and the Kondo effect of the residual quasiparticle in addition to the extended Mattis-Bardeen theory. It is also found that the change of the resonance frequency of the Nb thin film resonator with respect to temperature can be well explained by considering the temperature dependence of both the Kondo effect and the kinetic inductance of the residual quasiparticles. These results strongly indicate that a finite number of quasiparticles are present in the superconducting gap of the high-quality Nb film even at a sufficiently low temperature of T/T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <; 0.15 and form a Fermi liquid state.

A measurement method for responsivity of microwave kinetic inductance detector by changing power of readout microwaves

Superconducting detectors are a modern technology applied in various fields. The microwave kinetic inductance detector (MKID) is one of the cutting-edge superconducting detectors. It is based on the principle of a superconducting resonator circuit. A radiation entering the MKID breaks the Cooper pairs in the superconducting resonator, and the intensity of the radiation is detected as a variation of the resonant condition. Therefore, calibration of the detector responsivity, i.e., the variation of the resonant phase with respect to the number of Cooper-pair breaks (quasiparticles), is important. We propose a method for responsivity calibration. Microwaves used for the detector readout locally raise the temperature in each resonator, which increases the number of quasiparticles. Since the magnitude of the temperature rise depends on the power of readout microwaves, the number of quasiparticles also depends on the power of microwaves. By changing the power of the readout microwaves, we simultaneously measure the phase difference and lifetime of quasiparticles. We calculate the number of quasiparticles from the measured lifetime and by using a theoretical formula. This measurement yields a relation between the phase responses as a function of the number of quasiparticles. We demonstrate this responsivity calibration using the MKID maintained at 285 mK. We also confirm the consistency between the results obtained using this method and conventional calibration methods in terms of the accuracy.

Fermionic quantum spin liquids: Exact results for parametric pumping

The time dependence of the response of the quantum spin liquid with fermionic excitations to parametric pumping has been calculated exactly for the special case of periodic pumping, the steplike periodic field, without using the resonance approximation, and for any value of the pumping magnitude. In the closed regime each mode (related to each eigenstate of the system) oscillates with time. The oscillations persist about the steady-state values, which are determined by the parameters of the pumping. The magnitude of the oscillations is finite for any value of the magnitude of the pumping. Those features drastically differ from the well-known resonance parametric pumping of magnons in magnetically ordered system, where the number of resonance magnons grows exponentially in time. The interference of infinitely many modes generically yields only decaying-in-time modulated oscillations of the total number of quasiparticles per mode even in the closed regime. For the fermionic system only one mode is in resonance, while others are out of resonance. It is totally different from the bosonic behavior of magnons under parametric pumping, where all modes can exist in resonance. The inclusion of the linear relaxation in the open regime for that quantum spin liquid produces the decay of oscillations to the initial state.

Exact excited states of nonintegrable models

We discuss a method of numerically identifying exact energy eigenstates for a finite system, whose form can then be obtained analytically. We demonstrate our method by identifying and deriving exact analytic expressions for several excited states, including an infinite tower, of the one dimensional spin-1 AKLT model, a celebrated non-integrable model. The states thus obtained for the AKLT model can be interpreted as one-to-an extensive number of quasiparticles on the ground state or on the highest excited state when written in terms of dimers. Included in these exact states is a tower of states spanning energies from the ground state to the highest excited state. To our knowledge, this is the first time that exact analytic expressions for a tower of excited states have been found in non-integrable models. Some of the states of the tower appear to be in the bulk of the energy spectrum, allowing us to make conjectures on the strong Eigenstate Thermalization Hypothesis (ETH). We also generalize these exact states including the tower of states to the generalized integer spin AKLT models. Furthermore, we establish a correspondence between some of our states and those of the Majumdar-Ghosh model, yet another non-integrable model, and extend our construction to the generalized integer spin AKLT models.