Quantum coherent manipulation and readout of superconducting vortex states
Ameya Nambisan, Simon Günzler, Rieger, Dennis, Nicolas Gosling, Simon Geisert, Victor Carpentier, Nicolas Zapata, Mitchell Field, M. V. Miloševıć, Lopez, Carlos A. Diaz, Ciprian Padurariu, Björn Kubala, Joachim Ankerhold, Wolfgang Wernsdorfer, Martin Spiecker, Ioan M. Pop
A defining characteristic of superconductors is their tendency to expel magnetic fields, yet above a critical threshold, magnetic flux penetrates in discrete quanta carried by Abrikosov vortices. The superconducting gap is completely suppressed at the vortex core, rendering them dissipative, semi-classical entities that impact applications from high-current-density wires to quantum devices. Material disorder can drive a crossover to vortices that preserve an energy gap at the core owing to intrinsic or emergent granularity on the scale of the coherence length. Although quantum vortex behaviour could emerge in this effective tunnel-junction regime, and signatures have been observed in diverse systems, coherent manipulation of vortex states has remained elusive. Here we present evidence that vortices trapped in granular superconducting films can behave as two-level systems, exhibiting microsecond-range quantum coherence and energy relaxation times that reach fractions of a millisecond. Using the tools of circuit quantum electrodynamics, we perform coherent manipulation and quantum non-demolition readout of vortex states in granular aluminium microwave resonators, heralding future directions for quantum information processing, materials characterization and sensing.
A defining characteristic of superconductors is their tendency to expel magnetic fields, yet above a critical threshold, magnetic flux penetrates in discrete quanta carried by Abrikosov vortices. The superconducting gap is completely suppressed at the vortex core, rendering them dissipative, semi-classical entities that impact applications from high-current-density wires to quantum devices. Material disorder can drive a crossover to vortices that preserve an energy gap at the core owing to intrinsic or emergent granularity on the scale of the coherence length. Although quantum vortex behaviour could emerge in this effective tunnel-junction regime, and signatures have been observed in diverse systems, coherent manipulation of vortex states has remained elusive. Here we present evidence that vortices trapped in granular superconducting films can behave as two-level systems, exhibiting microsecond-range quantum coherence and energy relaxation times that reach fractions of a millisecond. Using the tools of circuit quantum electrodynamics, we perform coherent manipulation and quantum non-demolition readout of vortex states in granular aluminium microwave resonators, heralding future directions for quantum information processing, materials characterization and sensing.
Using a self-devised numerical approach, we developed a powerful tool to investigate vortex properties and interactions in mean-field theories for superconductors and superfluids, based on fixing the vortex phase distribution in the energy minimization process. The method was applied to (i) multi-component Bose-Einstein condensates (BECs) and (ii) superconductors with single- or multi-component superconducting condensates. In these systems, vortex-vortex interaction and other key vortex features are analytically described only in specific regimes, that do not account for a large part of vortex behavior observed experimentally. In multi-component BECs, for example, the vortex-vortex interaction is only known for inter-vortex distances much greater than the healing length, i.e. far from the vortex core. Under our approach, by assuming multi-vortex structures, within Gross-Pitaevskii theory, we report the vortex-vortex interaction in the full range of distances, capturing the mechanism behind unusual vortex conformations previously reported in literature, such as bound clusters with two or three vortices. Usually, these clusters emerge from a competition between intra- and inter-component vortex interaction, but we demonstrate they can also emerge from the phase-frustration between the components. In superconductors, the description of vortex-vortex interaction is usually restricted to bulk or very thin films, and most of the key vortex features, such as the spatial magnetic field and current density profiles, are known only in the limit of London theory, i.e. for coherence length negligible as compared to magnetic field penetration depth and other system dimensions. The parametric range outside this limit is actually relevant to many materials. We fill that gap by applying our method to Ginzburg-Landau theory. The vortex structure is investigated for single- and two-gap bulk superconductors, outside the London regime. This enables us to extend analytical expressions describing the condensate and magnetic profiles around the vortex available in literature by numerical calculations and suitable fitting functions. We expand our approach to account for films with finite thickness, to connect our findings to both bulk and Pearl’s description by adjusting the sample thickness. This also allowed us to describe how vortex configurations change for samples with intermediate thickness, where we observe the effective magnetic response of the superconductor changing between the textbook type-1 and type-2 behaviors, in a nontrivial manner, governed by the non-monotonic vortex interaction. As a result of a detailed analysis, we propose new critical parameters to define the crossover between different regimes and establish their relation with the superconducting critical fields.
We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving, it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.
Superconductivity is an electronic state of matter arising from the existence of a common wave function with a coherent phase extending on a truly macroscopic scale. One major manifestation of this striking quantum phenomenon is the dissipationless transport of electrical current, an asset deserving particular attention in the present times where the efficient energy distribution has become of utmost importance. Unfortunately, the motion of quantum units of magnetic flux (so-called vortices or fluxons), which is an unavoidable side-effect found in superconductors in the presence of transport currents and magnetic fields, severely limits the conditions to preserve dissipationless transport. This poses a challenge for achieving the functionalization of superconducting materials and threatens their spectrum of applications. It is widely known that any inhomogeneities (either material imperfections, or ones made artificially), which locally suppress superconductivity on the scale comparable to the core of the vortex, can pin the vortex and delay the onset of the vortex motion to higher applied currents. In recent years a substantial effort has been made to minimize the effects of current-induced vortex motion by tailoring arrays of artificial pinning centers. Besides improving the critical parameters of the superconducting state, a pinning matrix can be used for the manipulation of vortex matter, thus directly affecting the vortex dynamics, such as rectification of vortex motion under an ac drive (vortex diode) by introducing asymmetric pinning landscapes. In the literature one can find that the realization of the anchoring of the vortices can be based on nanostructured arrays of perforations, chemically grown defects, permanent nanomagnets, or even pinning sites produced by heavy ion bombardment. All of those realizations are based on a permanent imprint on the superconductor, without any possibility for subsequent modifications in the distribution and strength of the pinning. The principal objective of this thesis is to investigate the dynamical behavior of vortex matter under an entirely new kind of pinning landscape consisting of spatial and temporal modulation of the superconducting condensate. A particular case of spatial modulation is considered in a constricted structure where current lensing can cause extremely high vortex velocities. Subsequently, a time-dependent thermal potential introduced to the superconducting condensate will cause stroboscopic resonances during the vortex motion - a phenomenon that cannot be observed in the systems with static pinning imprints. Finally, a study of electronic gating is presented, where the local properties of superconductor, such as mean free path, or electronic band structure in general, can be influenced electronically. This is a completely unexplored interdisciplinary research topic, which will eventually allow one to manipulate individual vortices in superconducting materials by means of spatially confined and temporally controlled thermal and electromagnetic excitations. Furthermore, such techniques can provide one fundamental insight in different states of the vortex matter with respect to variation of the transport current, highly relevant for understanding the resistive state of superconducting materials and their applications.
Coherent control of quantum states has been demonstrated in a variety of superconducting devices. In all of these devices, the variables that are manipulated are collective electromagnetic degrees of freedom: charge, superconducting phase, or flux. Here we demonstrate the coherent manipulation of a quantum system based on Andreev bound states, which are microscopic quasi-particle states inherent to superconducting weak links. Using a circuit quantum electrodynamics setup, we performed single-shot readout of this Andreev qubit. We determined its excited-state lifetime and coherence time to be in the microsecond range. Quantum jumps and parity switchings were observed in continuous measurements. In addition to having possible quantum information applications, such Andreev qubits are a test-bed for the physics of single elementary excitations in superconductors.
Microwave resonators fabricated from superconducting thin films are playing a critical role with recent advances in superconducting quantum computing technology and photon detectors. There has been an intensive worldwide effort to study the sources of loss that limit the quality factors of these resonators. In this thesis, I have focused on the measurements of the microwave response of vortices in Al and Re superconducting thin film resonators cooled in magnetic fields comparable to or less than that of the Earth. Previous work on vortex dynamics at microwave frequencies has involved large magnetic fields, orders of magnitude larger than the Earth's fields. Al and Re are common materials used in superconducting resonant circuits for qubits and detectors. Despite the similarities of Al and Re superconductors, the microwave vortex response is strikingly different in the two materials from my resonator measurements. I present a quantitative model for the dissipation and reactance contributed by the vortices in terms of the elastic pinning forces and the viscous damping from the vortex cores. The differences in the vortex response in Al and Re were due to the vortex pinning strength in the two films The critical role played by pinning in determining the microwave response motivated us to try to modify the pinning in our Al films by nanostructuring the film surface. A single narrow slot along the center line of a resonator was used to increase the pinning in the resonator traces and resulted in a reduction of the loss from vortices by over an order of magnitude. Such patterned pinning techniques could be used on resonators in systems with insufficient shielding or pulsed control fields to reduce the loss from unwanted trapped vortices. Finally, we explored the possibility for using measurements of the power dependence of the resonators to determine if trapped vortices are present.
In this thesis work, the quantum behavior of a superconducting circuit implementing a quantum bit or qubit is studied. With the use of resonant microwave pulses the full manipulation of the quantum state of this system is demonstrated: any rotation of the state vector around the Bloch sphere can be achieved and by using particular NMR inspired sequences of microwave pulses, the robustness of an operation against particular types of errors, like slow fluctuations of the transition frequency of the qubit, can be improved. The phenomenon of decoherence which drives the system from a quantum behavior to a classical one, has been characterized in the free evolution regime. By properly tuning the working point in the external parameter space, the qubit can be decoupled to first order from the fluctuations of its environment, thus enhancing coherence. In these optimal conditions, low frequency charge noise probably of microscopic origin appears to be the limiting source of decoherence for our system. The study of decoherence during driven evolution demonstrated that by suppressing the effect of those fluctuations of the environment slower than that of the driving field, the coherence of the qubit can be improved. Finally a new non-dissipative readout method based on microwave reflectometry has been set up, which improves the sensitivity and could in principle lead to a non-demolition measurement of the qubit state.