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arXiv:cond-mat/0702566 · Physical Review A

Feasibility of studying vortex noise in two-dimensional superconductors with cold atoms

Stefan Scheel, R. Fermani, Edward A. Hinds

Published Jun 7, 2007• 22 citations
arXivHTMLPDF

Abstract

We investigate the feasibility of using ultracold neutral atoms trapped near a thin superconductor to study vortex noise close to the Kosterlitz-Thouless-Berezinskii transition temperature. Alkali atoms such as rubidium probe the magnetic field produced by the vortices. We show that the relaxation time ${T}_{1}$ of the Zeeman sublevel populations can be conveniently adjusted to provide long observation times. We also show that the transverse relaxation times ${T}_{2}$ for Zeeman coherences are ideal for studying the vortex noise. We briefly consider the motion of atom clouds held close to the surface as a method for monitoring the vortex motion.

DOI
10.1103/physreva.75.064901

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Quantum gases are well isolated, highly controllable, and defect-free systems which can simulate many body quantum phenomena that have been studied in condensed matter systems.To study two-dimensional superfluid, we have developed an experimental apparatus that can produce Bose-Einstein condensates (BEC) of 23 Na atoms.The apparatus can generate a pure condensate of 10 7 atoms in an optically plugged magnetic quadrupole trap within 17 s.The Berezinskii-Kosterlitz-Thouless (BKT) theory provides a general framework of the superfluid phase transition in two dimension, which does not involve spontaneous symmetry breaking and emergence of an order parameter below a critical temperature.Instead, it is the formation of vortex pairs with opposite circulations below the critical temperature that mediates the superfluid phase transition.Recently, it has been demonstrated that degenerate Bose gases confined in highly oblate harmonic potentials undergo the BKT phase transition.This thesis focuses on our experimental research on thermal phase fluctuations (i.e., long-wavelength phonons and vortex pairs) in the superfluid i phase of trapped quasi-2D BECs.We have developed a quantitative probe to measure phase fluctuations in the 2D superfluid by free expansion, where the phase fluctuations in the sample were revealed as density modulations in the course of expansion.The power spectrum of the density fluctuations showed an oscillatory shape and the scaling behavior of the peak positions could be understood as a Talbot effect in matter waves.Employing this method, we demonstrated the thermal origin of phase fluctuations.We also investigated relaxation dynamics of nonequilibrium states of the quasi-2D system using the power spectrum.Thermally excited vortex pairs are the characteristic feature of the 2D superfluid.The quantized vortices are conventionally observed by a densitydepleted core after expanding a trapped sample.The method, however, cannot be applied to the 2D sample because the density modulations after free expansion lower the vortex core visibility.We enhanced the core visibility by radial compression of the sample before the expansion so the phonon modes in the 2D sample were relaxed in a 3D environment.Measuring vortex distributions, we revealed the pairing feature by spatial correlations of the vortex positions.We also studied BKT-BEC crossover phenomena in a finite-size sample trapped in a quasi-2D harmonic potential by investigating the vortex profiles at various temperatures.Condensates of atoms have an internal spin structure so they can host various kinds of topological excitations.The two-dimensional Skyrmion is one of the topological spin textures in the anti-ferromagnetic spinor condensate and ii we imprinted the structure using the magnetic field sweep technique.The 2D Skyrmion spin texture has a finite Berry curvature because of the non-coplanar spin configuration.We studied a geometric Hall effect, with condensates trapped in a harmonic potential with the Skyrmion spin texture.Under a linear driving of the spin texture, we observed a condensate dipole motion resonantly developed into a circular motion, which demonstrates the existence of an effective Lorentz force.

•Jan 1, 2014•0 citations
We investigate the feasibility of using ultracold neutral atoms trapped near a thin superconductor to study vortex noise close to the Kosterlitz-Thouless-Berezinskii transition temperature. Alkali atoms such as rubidium probe the magnetic field produced by the vortices. We show that the relaxation time T1{T}_{1}T1​ of the Zeeman sublevel populations can be conveniently adjusted to provide long observation times. We also show that the transverse relaxation times T2{T}_{2}T2​ for Zeeman coherences are ideal for studying the vortex noise. We briefly consider the motion of atom clouds held close to the surface as a method for monitoring the vortex motion.
The aim of this thesis is to investigate the interaction of neutral atoms with conducting and superconducting surfaces. Experimental advances in the magnetic confinement of ultracold atoms have shown that they can act as a powerful tool in a wide range of phenomena such as electric and magnetic field imaging and matter wave interferometry. Coherent manipulation of atoms and ever smaller magnetic traps are essential elements in the implementation of integrated quantum devices for fundamental research, quantum information processing and precision measurements. This thesis considers main influences on atoms placed within three different environments which are useful in achieving miniaturization and efficient control in atomic magnetic traps: carbon nanotubes, dielectric surfaces and superconducting thin films. The possibility of holding atoms near the outside of a carbon nanotubes will be addressed. In order to give a qualitative analysis of the atom-nanotube interaction, thermally induced spin-flips and the Casimir-Polder potential have been considered. The comparison between these two effects is presented in this thesis. It indicates that the Casimir-Polder force is the dominant loss mechanism and an estimation of the minimum trapping distance is given based on its effect. Secondly, a first-principles derivation of spatial atomic-sublevel decoherence near dielectric and metallic surfaces will be presented. The rate obtained for the decay of spatial coherence has dual implications, on one hand, it can be considered as a measure of the coherence length of the fluctuations of the electromagnetic field arising from a given substrate. On the other hand, it turns out to be relevant for quantum information encoding in double well potentials. Finally, the known spin-flip transition rate will be linked to the flux noise spectrum in superconducting thin films showing the feasibility of using cold atomic clouds in the investigation of vortex dynamics.
We have developed an atomic beam technique for studying magnetic vortices and vortex lattices of superconductors. Atoms moving near a superconductor's surface see a fluctuating magnetic field as they pass vortices. This field may drive magnetic resonance transitions between hyperfine states. Measuring the magnetic resonance transition probability as a function of atom velocity probes the vortex lattice autocorrelation function. We demonstrate this technique by studying the vortex lattice of a niobium film sample and measuring the sample's penetration depth. We also identify a systematic problem that we think thwarted an earlier attempt to experimentally realize this technique.
Atom chips made of superconducting material can generate magnetic traps with significantly reduced noise. Recently, several designs for superconducting chips have been theoretically analyzed and experimentally tested for cases with many vortices considered as an average vortex density. Here we show theoretically how the magnetic field of a single vortex, pinned by a superconducting nanodisk of radius \ensuremath{\sim}100 nm and combined with an external bias field parallel to the disk surface, yields a closed three-dimensional trap for cold atoms. The size of the trap and its height above the superconductor surface are typically tens or hundreds of nanometers. We estimate the average lifetime \ensuremath{\tau} of 87Rb^{87}\mathrm{Rb}87Rb (rubidium) atoms (subject to thermal escape and Majorana spin flips) in the range 0.05--1.0 ms. We model the trap in a quantum adiabatic approximation and apply Fermi's rule to estimate the lifetime of 87Rb^{87}\mathrm{Rb}87Rb atoms in the ground state of this trap. We obtain similar lifetimes \ensuremath{\tau} as in the semiclassical estimate, in the range 0.05--3.5 ms. We find that \ensuremath{\tau} depends on the gradient B0{B}_{0}B0​ of the vortex's magnetic field according to $\ensuremath{\tau}\ensuremath{\sim}{B}_{0}^{\ensuremath{-}2/3}$.
Abstract A lattice of traps for ultracold neutral atoms is a promising tool for experimental investigation in quantum physics and quantum information processing. We consider regular arrays of thin film type-II superconducting nanodisks, with only one pinned vortex in each of them, and also arrays of mesoscopic disks, each containing many vortices whose distribution is characterized by the superconducting current density. In both cases we show theoretically that the induced magnetic field can create a 3D lattice of magnetic traps for cold atoms without any additional bias field. Applying a bias DC field parallel to the superconductor surface, one can control the depth and sizes of the traps, their heights above the chip surface, potential barriers between the traps, as well as the structure and dimension of the lattices. In the adiabatic approximation the atom cloud shape is represented by the shape of a closed iso-surface of the magnetic field magnitude chosen in accordance with the atom cloud temperature. The computed trap sizes, heights and the distances between the neighboring traps are typically from tens to hundreds nanometers for nanodisks and of the order of 1 μ m for mesoscopic disks. Our calculations show that the depth of magnetic traps on mesoscopic disks is, typically, between 0.3 G and 7.6 G; for the nanodisks the depth is about 0.3 G.
A single-spin qubit placed near the surface of a conductor acquires an additional contribution to its 1/T 1 relaxation rate due to magnetic noise created by electric current fluctuations in the material.We analyze this technique as a wireless probe of superconductivity in atomically thin two-dimensional materials.At temperatures T T c , the dominant contribution to the qubit relaxation rate is due to transverse electric current fluctuations arising from quasiparticle excitations.We demonstrate that this method enables detection of metal-to-superconductor transitions, as well as investigation of the symmetry of the superconducting gap function, through the noise scaling with temperature.We show that scaling of the noise with sample-probe distance provides a window into the nonlocal quasistatic conductivity of superconductors, both clean and disordered.At low temperatures the quasiparticle fluctuations get suppressed, yet the noise can be substantial due to resonant contributions from collective longitudinal modes, such as plasmons in monolayers and Josephson plasmons in bilayers.Potential experimental implications are discussed.
Quantum gases are well isolated, highly controllable, and defect-free systems which can simulate many body quantum phenomena that have been studied in condensed matter systems.To study two-dimensional superfluid, we have developed an experimental apparatus that can produce Bose-Einstein condensates (BEC) of 23 Na atoms.The apparatus can generate a pure condensate of 10 7 atoms in an optically plugged magnetic quadrupole trap within 17 s.The Berezinskii-Kosterlitz-Thouless (BKT) theory provides a general framework of the superfluid phase transition in two dimension, which does not involve spontaneous symmetry breaking and emergence of an order parameter below a critical temperature.Instead, it is the formation of vortex pairs with opposite circulations below the critical temperature that mediates the superfluid phase transition.Recently, it has been demonstrated that degenerate Bose gases confined in highly oblate harmonic potentials undergo the BKT phase transition.This thesis focuses on our experimental research on thermal phase fluctuations (i.e., long-wavelength phonons and vortex pairs) in the superfluid i phase of trapped quasi-2D BECs.We have developed a quantitative probe to measure phase fluctuations in the 2D superfluid by free expansion, where the phase fluctuations in the sample were revealed as density modulations in the course of expansion.The power spectrum of the density fluctuations showed an oscillatory shape and the scaling behavior of the peak positions could be understood as a Talbot effect in matter waves.Employing this method, we demonstrated the thermal origin of phase fluctuations.We also investigated relaxation dynamics of nonequilibrium states of the quasi-2D system using the power spectrum.Thermally excited vortex pairs are the characteristic feature of the 2D superfluid.The quantized vortices are conventionally observed by a densitydepleted core after expanding a trapped sample.The method, however, cannot be applied to the 2D sample because the density modulations after free expansion lower the vortex core visibility.We enhanced the core visibility by radial compression of the sample before the expansion so the phonon modes in the 2D sample were relaxed in a 3D environment.Measuring vortex distributions, we revealed the pairing feature by spatial correlations of the vortex positions.We also studied BKT-BEC crossover phenomena in a finite-size sample trapped in a quasi-2D harmonic potential by investigating the vortex profiles at various temperatures.Condensates of atoms have an internal spin structure so they can host various kinds of topological excitations.The two-dimensional Skyrmion is one of the topological spin textures in the anti-ferromagnetic spinor condensate and ii we imprinted the structure using the magnetic field sweep technique.The 2D Skyrmion spin texture has a finite Berry curvature because of the non-coplanar spin configuration.We studied a geometric Hall effect, with condensates trapped in a harmonic potential with the Skyrmion spin texture.Under a linear driving of the spin texture, we observed a condensate dipole motion resonantly developed into a circular motion, which demonstrates the existence of an effective Lorentz force.