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arXiv:2109.15071 · IEEE Transactions on Applied Superconductivity

A Chip-Based Superconducting Magnetic Trap for Levitating Superconducting Microparticles

Martí Gutierrez Latorre, Achintya Paradkar, David Hambraeus, Gerard T. Higgins, Witlef Wieczorek

Published Feb 1, 2022• 14 citations
arXivHTMLPDF

Abstract

Magnetically-levitated superconducting microparticles have been recently proposed as a promising platform for performing quantum experiments with particles in the picogram regime. Here, we demonstrate the superconducting technology to achieve chip-based magnetic levitation of superconducting microparticles. We simulate and fabricate a chip-based magnetic trap capable of levitating superconducting particles with diameters from 0.5$\,\mu$m to 200$\,\mu$m. The trap consists of two stacked silicon chips, each patterned with a planar multi-winding superconducting coil made of niobium. The two coils generate a magnetic field resembling a quadrupole near the trap center, in which we demonstrate trapping of a spherical 50$\mu$m diameter SnPb microparticle at temperatures of 4 K and 40 mK.

DOI
10.1109/tasc.2022.3147730

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Magnetically-levitated superconducting microparticles have been recently proposed as a promising platform for performing quantum experiments with particles in the picogram regime. Here, we demonstrate the superconducting technology to achieve chip-based magnetic levitation of superconducting microparticles. We simulate and fabricate a chip-based magnetic trap capable of levitating superconducting particles with diameters from 0.5 μ\,\muμm to 200 μ\,\muμm. The trap consists of two stacked silicon chips, each patterned with a planar multi-winding superconducting coil made of niobium. The two coils generate a magnetic field resembling a quadrupole near the trap center, in which we demonstrate trapping of a spherical 50μ\muμm diameter SnPb microparticle at temperatures of 4 K and 40 mK.
Magnetically levitated superconducting microparticles provide a promising platform for fundamental quantum experiments and quantum-limited sensing. In the Meissner state, the levitated particle is trapped without mechanical clamping, allowing its center-of-mass motion to exhibit ultralow dissipation. The particle's displacement can be read out dispersively via magnetic flux coupling to superconducting resonators. A challenge for magnetomechanical coupling is to realize a flux-tunable microwave circuit that provides strong flux-to-frequency transduction, low dissipation, and a sufficiently large linear operating range for readout and cooling. This thesis develops and characterizes a chip-based superconducting platform for realizing this transduction.Chip-based levitation of a superconducting microparticle is demonstrated at 40 mK. Passive cryogenic vibration isolation is developed to increase the mechanical quality factors of the levitated particle. For coupling to a microwave circuit, a superconducting flip-chip process based on indium microspheres was developed. The need for Au passivation of Nb or NbN under-bump metallization is demonstrated, and indium-based superconducting interconnects are shown to carry ampere-scale currents. Flux-tunable resonators with 100-200 µm SQUID loops and integrated input coils are designed, fabricated, and characterized. A peak flux responsivity of 20 GHz/Φ₀ is achieved, with one flux quantum modulation requiring only 10-20 µA of input-coil current. Two integrated flux-biasing architectures are developed with flip-chip and on-chip input coils, achieving a total flux transfer efficiency of 1.6%. Junction asymmetry is shown to suppress branch-switching behavior associated with finite SQUID screening.Together, these results establish the superconducting subsystems required for dispersive microwave readout of the center-of-mass motion of a levitated microparticle. Such a magnetomechanical coupling provides a route toward cooling the center-of-mass motion to the ground state, paving the way for the preparation of nonclassical motional states. More broadly, such systems are well-suited for quantum-limited force and acceleration sensing, as well as for probing quantum physics in a previously unexplored mass regime.
Levitation of microscopic objects in vacuum combines exceptional environmental isolation with precise control of their dynamics, pushing the limits of sensing and macroscopic quantum physics. In particular, magnetic levitation allows a large range of particle sizes, while avoiding detrimental effects from high-intensity optical trapping beams and electric field noise. However, existing diamagnetic and Meissner levitation approaches are typically constrained by low mechanical eigenfrequencies, limited integrability with other systems due to bulky coils or magnets, and, for Meissner levitation, the need for cryogenic operation. Here, we demonstrate a room-temperature on-chip magnetic levitation platform capable of stably levitating a nanogram (6.5 micrometer radius) ferromagnetic microsphere. The platform is scalable and tunable, and supports librational modes with eigenfrequencies exceeding 10 kHz. Further miniaturization and coupling to solid-state spin qubits could enable cooling to the quantum ground state. Beyond quantum experiments, this architecture enables integrated precision sensing and studies of isolated ferromagnet thermodynamics.
We introduce a method to suspend an optical micromirror, with a total mass of \SI{30}{\micro\gram}, using superconducting magnetic levitation. The micromirror is formed on a silicon membrane, coated with a high-reflectivity dielectric stack and attached to superconducting microspheres. The object is stably levitated inside a magnetic quadrupole field at cryogenic temperatures. Magnetic feedback on the transverse motion is used to stabilize the position of the levitator within the trapping field, allowing to measure the axial displacement of the levitator using optical interferometry. The system reaches a sensitivity of order \SI{100}{\pico\metre/\sqrt{\hertz}} near the axial trap frequency of \SI{167}{Hz}. This approach enables free-standing mirrors with minimal dissipation and tunable oscillation frequencies, offering a platform for precision sensing and quantum cavity optomechanics in the microgram regime.
We propose a current-carrying-chip scheme for generating spatial quantum superpositions using a levitating nanodiamond with a built-in nitrogen-vacancy (NV) centre defect. Our setup is quite versatile and we aim to create the superposition for a mass range of 10−19 kg<m<10−15 kg10^{-19}~{\rm kg}< m< 10^{-15}~{\rm kg}10−19 kg<m<10−15 kg and a superposition size O(10)μm<Δx<O(1)nm{\cal O}(10) {\rm μm} < Δx < {\cal O}(1){\rm nm}O(10)μm<Δx<O(1)nm, respectively, in t≤0.1t\leq 0.1t≤0.1s, depending on the position we launch from the center of the diamagnetic trap. We provide an in-depth analysis of two parallel chips that can create levitation and spatial superposition along the xxx-axis, while producing a very tight trap in the yyy direction, and the direction of gravity, i.e., the zzz direction. Numerical simulations demonstrate that our setup can create a one-dimensional spatial superposition state along the x-axis. Throughout this process, the particle is stably levitated in the z-direction, and its motion is effectively confined in the y-direction for a Gaussian initial condition. This setup presents a viable platform for a diamagnetically levitated nanoparticle for a table-top experiment exploring the possibility of creating a macroscopic Schrödinger Cat state to test the quantum gravity induced entanglement of masses (QGEM) protocol.
We report the levitation of a superconducting lead-tin sphere with 100 μm diameter (corresponding to a mass of 5.6 μg) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240 Hz. The center-of-mass motion of the sphere is monitored magnetically using a dc superconducting quantum interference device as well as optically and exhibits quality factors of up to 2.6×10^{7}. We also demonstrate 3D magnetic feedback control of the motion of the sphere. The setup is housed in a dilution refrigerator operating at 15 mK. By implementing a cryogenic vibration isolation system, we can attenuate environmental vibrations at 200 Hz by approximately 7 orders of magnitude. The combination of low temperature, large mass, and high quality factor provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times.