Abstract
A crucial point in the experimental implementation of hybrid quantum systems consisting of superconducting circuits and atomic ensembles is bringing the two partners close enough to each other that a strong quantum coherent coupling can be established. Here, we propose to use the metallization structures of a half wavelength superconducting coplanar waveguide resonator as a persistent current trap for ultracold paramagnetic atoms. Trapping atoms with the resonator structure itself is provided by using short-ended and inductively coupled resonators instead of capacitively coupled ones as customary in circuit quantum electrodynamics. We analyze the external quality factor of short-ended coplanar waveguide resonators and show that it can be easily designed for the desired regime of quantum circuits. The magnetic field configuration at the resonator is calculated by means of numerical three-dimensional simulations of the London equations. We present a way to transport an atomic ensemble into the coplanar resonator gap where the magnetic field of the cavity mode is maximum. The configuration allows stable trapping by persistent currents and paves the route toward strong coupling between atomic clouds and the cavity mode which is required for cooperative effects and gives the interface between atoms and circuit quantum electrodynamics.
Highlights
A crucial point in the experimental implementation of hybrid quantum systems consisting of superconducting circuits and atomic ensembles is bringing the two partners close enough to each other that a strong quantum coherent coupling can be established
In this work we propose to use a half wavelength superconducting microwave resonator that realizes a quantum bus and a persistent current trap for ultracold paramagnetic atoms in a single device
By means of threedimensional (3D) simulations of the London equations we demonstrate in section 3 how freezing magnetic flux into the closed loops of these resonators creates a trap for paramagnetic atoms when the corresponding magnetic field is combined with additional externally applied fields
Summary
In circuit quantum electrodynamics and quantum information processing with superconducting circuits, resonators in a planar structure are very favorable, as they are easy to fabricate and to integrate with other superconducting circuits. As the discussion is only valid close to the resonance frequency, L∗ and R∗ can be made frequency independent, to a good approximation, by setting ω = ω0 After this transformation, the loaded quality factor of the circuit can be expressed by QL = ω0 Ltot/Rtot, where the total inductance frequency ω0 =. As a final part of the analysis of the inductively coupled half wavelength resonator, we have calculated the inductance of different types of shorts between the center conductor and ground plane, and calculated the resulting transmission spectra by means of the ABC D matrix method. It has been demonstrated that the resonance frequency of coplanar resonators can be made tunable by integrating SQUIDs as tunable lumped element series inductances into the waveguide center conductor [24, 42, 43]
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