We propose the "Andreev molecule," an artificial quantum system composed of two closely spaced Josephson junctions. The coupling between Josephson junctions in an Andreev molecule occurs through the overlap and hybridization of the junction's "atomic" orbitals, Andreev Bound States. A striking consequence is that the supercurrent flowing through one junction depends on the superconducting phase difference across the other junction. Using the Bogolubiov-de-Gennes formalism, we derive the energy spectrum and non-local current-phase relation for arbitrary separation. We demonstrate the possibility of creating a ϕ-junction and propose experiments to verify our predictions. Andreev molecules may have potential applications in quantum information, metrology, sensing, and molecular simulation. 1 arXiv:1809.11011v3 [cond-mat.mes-hall] 4 Sep 2019 Keywords superconductivity, Josephson junction, Andreev bound states, superconducting circuits, quantum informationUnderstanding and exploiting the interaction between Josephson junctions is paramount for superconducting device applications in quantum information 1 , magnetometry 2 , metrology 3 , and quantum simulation 4 . In typical superconducting circuits, junctions interact indirectly via electromagnetic coupling to inductors, capacitors, transmission lines, and microwave resonators. In addition to this well understood long-range interaction 5 , there is a short range interaction via quasiparticle diffusion which can modify superconducting energy gaps and critical currents, but is only important close to T c , the superconducting transition temperature, or at large bias voltages 6 .A second short-range interaction, mediated by Cooper pairs, is relevant to the majority of applications where characteristic energies are much smaller than the gap, but is still poorly understood. It becomes significant when the distance between Josephson junctions is comparable to ξ 0 , the superconducting coherence length, and can modify the electrical properties in a dramatic way.Initially, minor effects resulting from this "order-parameter interaction" were calculated for temperatures near T c using the Ginzburg-Landau equations 7 . More recently, theorists have investigated this problem at arbitrary temperature using Green's function techniques.In the two-electrode geometry, where it is not possible to independently apply a phase difference to each junction, the overall current-phase relation and dc current were obtained 8,9 .For the more relevant three-electrode geometry, non-local out-of-equilibrium supercurrents were calculated and the existence of π shifts in the current-phase relation were demonstrated 10-15 . A remarkable phase-locking similar to Shapiro steps was predicted and subsequently measured experimentally in superconducting bi-junctions biased with commensurate voltages 16,17 . The authors attribute these phenomena to the formation of entangled Cooper pairs called "quartets."
An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local transport processes leading to the formation of Andreev molecules.
We report measurements of the polar Kerr effect, proportional to the out-of-plane component of the magnetization, in thin films of the magnetically doped topological insulator (Cr0.12Bi0.26Sb0.62)2Te3. Measurements of the complex Kerr angle, ΘK , were performed as a function of photon energy in the range 0.8 eV < ω < 3.0 eV. We observed a peak in the real part of ΘK (ω) and zero crossing in the imaginary part that we attribute to resonant interaction with a spin-orbit avoided crossing located ≈ 1.6 eV above the Fermi energy. The resonant enhancement allows measurement of the temperature and magnetic field dependence of ΘK in the ultrathin film limit, d ≥ 2 quintuple layers. We find a sharp transition to zero remanent magnetization at 6 K for d < 8 QL, consistent with theories of the dependence of impurity spin interactions on film thickness and their location relative to topological insulator surfaces.
We present an efficient fabrication method for absorptive microwave filters based on Eccosorb CR-124. Filters are fabricated from readily available parts, and their cutoff frequency can be set by their length. They exhibit desirable properties such as a very large and deep stop band with rejection beyond 120 dB at least up to 40 GHz, more than 10 dB return loss in both the pass and the stop band, and an error-function shaped step response without overshoot. Measurements at very low temperatures show that the filters thermalize on a time scale of approximately 100 s, and that they can absorb power as high as 100 nW with their noise temperature staying remarkably low, below 100 mK. These properties make the filters ideal for cryogenic filtering and filtering of intermediate frequency port signals of mixers.
So far, quantum-limited power meters are not available in the microwave domain, hindering measurement of photon number in itinerant quantum states. On the one hand, single photon detectors [1-6] accurately detect single photons, but saturate as soon as two photons arrive simultaneously. On the other hand, more linear watt meters, such as bolometers [7][8][9], are too noisy to accurately detect single microwave photons. Linear amplifiers [10][11][12] probe non-commuting observables of a signal so that they must add noise [13] and cannot be used to detect single photons, either. Here we experimentally demonstrate a microwave photon-multiplication scheme which combines the advantages of a single photon detector and a power meter by multiplying the incoming photon number by an integer factor. Our first experimental implementation achieves a n = 3-fold multiplication with 0.69 efficiency in a 116 MHz bandwidth up to a input photon rate of 400 MHz. It loses phase information but does not require any dead time or time binning. We expect an optimised device cascading such multipliers to achieve number-resolving measurement of itinerant photons with low dark count, which would offer new possibilities in a wide range of quantum sensing and quantum computing applications.
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