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Quantum Numbers02:43

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First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
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A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
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Tantalum alloy-based resonators for quantum information systems.

Chen Yang1, Faranak Bahrami1, Guangming Cheng2

  • 1Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08540.

Proceedings of the National Academy of Sciences of the United States of America
|January 29, 2026
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Summary

Researchers enhanced superconducting circuits by alloying hafnium into tantalum thin films. This material engineering approach increased the superconducting transition temperature (Tc) by 40%, showing promise for future superconducting device development.

Keywords:
Ta-Hf alloy thin filmssuperconducting gap engineeringsuperconducting qubit

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Superconducting Circuits

Background:

  • Tantalum (Ta) is crucial for high-performance superconducting circuits, improving qubit lifetime and quality factors.
  • Material optimization is key to advancing superconducting circuit technology.
  • Superconducting gap engineering offers a strategy to expand suitable host materials.

Purpose of the Study:

  • To explore superconducting gap engineering in tantalum-based devices.
  • To investigate the effect of alloying hafnium into tantalum thin films on superconducting properties.
  • To enhance the superconducting transition temperature (Tc) for broader applications.

Main Methods:

  • Alloying 20 atomic percent (at.%) hafnium into tantalum (Ta) thin films.
  • Systematic variation of deposition conditions to control film orientation and transport properties.
  • Direct current (DC) transport measurements and microwave measurements at millikelvin temperatures.

Main Results:

  • Achieved a superconducting transition temperature (Tc) of 6.09 K in Ta-Hf alloy films.
  • Observed a 40% increase in Tc compared to bare Ta devices.
  • Confirmed unchanged loss contributions from two-level systems and quasi-particles at low temperatures.

Conclusions:

  • Material engineering, specifically alloying hafnium into tantalum, significantly enhances superconducting properties.
  • Ta-Hf alloys show promise for expanding the range of materials in superconducting circuits.
  • Further exploration of material candidates is warranted for advanced superconducting devices.