Finding E_J Value of a Qubit: Step-by-Step Guide

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Discussion Overview

The discussion revolves around finding the E_J value of a qubit, specifically a 3D transmon, through microwave measurements and theoretical expressions. Participants explore the methodologies for determining E_J, including the relationship between E_J and E_C, and the use of spectroscopy data.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks assistance in determining the E_J value from measurements on a 3D transmon, referencing Koch et al. papers.
  • Another participant requests clarification on Koch et al. and the definition of a transmon.
  • It is noted that a transmon is a type of superconducting qubit, and Koch et al. refers to a series of papers from the Yale group.
  • Questions are raised about the type of measurements conducted, specifically whether the transmon was fixed or variable frequency, and whether E_C has been determined.
  • Some participants suggest that E_J cannot be directly measured in a 3D transmon and that it is often inferred from the resistance of a test junction or through fitting theoretical expressions to spectroscopy data.
  • A participant mentions having data from a two-tone spectroscopic measurement and seeks guidance on which theoretical expressions to fit, referencing an approximation found in lecture notes.
  • There is a specific inquiry about obtaining the original or exact expression for the transition frequency of the qubit, which is given as an approximation in the lecture notes.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the direct measurement of E_J in a 3D transmon and the methods for determining it, indicating that multiple competing views remain on the best approach to take.

Contextual Notes

Participants discuss the limitations of the available data and the dependence on theoretical models, with some expressions being approximations rather than exact formulations.

ramyasuresh
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Hi everyone,

I’ve performed microwave measurements on a 3D transmon and want to find the E_J value of the qubit. I’ve tried searching through many papers, particularly Koch et al, about how to do this, but I am stumped. Could someone please help me out?

Thanks in advance.
 
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What is Koch et al.? Please give a link, also to an explanation of what a transmon is
 
A transmon is a type of superconducting qubit.
Koch et al refers to a a series of papers from the Yale group.

What type of measurements have you done? Was it a fixed or variable frequency transmon?
Have you determined Ec? Could you get an idea of Ej by looking at the Ej/Ec ratio via the band structure?
I don't think there is a "direct" measurement of a Ej in a 3D transmon (most of the time we just "measure" it by measuring the resistance of a test junction fabricated at the same time) ; you would need to fit the theoretical expressions to different types of spectroscopy data .
 
f95toli said:
A transmon is a type of superconducting qubit.
Koch et al refers to a a series of papers from the Yale group.

What type of measurements have you done? Was it a fixed or variable frequency transmon?
Have you determined Ec? Could you get an idea of Ej by looking at the Ej/Ec ratio via the band structure?
I don't think there is a "direct" measurement of a Ej in a 3D transmon (most of the time we just "measure" it by measuring the resistance of a test junction fabricated at the same time) ; you would need to fit the theoretical expressions to different types of spectroscopy data .

Thanks for your reply! I guess I should have made my question a bit more lucid; I had the data of a two-tone spectroscopic measurement (which yielded the avoided crossing plot of a variable frequency transmon with a 3D cavity). This was all I had at the moment, from which I had to find Ec, Ej, etc.

Which theoretical expressions would I have to fit to this? I found an approximated version in lecture notes from a 2011 Les Houches School. The transition frequency of the qubit is given by $\sqrt{8EcEj} - Ec$. However, it's explicitly mentioned that it's an approximation. Is there any reference from which I can obtain the original/exact expression (for understanding purposes).
 

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