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Charge quantization and detector resolution

by Roman-Pascal Riwar

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Submission summary

Authors (as registered SciPost users): Roman-Pascal Riwar
Submission information
Preprint Link:  (pdf)
Date accepted: 2021-04-15
Date submitted: 2021-03-24 17:20
Submitted by: Riwar, Roman-Pascal
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


Charge quantization, or the absence thereof, is a central theme in quantum circuit theory, with dramatic consequences for the predicted circuit dynamics. Very recently, the question of whether or not charge should actually be described as quantized has enjoyed renewed widespread interest, with however seemingly contradictory propositions. Here, we intend to reconcile these different approaches, by arguing that ultimately, charge quantization is not an intrinsic system property, but instead depends on the spatial resolution of the charge detector. We show that the latter can be directly probed by unique geometric signatures in the correlations of the supercurrent. We illustrate these findings at the example Josephson junction arrays in the superinductor regime, where the transported charge appears to be continuous. Finally, we comment on potential consequences of charge quantization beyond superconducting circuits.

Author comments upon resubmission

Dear editor,

Thank you for providing the referee reports. I am very happy to learn that both of the reports are favourable and recommend the publication of the manuscript. One of the referees suggested optional changes, which have been fully addressed in the new revised manuscript (see list of changes, in particular changes 2-5). I herewith resubmit this new manuscript for you consideration.

Sincerely yours,
the author.

List of changes

1) On page 4, a footnote is added to comment on the completeness of the charge eigenbasis defined in Eq. (2).

2) On page 5, in the paragraph beginning with “The above leads us to our first observation …”, the term "gauge choice" is explicitly defined, in that it refers to the different choices for the detector basis.

3) On page 5, in the paragraph beginning with “In the here considered context …”, a phrase and a new reference ([46] Burkard et al., 2004) is added to highlight that within the paper, the circuit degrees of freedom N and \varphi are interchangeably used to mean either the charge and phase inside a given region (node variables), or the charge and phase difference across an interface (branch variables).

4) On page 7, a footnote is added to explain the nature of the counting field \chi, in particular pointing out that \chi can be regarded as the classical component of \varphi.

5) On page 10, the phrase following Eq. (10), is slightly modified, in order to clearly refer to the above defined term "gauge choice".

6) On page 8, in the final paragraph of Sec. 2.2, a phrase is added to stress that the central result, the current correlator in Eq. (7), is valid in the limit for long measurement times, in particular, measurement times longer than the internal circuit dynamics.

7) The name of a colleage is added in the list of people in the acknowledgements.

Published as SciPost Phys. 10, 093 (2021)

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