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arxiv: 2511.02350 · v2 · submitted 2025-11-04 · 🪐 quant-ph · cond-mat.mes-hall

Decay of transmon qubit in a broadband one-dimensional cavity

Ya. S. Greenberg , A. A. Shtygashev , O. V. Kibis This is my paper

Pith reviewed 2026-05-18 01:35 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords transmon qubitqubit decaynon-Markovian dynamicsone-dimensional cavityresonance shifts and widthstwo-photon decaysuperconducting quantum circuits
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The pith

A transmon qubit in a broadband one-dimensional cavity displays Markovian decay at weak coupling and non-Markovian decay with energy-dependent widths at stronger coupling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper analyzes the decay of a three-level transmon qubit weakly coupled to a continuum of modes in a one-dimensional broadband cavity. Using the resolvent formalism, it derives expressions for resonance frequency shifts and widths, evaluated for a Gaussian density of states. The key finding is two dynamical regimes separated by the ratio of coupling strength to bandwidth: Markovian when the ratio is much less than one, with nearly constant resonance width, and non-Markovian when the ratio is larger, with strongly energy-dependent width. The coupling to the second level opens a two-photon decay channel that broadens the second level and influences the third level's decay. This matters for controlling qubit lifetimes in superconducting quantum circuits.

Core claim

We identify two distinct dynamical regimes in the decay of a three-level transmon qubit coupled to a broadband 1D cavity continuum, separated by the ratio of coupling strength to bandwidth. In the Markovian regime the resonance width is independent of energy, while in the non-Markovian regime it becomes strongly energy-dependent, and the second-to-ground-state coupling provides a fast two-photon decay channel.

What carries the argument

Resolvent formalism for a three-level system with Gaussian density of states, which computes energy-dependent shifts and widths of resonances.

If this is right

  • When the coupling strength is much smaller than the bandwidth, the resonance width remains practically independent of energy within the band.
  • As the ratio of coupling to bandwidth increases, the system enters a non-Markovian regime with energy-dependent resonance widths.
  • The interaction between the second level and ground state opens a fast two-photon decay channel that broadens the second level.
  • This coupling significantly influences the decay dynamics of the third level.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Engineers could tune the cavity bandwidth to select between regimes for desired qubit behavior.
  • Non-Markovian dynamics might preserve quantum information longer in certain energy ranges.
  • Similar transitions could be studied in other qubit-cavity systems beyond transmons.

Load-bearing premise

The transmon is modeled as a three-level system that remains weakly coupled to the cavity continuum with a Gaussian density of states.

What would settle it

An experiment that measures the resonance width versus qubit energy for different coupling strengths to the cavity modes; the width should be flat in the weak-coupling limit but vary with energy when coupling is comparable to the bandwidth.

Figures

Figures reproduced from arXiv: 2511.02350 by A. A. Shtygashev, O. V. Kibis, Ya. S. Greenberg.

Figure 1
Figure 1. Figure 1: FIG. 1: Transmon levels [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Transmon decay parameters for weak coupling, [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Fig.5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Transmon decay parameters for ultra coupling, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Transmon decay parameters for strong coupling, [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Dependence of the intersection points [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

We investigate the decay dynamics of a three-level artificial atom, a superconducting transmon qubit, weakly coupled to a continuum of modes in a broadband, one-dimensional cavity. Using the resolvent formalism, we derive analytical expressions for the resonance frequency shifts and widths, which are then evaluated numerically for a Gaussian density of states. We identify two distinct dynamical regimes, differentiated by the ratio of the qubit's coupling strength to the continuum bandwidth. When this ratio is much less than one, the system exhibits a Markovian regime in which the resonance width is practically independent of energy within the continuum band. As the ratio increases, the system transitions to a non-Markovian regime where the resonance width becomes strongly energy-dependent. In this regime, the qubit interacts with the continuum faster than the continuum can erase the information from the qubit's past. Furthermore, we demonstrate that the coupling between the transmon's second level and its ground state significantly influences the decay dynamics of the third level. The interaction between these two levels opens a fast two-photon decay channel, which broadens the transmon's second level.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The manuscript investigates the decay dynamics of a three-level transmon qubit weakly coupled to a continuum of modes in a broadband one-dimensional cavity. Using the resolvent formalism, analytical expressions for resonance frequency shifts and widths are derived and then evaluated numerically assuming a Gaussian density of states. Two distinct dynamical regimes are identified based on the ratio of the qubit coupling strength to the continuum bandwidth: a Markovian regime (ratio ≪ 1) in which the resonance width is practically energy-independent within the band, and a non-Markovian regime (larger ratio) in which the width becomes strongly energy-dependent. The coupling between the transmon's second level and ground state is shown to open a fast two-photon decay channel that broadens the second level and influences the decay of the third level.

Significance. If the central claims hold, the work offers concrete analytical and numerical insight into the crossover from Markovian to non-Markovian decay for a realistic multi-level superconducting qubit in a structured 1D continuum. The explicit treatment of the three-level structure and the two-photon channel provides a useful refinement over two-level models. The combination of closed-form resolvent expressions with numerical evaluation for a Gaussian DOS constitutes a clear strength, as does the direct link drawn between the coupling-to-bandwidth ratio and the energy dependence of the width.

major comments (1)
  1. [Derivations of resonance widths and regime identification] The classification of the two regimes as Markovian versus non-Markovian rests on the energy dependence of the resonance width extracted from the resolvent self-energy (abstract and the derivations that follow). While an essentially constant width is consistent with the Markovian limit, the manuscript does not present explicit time-domain results (inverse Laplace transform of the resolvent or direct integration of the Schrödinger equation) that would confirm exponential versus visibly non-exponential population decay. Because the central claim concerns dynamical regimes, this verification is load-bearing and should be added or explicitly justified by reference to the standard association between flat self-energy and Weisskopf-Wigner decay.
minor comments (3)
  1. [Abstract] The abstract states that the qubit 'interacts with the continuum faster than the continuum can erase the information from the qubit's past' in the non-Markovian regime; a short sentence referencing a standard non-Markovianity measure (e.g., information backflow or divisibility) would make this interpretation more precise.
  2. [Model and Hamiltonian] The three-level labeling (ground, second, third) is used throughout but never shown in a diagram or table; adding an explicit level diagram in the model section would improve readability.
  3. [Numerical results] The numerical evaluation assumes a Gaussian DOS whose width is a free parameter; a brief sensitivity check against a different functional form (e.g., Lorentzian) would strengthen the claim that the regime distinction is controlled primarily by the coupling-to-bandwidth ratio.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comment. We appreciate the positive assessment of the work's significance and address the major point raised below. We will revise the manuscript to strengthen the presentation of the dynamical regimes.

read point-by-point responses

  1. Referee: [Derivations of resonance widths and regime identification] The classification of the two regimes as Markovian versus non-Markovian rests on the energy dependence of the resonance width extracted from the resolvent self-energy (abstract and the derivations that follow). While an essentially constant width is consistent with the Markovian limit, the manuscript does not present explicit time-domain results (inverse Laplace transform of the resolvent or direct integration of the Schrödinger equation) that would confirm exponential versus visibly non-exponential population decay. Because the central claim concerns dynamical regimes, this verification is load-bearing and should be added or explicitly justified by reference to the standard association between flat self-energy and Weisskopf-Wigner decay.

    Authors: We thank the referee for this observation. The distinction between the regimes in our work follows the standard criterion in open quantum systems: an energy-independent self-energy (flat within the relevant band) corresponds to the Markovian Weisskopf-Wigner limit with exponential decay, while energy dependence signals non-Markovian dynamics. This association is well-established in the literature on structured reservoirs and non-Markovian quantum optics. Nevertheless, to make the connection explicit and address the load-bearing nature of the claim, we will add a new subsection to the revised manuscript. This subsection will present numerical results for the time-domain qubit population obtained via the inverse Laplace transform of the resolvent for representative parameter sets in each regime, thereby directly illustrating the crossover from exponential to visibly non-exponential decay. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies standard resolvent formalism to stated Hamiltonian and assumptions

full rationale

The paper starts from an explicit Hamiltonian for a three-level transmon weakly coupled to a one-dimensional continuum with assumed Gaussian density of states. It applies the resolvent formalism to obtain closed-form expressions for the complex pole (shift and width) and then evaluates those expressions numerically for varying values of the coupling-to-bandwidth ratio. The Markovian/non-Markovian distinction is attached to the resulting energy dependence of the width inside the band; this is a direct computational consequence of the input model rather than a quantity defined in terms of itself or a fitted parameter later renamed as a prediction. No load-bearing self-citation, imported uniqueness theorem, or ansatz smuggled via prior work is required for the central steps. The derivation chain therefore remains self-contained against the stated assumptions and does not reduce to its own outputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the resolvent formalism for open quantum systems and the three-level truncation of the transmon; no new free parameters are introduced beyond the assumed Gaussian density of states and the coupling strength.

free parameters (1)
  • Gaussian density-of-states width
    Chosen to model the broadband cavity continuum; used in the numerical evaluation of the derived expressions.
axioms (2)
  • standard math Resolvent formalism yields the resonance shifts and widths for a weakly coupled system
    Invoked to obtain analytical expressions for frequency shifts and decay widths.
  • domain assumption Transmon can be truncated to three levels
    Used throughout the derivation of decay channels, including the two-photon process.

pith-pipeline@v0.9.0 · 5731 in / 1571 out tokens · 35523 ms · 2026-05-18T01:35:37.127490+00:00 · methodology

discussion (0)

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Reference graph

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