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Tunneling Spectroscopy in Superconducting Circuit Lattices

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Pith's one-line read Site-resolved tunneling spectroscopy with separate particle and hole probes is demonstrated in a four-transmon Bose-Hubbard lattice, reproducing calculated spectra without free parameters.

arxiv 2411.07997 v2 pith:5WHHV7XZ submitted 2024-11-12 cond-mat.quant-gas quant-ph

Botao Du , Qihao Guo , Santiago López , Ruichao Ma This is my paper · ORCID
classification cond-mat.quant-gasquant-ph
keywords spectroscopytunnelingcircuitlatticelatticesparticlequantumspectra
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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The reading

Superconducting circuits can be arranged into lattices where microwave photons behave like interacting particles, forming states of synthetic quantum matter. This experiment puts four such lattice sites, each a small superconducting qubit, into a row, and attaches a special probe to one site. The probe is a lossy microwave resonator driven by a fast frequency modulation. Depending on the modulation, the probe acts either as a narrow-band particle source, which can add a photon to the lattice only when its energy matches an available excitation, or as a particle drain, which can remove a photon only when its energy matches an available hole. By scanning the probe energy and watching how the total photon number changes, the authors extract the local quasi-particle and quasi-hole spectra of the many-body state.
Extended reading notes

Core claim

The load-bearing claim is that a narrow-band incoherent particle source or drain locally coupled to a lattice site measures the quasi-particle or quasi-hole spectral function of the many-body state (Eqs. 1 and 2), and that in a four-site transmon Bose-Hubbard lattice this yields spectra that agree with numerical calculation using independently calibrated parameters. As stated in the abstract: 'Using incoherent particle source and drain, we independently extract quasi-particle and quasi-hole spectra and reconstruct the spatial structure of collective excitations.'

Load-bearing premise

The density-dependent spectroscopy in Sec. III.C assumes that the global Landau-Zener sweeps prepare the intended N-particle highest-energy eigenstates (N=1 to 8) with sufficient fidelity, so that the measured spectra are dominated by excitations of that state. The authors do not quantify preparation fidelity for N=5 to 8, and they acknowledge residual ground-band amplitude for N=4 from imperfect preparation. If the initial state contains a significant admixture of N±1 components, the assignment of spectral peaks (notably the third-band feature at 2U2+U3) would be correspondingly uncertain.

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Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central comparison relies on independently measured lattice parameters (SM Table S1), so no free spectral fitting except the 0.9 scale for hole spectra. The main axioms are the validity of the Bose-Hubbard/transmon description, the Markovian weak-coupling probe model, and state preparation fidelity. No new particles, forces, or conserved quantities are introduced; the particle source and drain are engineered from the existing qubit-resonator parametric coupling and lossy resonator.

free parameters (1)
  • Quasi-hole spectral amplitude scaling = ≈0.9
    The measured quasi-hole spectrum for the n=1 Mott state is scaled by about 90% relative to the parameter-free calculation, attributed to state preparation errors; this is an ad hoc normalization and not independently calibrated.
assumptions (4)
  • domain assumption The transmon lattice is described by the Bose-Hubbard Hamiltonian with two- and three-body on-site interactions (Eq. 3)
    Used throughout; parameters J, U2, U3, JNNN are measured in separate calibrations (SM Table S1), but the validity of this effective model for the device is assumed from transmon theory.
  • domain assumption In the weak-coupling limit gS/D << κr, the driven-dissipative probe acts as a Markovian bath and the particle number change rate is proportional to the local spectral function convolved with a Lorentzian kernel (Eq. 2)
    This is the theoretical basis of the spectroscopy; justified by standard Born-Markov elimination in SM Sec. B, but not independently verified beyond the reported agreement.
  • domain assumption Initial many-body states at each filling are the intended highest-energy eigenstates prepared by global Landau-Zener sweeps (Sec. III.C)
    Load-bearing for density-dependent spectra; preparation fidelity is not quantified and residual imperfections are acknowledged.
  • domain assumption Intrinsic decoherence can be modeled by independent T1 and T2* with thermal population and subtracted off-resonant background (SM Sec. C.3)
    Used in Lindblad simulations and background subtraction; thermal population measured at 5% per site.

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Pith. "Pith review of Tunneling Spectroscopy in Superconducting Circuit Lattices." pith.science (2026). https://pith.science/paper/5WHHV7XZ

@misc{pith2026241107997,
  author       = {Pith},
  title        = {Pith review of: Tunneling Spectroscopy in Superconducting Circuit Lattices},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5WHHV7XZ}},
  note         = {Machine review of arXiv:2411.07997}
}
read the original abstract

We demonstrate tunneling spectroscopy of synthetic quantum matter in superconducting circuit lattices. We measure site-resolved excitation spectra by coupling the lattice to engineered driven-dissipative particle baths that serve as local tunneling probes. Using incoherent particle source and drain, we independently extract quasi-particle and quasi-hole spectra and reconstruct the spatial structure of collective excitations. We perform spectroscopy of a strongly interacting Bose-Hubbard lattice at different densities, observing changes in energy gaps across the superfluid to Mott-insulator transition and the effects of three-body interactions. Our results provide a new toolset for characterizing many-body states in analog quantum simulators.

Figures

Figures reproduced from arXiv: 2411.07997 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of site-resolved tunneling spectroscopy. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Measuring local excitation spectra of a Bose-Hubbard lattice. (a) Tunnel-coupled particle source probes quasi-particle [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Reconstruct single-particle wavefunctions using site [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Density-dependent tunneling spectroscopy. (a) Many-body spectra of the Bose-Hubbard lattice beyond the hard-core [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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