# SciPost Commentary Page

### Original publication:

Title: | Revealing the finite-frequency response of a bosonic quantum impurity |

Author(s): | Sébastien Léger, Théo Sépulcre, Dorian Fraudet, Olivier Buisson, Cécile Naud, Wiebke Hasch-Guichard, Serge Florens, Izak Snyman, Denis M. Basko, Nicolas Roch |

As Contributors: | (none claimed) |

Journal ref.: | SciPost Physics 14, 130 |

DOI: | https://doi.org/10.21468/SciPostPhys.14.5.130 |

Date: | 2023-05-25 |

### Abstract:

Quantum impurities are ubiquitous in condensed matter physics and constitute the most stripped-down realization of many-body problems. While measuring their finite-frequency response could give access to key characteristics such as excitations spectra or dynamical properties, this goal has remained elusive despite over two decades of studies in nanoelectronic quantum dots. Conflicting experimental constraints of very strong coupling and large measurement bandwidths must be met simultaneously. We get around this problem using cQED tools, and build a precisely characterized quantum simulator of the boundary sine-Gordon model, a non-trivial bosonic impurity problem. We succeeded to fully map out the finite frequency linear response of this system. Its reactive part evidences a strong renormalisation of the nonlinearity at the boundary in agreement with non-perturbative calculations. Its dissipative part reveals a striking many-body broadening caused by multi-photon conversion. The experimental results are matched quantitatively to a perturbative calculation based on a microscopically calibrated model. Furthermore, we push the device into a regime where perturbative calculations break down, which calls for more advanced theoretical tools to model many-body quantum circuits. We also critically examine the technological limitations of cQED platforms to reach universal scaling laws. This work opens exciting perspectives for the future such as quantifying quantum entanglement in the vicinity of a quantum critical point or accessing the dynamical properties of non-trivial many-body problems.

## Théo Sépulcre on 2023-10-23 [id 4056]

It has been recently brought to the attention of the authors that some statements in this publication could be misconstrued.

In particular, the message we attempted to convey is that reference [45] detected many-body losses at Z>R_Q and Z<R_Q, but did not have a theory capable of handling Z<R_Q. However, feedback we have received, indicate that readers of our article may get the impression that [45] did not explore Z<R_Q experimentally. To avoid potential confusion, we add the following errata (see list below) to the publication. They do not affect the substance of the work.

List of replacements:

“Of particular relevance is [45] in which the relatively large Josephson to charging energy ratio EJ=EC of the terminal SQUID combined with an environmental impedance larger than RQ put the device in a regime where the losses are dominated by phase slips. We target here the exploration of quantum non-linear effects at somewhat lower dimensionless impedances alpha = Z/RQ ~ 0.3 and at EJ/EC < 1, where quartic (Kerr type) and higher order processes at the terminal junction are the dominant source of non-linear effects.”

should read“Of particular relevance is [45] in which strong non-linear losses were reported. A clear explanation in terms of quantum phase slips was given in the regime alpha = Z/R> 1 whereas the loss in the alpha < 1 regime could not be quantitatively reproduced with a model based on the non-linearity of the confining potential of the impurity. We target here the exploration of quantum non-linear effects at somewhat lower dimensionless impedances alpha ~ 0.3 and at EJ/EC < 1, where quartic (Kerr type) and higher order processes at the terminal junction are the dominant source of non-linear effects.”“These features are not reproduced when the SQUID is modelled as a linear circuit element as in (16), suggesting that the measured transmission contains significant information about inelastic photon processes due to the boundary SQUID”

should read“These features are not reproduced when the SQUID is modelled as a linear circuit element as in (16), suggesting that the measured transmission contains significant information about inelastic photon processes due to the boundary SQUID, in agreement with what has been observed in [45].”“Obvious candidates are coupling with normal quasiparticles [51,52]”

should read“Obvious candidates are coupling with normal quasiparticles or dielectric loss [45, 51, 52]”“On the other hand, the boundary is also able to induce a dramatic dissipative response onto its environment, due to e cient frequency conversion into multi-photon states, which were shown to dominate over known sources of photonic losses”

should read“On the other hand, the boundary is also able to induce a dramatic dissipative response onto its environment, due to efficient frequency conversion into multi-photon states, which were shown to dominate over known sources of photonic losses, in accordance with what was reported in [45].”Reference [46] was added to “The direct detection of the down-converted photons in cQED remains also a topic of interest, not only from the point of view of many-body physics [27, 31, 46]”