Josephson-Kondo screening cloud in circuit quantum electrodynamics

We show that the non-local polarization response in a multimode circuit-QED setup, devised from a Cooper pair box coupled to a long chain of Josephson junctions, provides an alternative route to access the elusive Kondo screening cloud. For moderate circuit impedance, we compute analytically the universal lineshape for the decay of the charge susceptibility along the circuit, that relates to spatial entanglement between the qubit and its electromagnetic environment. At large circuit impedance, we numerically find further spatial correlations that are specific to a true many-body state.Comment: 4 pages, 3 figures (extra Supplementary Information attached

Microscopic bosonization of band structures: X-ray processes beyond the Fermi edge

Bosonization provides a powerful analytical framework to deal with one-dimensional strongly interacting fermion systems, which makes it a cornerstone in quantum many-body theory. Yet, this success comes at the expense of using effective infrared parameters, and restricting the description to low energy states near the Fermi level. We propose a radical extension of the bosonization technique that overcomes both limitations, allowing computations with microscopic lattice Hamiltonians, from the Fermi level down to the bottom of the band. The formalism rests on the simple idea of representing the fermion kinetic term in the energy domain, after which it can be expressed in terms of free bosonic degrees of freedom. As a result, one- and two-body fermionic scattering processes generate anharmonic boson-boson interactions, even in the forward channel. We show that up to moderate interaction strengths, these nonlinearities can be treated analytically at all energy scales, using the x-ray emission problem as a showcase. In the strong interaction regime, we employ a systematic variational solution of the bosonic theory, and obtain results that agree quantitatively with an exact diagonalization of the original one-particle fermionic model. This provides a proof of the fully microscopic character of bosonization on all energy scales for an arbitrary band structure. Besides recovering the known x-ray edge singularity at the emission threshold, we find strong signatures of correlations even at emission frequencies beyond the band bottom.Comment: 26 + 4 pages. Published versio

Universal spatial correlations in the anisotropic Kondo screening cloud: analytical insights and numerically exact results from a coherent state expansion

We analyze the spatial correlations in the spin density of an electron gas in the vicinity of a Kondo impurity. Our analysis extends to the spin-anisotropic regime, which was not investigated in the literature. We use an original and numerically exact method, based on a systematic coherent-state expansion of the ground state of the underlying spin-boson Hamiltonian, which we apply to the computation of observables that are specific to the fermionic Kondo model. We also present an important technical improvement to the method, that obviates the need to discretize modes of the Fermi sea, and allows one to tackle the problem in the thermodynamic limit. One can thus obtain excellent spatial resolution over arbitrary length scales, for a relatively low computational cost, a feature that gives the method an advantage over popular techniques such as NRG and DMRG. We find that the anisotropic Kondo model shows rich universal scaling behavior in the spatial structure of the entanglement cloud. First, SU(2) spin-symmetry is dynamically restored in a finite domain in parameter space in vicinity of the isotropic line, as expected from poor man's scaling. We are also able to obtain in closed analytical form a set of different, yet universal, scaling curves for strong exchange asymmetry, which are parametrized by the longitudinal exchange coupling. Deep inside the cloud, i.e. for distances smaller than the Kondo length, the correlation between the electron spin density and the impurity spin oscillates between ferromagnetic and antiferromagnetic values at the scale of the Fermi wavelength, an effect that is drastically enhanced at strongly anisotropic couplings. Our results also provide further numerical checks and alternative analytical approximations for the recently computed Kondo overlaps [PRL 114, 080601 (2015)].Comment: 27 pages + 2 pages of Supplementary materials. The manuscript was largely extended in V2, and contains now a comparison to the Toulouse limit, and well as a detailed study of the restoration of SU(2) symmetry. The displayed html abstract has been shortened compared to the pdf versio

Mitigation of Mine Blast Loading by Collapsible Structures

This paper presents research results on the mitigation of mine blast loading by collapsible structures. A baseline test consisting of a test platform with a V-shape body exposed to the charge was executed, recording the imparted impulse and the deformation of the test item. A collapsible structure is added to the test platform and tested (two tests). By the law of conservation of momentum, similar peak imparted impulse values were obtained. However, the average imparted impulse reduced by between 16 % to 18% by adding this collapsible element in the load path. The average impulse is the total momentum transferred after the response of the damping system is filtered into the measurement system. The results are analysed with ANSYS AUTODYN and support the measured effects of the introduction of the mitigation measure.Defence Science Journal, 2013, 63(3), pp.262-270, DOI:http://dx.doi.org/10.14429/dsj.63.230

Comment on "Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions''

In a recent Letter [Phys. Rev. Lett. 129, 087001, (2022)], Masuki, Sudo, Oshikawa, and Ashida studied a Josephson junction, with Josephson energy $E_{\rm J}$ and charging energy $E_{\rm C}$, shunted by an ohmic transmission line with conductance $\alpha (2e)^2/h$. Their model includes a realistic high frequency cutoff of order $\alpha E_c$, that is typically smaller than the plasma frequency $W$. The authors present a phase diagram showing surprising features, not anticipated in the established literature [eg. Sch\"on and Zaikin, Phys. Reports 198, 237, (1990)]. For $E_{\rm J}/E_{\rm C}$ above a certain value, they find that the junction remains superconducting for all $\alpha$, while below this value, they find that the insulating phase leads to re-entrant superconductivity at small $\alpha$. In this Comment, we show that their Numerical Renormalization Group (NRG) implementation is uncontrolled, and that there is no evidence for the re-entrant superconductivity in the phase diagram presented in Fig. 1a of PRL 129, 087001.Comment: 3 pages. Text of the version accepted for publication, plus an appendix with additional informatio

Few-body nature of Kondo correlated ground states

The quenching of degenerate impurity states in metals generally induces a long-range correlated quantum state known as the Kondo screening cloud. While a macroscopic number of particles clearly take part in forming this extended structure, assessing the number of truly entangled degrees of freedom requires a careful analysis of the relevant many-body wavefunction. For this purpose, we examine the natural single-particle orbitals that are eigenstates of the single-particle density (correlation) matrix for the ground state of two quantum impurity problems: the interacting resonant level model (IRLM) and the single impurity Anderson model (SIAM). As a simple and general probe for few-body versus many-body character we consider the rate of exponential decay of the correlation matrix eigenvalues towards inactive (fully empty or filled) orbitals. We find that this rate remains large in the physically most relevant region of parameter space, implying a few-body character. Genuine many-body correlations emerge only when the Kondo temperature becomes exponentially small, for instance near a quantum critical point. In addition, we demonstrate that a simple numerical diagonalization of the few-body problem restricted to the Fock space of the most correlated orbitals converges exponentially fast with respect to the number of orbitals, to the true ground state of the IRLM. We also show that finite size effects drastically affect the correlation spectrum, shedding light on an apparent paradox arising from previous studies on short chains.Comment: 8 pages + 3 pages of appendices. Main changes from previous version: Previous version focussed exclusively on the Interacting Resonant Level Model. New version contains new section (Sec. V) showing similar results for the Single Impurity Anderson Mode

Revealing the finite-frequency response of a bosonic quantum impurity

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 dramatic many-body broadening caused by multi-photon conversion. The experimental results are matched quantitatively to a resummed diagrammatic calculation based on a microscopically calibrated model. Furthermore, we push the device into a regime where diagrammatic 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.Comment: 39 pages, 14 figure

A tunable Josephson platform to explore many-body quantum optics in circuit-QED

Coupling an isolated emitter to a single mode of the electromagnetic field is now routinely achieved and well understood. Current efforts aim to explore the coherent dynamics of emitters coupled to several electromagnetic modes (EM). freedom. Recently, ultrastrong coupling to a transmission line has been achieved where the emitter resonance broadens to a significant fraction of its frequency. In this work we gain significantly improved control over this regime. We do so by combining the simplicity of a transmon qubit and a bespoke EM environment with a high density of discrete modes, hosted inside a superconducting metamaterial. This produces a unique device in which the hybridisation between the qubit and up to 10 environmental modes can be monitored directly. Moreover the frequency and broadening of the qubit resonance can be tuned independently of each other in situ. We experimentally demonstrate that our device combines this tunability with ultrastrong coupling and a qubit nonlinearity comparable to the other relevant energy scales in the system. We also develop a quantitative theoretical description that does not contain any phenomenological parameters and that accurately takes into account vacuum fluctuations of our large scale quantum circuit in the regime of ultrastrong coupling and intermediate non-linearity. The demonstration of this new platform combined with a quantitative modelling brings closer the prospect of experimentally studying many-body effects in quantum optics. A limitation of the current device is the intermediate nonlinearity of the qubit. Pushing it further will induce fully developed many-body effects, such as a giant Lamb shift or nonclassical states of multimode optical fields. Observing such effects would establish interesting links between quantum optics and the physics of quantum impurities.Comment: Main paper and Supplementary Information combined in one file. List of the modifications in the final version: new abstract and introduction, comparison to RWA treatment, more precise capacitance mode

Efficient impurity-bath trial states from superposed Slater determinants

The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation. [S. Bravyi and D. Gosset, Comm. Math. Phys. 356, 451 (2017)]. It is natural to ask how many parameters are required for an efficient variational scheme based on this representation. An upper bound is $\mathcal O(N^2)$, where $N$ is the system size, which corresponds to the number parameters needed to specify an arbitrary Gaussian state. We provide an alternative representation, with more favorable scaling, only requiring $\mathcal O(N)$ parameters, that we illustrate for the interacting resonant level model. We achieve the reduction by associating mean-field-like parent Hamiltonians with the individual terms in the superposition, using physical insight to retain only the most relevant channels in each parent Hamiltonian. We benchmark our variational ansatz against the Numerical Renormalization Group, and compare our results to existing variational schemes of a similar nature to ours. Apart from the ground state energy, we also study the spectrum of the correlation matrix -- a very stringent measure of accuracy. Our approach outperforms some existing schemes and remains quantitatively accurate in the numerically challenging near-critical regime.Comment: Main text, 9 pages. Total length including appendices, 13 page