Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2308.15542 · PRX Quantum

Inelastic Decay from Integrability

Amir Burshtein, Moshe Goldstein

Published Apr 29, 2024• 13 citations
arXivHTMLPDF

Abstract

A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems possess an extensive number of locally conserved charges, leading to the conservation of the number of scattered excitations, as well as their set of individual momenta. In this work, we show that inelastic decay can nevertheless be observed in circuit-QED realizations of integrable boundary models. We consider the scattering of microwave photons off impurities in superconducting circuits implementing the boundary sine-Gordon and Kondo models, which are both integrable. We show that not only is inelastic decay possible for the microwave photons, in spite of integrability, and due to a nonlinear relation between them and the elastically scattered excitations, but also that integrability in fact provides powerful analytical tools allowing us to obtain exact expressions for response functions describing the inelastic decay. Using the framework of form factors, we calculate the total inelastic decay rate and elastic phase shift of the microwave photons, extracted from a two-point response function. We then go beyond linear response and obtain the exact energy-resolved inelastic decay spectrum, using a novel method to evaluate form-factor expansions of three-point response functions, which could prove useful in other applications of integrable quantum field theories. Our results could be relevant to several recent photon-splitting experiments and, in particular, to recent experimental works that provide evidence for the elusive Schmid-Bulgadaev dissipative quantum phase transition. Published by the American Physical Society 2024

DOI
10.1103/prxquantum.5.020323

Related papers

Inelastic Scattering of a Photon by a Quantum Phase Slip

Roman Kuzmin, Nicholas Grabon, N. Mehta +5 more

Spontaneous decay of a single photon is a notoriously inefficient process in nature irrespective of the frequency range. We report that a quantum phase-slip fluctuation in high-impedance superconducting waveguides can split a single incident microwave photon into a large number of lower-energy photons with a near unit probability. The underlying inelastic photon-photon interaction has no analogs in nonlinear optics. Instead, the measured decay rates are explained without adjustable parameters in the framework of a new model of a quantum impurity in a Luttinger liquid. Our result connects circuit quantum electrodynamics to critical phenomena in two-dimensional boundary quantum field theories, important in the physics of strongly correlated systems. The photon lifetime data represent a rare example of verified and useful quantum many-body simulation.

arXiv:2010.02099•Physical Review Letters•May 12, 2021•27 citations

Photon-instanton scattering in a superconducting circuit: Beyond the very high impedance regime

Amir Burshtein, David Shuliutsky, Roman Kuzmin +2 more

Instantons, semiclassical trajectories of quantum tunneling in imaginary time, have long been used to study thermodynamic and transport properties in a myriad of condensed matter and high-energy systems. A recent experiment in superconducting circuits [R. Kuzmin et al., Phys. Rev. Lett. 126, 197701 (2021)] provided first evidence for direct dynamical signatures of instantons (phase slips), manifested by order-unity inelastic decay probabilities for photons with which they interact, motivating the development of a scattering theory of instantons [A. Burshtein et al., Phys. Rev. Lett. 126, 137701 (2021)]. While this framework successfully predicted the measured inelastic decay rates of the photons for several experimental devices, it is valid only if the tunneling time of the instantons is much shorter than the relaxation time due to the environment in which they are embedded, and requires a closed analytical expression for the instanton trajectory. Here, we alleviate these restrictions by incorporating numerical methods that eliminate some of the previously applied approximations. Our results improve the agreement with the experimental measurements, also for devices with lower impedances and thus shorter relaxation times, without fitting parameters. This framework should be useful in many other quantum field theoretical contexts.

arXiv:2410.23062•Physical review. B./Physical review. B•Aug 7, 2025•0 citations

INTERACTING PHOTONS IN CIRCUIT QUANTUM ELECTRODYNAMICS: DECAY OF THE COLLECTIVE PHASE MODE IN ONE-DIMENSIONAL JOSEPHSON JUNCTION ARRAYS DUE TO QUANTUM PHASE-SLIP FLUCTUATIONS

Nicholas Grabon

Light does not typically scatter light, as witnessed by the linearity of Maxwell’s equations. In this work, we demonstrate two superconducting circuits, in which microwave photons have well-defined energy and momentum, but their lifetime is finite due to decay into lower energy photons. The circuits we present are formed with Josephson junction arrays where strong quantum phase-slip fluctuations are present either in all of the junctions or in only a single junction. The quantum phase-slip fluctuations are shown to result in the strong inelastic photon-photon interaction observed in both circuits. The phenomenon of a single photon decay provides a new way to study multiple long-standing many-body problems important for condensed matter physics. The examples of such problems, which we cover in this work include superconductor to insulator quantum phase transition in one dimension and a general quantum impurity problem. The photon lifetime data can be treated as a rare example of a verified and useful quantum many-body simulation.

•Jan 1, 2020•0 citations

Topics in 2D integrable field theories with boundary interactions

Sergei Skorik

We study different aspects of integrable boundary quantum field theories, focusing mostly on the ``boundary sine-Gordon model'' and its applications to condensed matter physics. The first part of the review deals with formal problems. We analyze the classical limit and perform semi-classical quantization. We show that the non-relativistic limit corresponds to the Calogero-Moser model with a boundary potential. We construct a lattice regularization of the problem via the XXZ chain. We classify boundary bound states. We generalize the Destri de Vega method to compute the ground state energy of the theory on a finite interval. The second part deals with some applications to condensed matter physics. We show how to compute analytically time and space dependent correlations in one-dimensional quantum integrable systems with an impurity. Our approach is based on a description of these systems in terms of massless scattering of quasiparticles. Correlators follow then from matrix elements of local operators between multiparticle states -- the massless form-factors. Although, in general an infinite sum of these form-factors has to be considered, we find that for the current, spin and energy operators only a few (two or three) are necessary to obtain an accuracy of more than 1\%. Our results hold for arbitrary impurity strength, in contrary to the perturbative expansions in the coupling constants. As an example, we compute the frequency dependent condunctance, at zero temperature, in a Luttinger liquid with an impurity, and also discuss the susceptibility in the Kondo model and the time-dependent properties of the two-state problem with dissipation.

arXiv:hep-th/9604174•Apr 28, 1996•2 citations

Theory of inelastic scattering from quantum impurities

L. Borda, Lars Fritz, Natan Andrei +1 more

We use the framework setup recently to compute nonperturbatively inelastic scattering from quantum impurities [G. Zar\'and et al., Phys. Rev. Lett. 93, 107204 (2004)] to study the energy dependence of the single-particle $S$ matrix and the inelastic scattering cross section for a number of quantum impurity models. We study the case of the spin $S=1∕2$ two-channel Kondo model, the Anderson model, and the usual $S=1∕2$ single-channel Kondo model. We discuss the difference between non-Fermi-liquid and Fermi-liquid models and study how a crossover between the non-Fermi-liquid and Fermi-liquid regimes appears in the case of channel anisotropy for the $S=1∕2$ two-channel Kondo model. We show that for the most elementary non-Fermi-liquid system, the two-channel Kondo model, half of the scattering remains inelastic even at the Fermi energy. Details of the derivation of the reduction formulas and a simple path integral approach to connect the $T$ matrix to local correlation functions are also presented.

arXiv:cond-mat/0703293•Physical Review B•Jun 15, 2007•51 citations

Formation of robust bound states of interacting microwave photons

Alexis Morvan, Trond I. Andersen, Xiao Mi +97 more

Abstract Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2–9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

arXiv:2206.05254•Nature•Dec 7, 2022•75 citations
A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems possess an extensive number of locally conserved charges, leading to the conservation of the number of scattered excitations, as well as their set of individual momenta. In this work, we show that inelastic decay can nevertheless be observed in circuit-QED realizations of integrable boundary models. We consider the scattering of microwave photons off impurities in superconducting circuits implementing the boundary sine-Gordon and Kondo models, which are both integrable. We show that not only is inelastic decay possible for the microwave photons, in spite of integrability, and due to a nonlinear relation between them and the elastically scattered excitations, but also that integrability in fact provides powerful analytical tools allowing us to obtain exact expressions for response functions describing the inelastic decay. Using the framework of form factors, we calculate the total inelastic decay rate and elastic phase shift of the microwave photons, extracted from a two-point response function. We then go beyond linear response and obtain the exact energy-resolved inelastic decay spectrum, using a novel method to evaluate form-factor expansions of three-point response functions, which could prove useful in other applications of integrable quantum field theories. Our results could be relevant to several recent photon-splitting experiments and, in particular, to recent experimental works that provide evidence for the elusive Schmid-Bulgadaev dissipative quantum phase transition. Published by the American Physical Society 2024
Spontaneous decay of a single photon is a notoriously inefficient process in nature irrespective of the frequency range. We report that a quantum phase-slip fluctuation in high-impedance superconducting waveguides can split a single incident microwave photon into a large number of lower-energy photons with a near unit probability. The underlying inelastic photon-photon interaction has no analogs in nonlinear optics. Instead, the measured decay rates are explained without adjustable parameters in the framework of a new model of a quantum impurity in a Luttinger liquid. Our result connects circuit quantum electrodynamics to critical phenomena in two-dimensional boundary quantum field theories, important in the physics of strongly correlated systems. The photon lifetime data represent a rare example of verified and useful quantum many-body simulation.
Instantons, semiclassical trajectories of quantum tunneling in imaginary time, have long been used to study thermodynamic and transport properties in a myriad of condensed matter and high-energy systems. A recent experiment in superconducting circuits [R. Kuzmin et al., Phys. Rev. Lett. 126, 197701 (2021)] provided first evidence for direct dynamical signatures of instantons (phase slips), manifested by order-unity inelastic decay probabilities for photons with which they interact, motivating the development of a scattering theory of instantons [A. Burshtein et al., Phys. Rev. Lett. 126, 137701 (2021)]. While this framework successfully predicted the measured inelastic decay rates of the photons for several experimental devices, it is valid only if the tunneling time of the instantons is much shorter than the relaxation time due to the environment in which they are embedded, and requires a closed analytical expression for the instanton trajectory. Here, we alleviate these restrictions by incorporating numerical methods that eliminate some of the previously applied approximations. Our results improve the agreement with the experimental measurements, also for devices with lower impedances and thus shorter relaxation times, without fitting parameters. This framework should be useful in many other quantum field theoretical contexts.
Light does not typically scatter light, as witnessed by the linearity of Maxwell’s equations. In this work, we demonstrate two superconducting circuits, in which microwave photons have well-defined energy and momentum, but their lifetime is finite due to decay into lower energy photons. The circuits we present are formed with Josephson junction arrays where strong quantum phase-slip fluctuations are present either in all of the junctions or in only a single junction. The quantum phase-slip fluctuations are shown to result in the strong inelastic photon-photon interaction observed in both circuits. The phenomenon of a single photon decay provides a new way to study multiple long-standing many-body problems important for condensed matter physics. The examples of such problems, which we cover in this work include superconductor to insulator quantum phase transition in one dimension and a general quantum impurity problem. The photon lifetime data can be treated as a rare example of a verified and useful quantum many-body simulation.
We study different aspects of integrable boundary quantum field theories, focusing mostly on the ``boundary sine-Gordon model'' and its applications to condensed matter physics. The first part of the review deals with formal problems. We analyze the classical limit and perform semi-classical quantization. We show that the non-relativistic limit corresponds to the Calogero-Moser model with a boundary potential. We construct a lattice regularization of the problem via the XXZ chain. We classify boundary bound states. We generalize the Destri de Vega method to compute the ground state energy of the theory on a finite interval. The second part deals with some applications to condensed matter physics. We show how to compute analytically time and space dependent correlations in one-dimensional quantum integrable systems with an impurity. Our approach is based on a description of these systems in terms of massless scattering of quasiparticles. Correlators follow then from matrix elements of local operators between multiparticle states -- the massless form-factors. Although, in general an infinite sum of these form-factors has to be considered, we find that for the current, spin and energy operators only a few (two or three) are necessary to obtain an accuracy of more than 1\%. Our results hold for arbitrary impurity strength, in contrary to the perturbative expansions in the coupling constants. As an example, we compute the frequency dependent condunctance, at zero temperature, in a Luttinger liquid with an impurity, and also discuss the susceptibility in the Kondo model and the time-dependent properties of the two-state problem with dissipation.
We use the framework setup recently to compute nonperturbatively inelastic scattering from quantum impurities [G. Zar\'and et al., Phys. Rev. Lett. 93, 107204 (2004)] to study the energy dependence of the single-particle SSS matrix and the inelastic scattering cross section for a number of quantum impurity models. We study the case of the spin S=1∕2S=1∕2S=1∕2 two-channel Kondo model, the Anderson model, and the usual S=1∕2S=1∕2S=1∕2 single-channel Kondo model. We discuss the difference between non-Fermi-liquid and Fermi-liquid models and study how a crossover between the non-Fermi-liquid and Fermi-liquid regimes appears in the case of channel anisotropy for the S=1∕2S=1∕2S=1∕2 two-channel Kondo model. We show that for the most elementary non-Fermi-liquid system, the two-channel Kondo model, half of the scattering remains inelastic even at the Fermi energy. Details of the derivation of the reduction formulas and a simple path integral approach to connect the TTT matrix to local correlation functions are also presented.
Abstract Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2–9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.