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:1910.08340 · Nature Communications

Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits

Sébastien Leger, Javier Puertas-Martínez, Karthik Srikanth Bharadwaj, Rémy Dassonneville, Jovian Delaforce, Farshad Foroughi, Vladimir Milchakov, Luca Planat, O. Buisson, Cécile Naud, Wiebke Guichard, Serge Florens, Izak Snyman, Nicolas Roch

Published Nov 20, 2019• 58 citations
arXivHTMLPDF

Abstract

Electromagnetic fields possess zero point fluctuations which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain, these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by zero point fluctuations in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modeling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about thirty environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits.

DOI
10.1038/s41467-019-13199-x

Related papers

Superstrong coupling in circuit quantum electrodynamics

Roman Kuzmin, Nitish Mehta, Nicholas Grabon +2 more

Abstract Vacuum fluctuations fundamentally affect an atom by inducing a finite excited state lifetime along with a Lamb shift of its transition frequency. Here we report the reverse effect: modification of vacuum modes by a single atom in circuit quantum electrodynamics. Our one-dimensional vacuum is a long section of a high wave impedance (comparable to resistance quantum) superconducting transmission line. It is directly wired to a transmon qubit circuit. Owing to the combination of high impedance and galvanic connection, the transmon’s spontaneous emission linewidth can greatly exceed the discrete transmission line modes spacing. This condition defines a previously unexplored superstrong coupling regime of quantum electrodynamics where many frequency-resolved vacuum modes hybridize with a single atom. We establish this regime by observing the spontaneous emission line of the transmon, revealed through the mode-by-mode measurement of the vacuum’s density of states. The linewidth as well as the atom-induced dispersive photon−photon interaction are accurately described by a physically transparent Caldeira−Leggett model, with the transmon’s quartic nonlinearity treated as a perturbation. Nonperturbative modification of vacuum, including inelastic scattering of single photons, can be enabled by the superstrong coupling regime upon replacing the transmon by more anharmonic qubits, with broad implications for simulating quantum impurity models of many-body physics.

arXiv:1809.10739•npj Quantum Information•Feb 25, 2019•68 citations

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

Javier Puertas Martínez, Sébastien Leger, Nicolas Gheeraert +10 more

Abstract The interaction between light and matter remains a central topic in modern physics despite decades of intensive research. Coupling an isolated emitter to a single mode of the electromagnetic field is now routinely achieved in the laboratory, and standard quantum optics provides a complete toolbox for describing such a setup. Current efforts aim to go further and explore the coherent dynamics of systems containing an emitter coupled to several electromagnetic degrees of freedom. Recently, ultrastrong coupling to a transmission line has been achieved where the emitter resonance broadens to a significant fraction of its frequency, and hybridizes with a continuum of electromagnetic (EM) modes. In this work we gain significantly improved control over this regime. We do so by combining the simplicity and robustness 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 many modes (up to ten in the current device) of its environment 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

arXiv:1802.00633•npj Quantum Information•Feb 25, 2019•103 citations

Spectral signature of high-order photon processes enhanced by Cooper-pair pairing

W. C. Smith, A. Borgognoni, Marius Villiers +7 more

Inducing interactions between individual photons is key for photonic quantum information and studying many-body photon states. Superconducting circuits are well suited to combine strong interactions with low losses. Typically, microwave photons are stored in an LC oscillator shunted by a Josephson junction, where the zero-point phase fluctuations across the junction determine the strength and order of photon interactions. Most superconducting nonlinear oscillators operate with small phase fluctuations, where two-photon Kerr interactions dominate. In our experiment, we shunt a high-impedance LC oscillator with a dipole element favoring the tunneling of paired Cooper pairs. This leads to large phase fluctuations of 3.4, accessing a regime where transition frequencies shift non-monotonically with excitation number. From spectroscopy, we extract two-, three-, and four-photon interaction energies, all of similar strength and exceeding the photon loss rate. Our results open a new regime of high-order photon interactions in microwave quantum optics. In superconducting circuits, the nonlinearity of Josephson junctions mediates photon interactions, but they are typically dominated by two-photon processes. Here the authors observe multi-photon interactions in a superconducting circuit with Cooper-pair pairing, revealing a new regime of microwave quantum optics.

arXiv:2312.15075•Nature Communications•Sep 24, 2025•2 citations

CLEO®/Europe-IQEC 2013: Strongly interacting many body physics with circuit quantum electrodynamics networks

Martin Leib, Lukas Neumeier, Frank Deppe +3 more

In its infancy circuit quantum electrodynamics (cQED) has quickly started reproducing fundamental quantum optical experiments, e.g. observation of vacuum rabi oscillations in frequency and time domain, with unprecedented cooperativity. This was possible because of the large coupling of the quasi one-dimensional microwave field of the superconducting transmission line resonators to the macroscopic dipole moment of superconducting qubits. cQED has matured to a discipline of experimental physics capable of performing fundamental quantum information tasks and is currently on the verge of crossing the border between few- to many body physics [1]. This opens up a exciting realm of completely new physical phenomena. Because of the ubiquitous influence of the electromagnetic environment however the number of microwave photons is not conserved which separates cQED systems from other quantum simulators involving atoms, e.g. cold atoms in optical latices. Instead cQED is ideally suited for exploring quantum many-body physics in the driven dissipative regime where the interplay of constantly injecting microwave photons and the unpreventable loss of microwave photons into the electromagnetic environment generates a whole new class of steady- but not equilibrium states. We propose an array of capacitively coupled superconducting resonators each coupled to an superconducting charge qubit and show that this device can be considered as an simulator for Bose Hubbard physics combined with the high flexibility of network topologies unique to cQED systems[2]. We further investigate the driven dissipative dynamics of this device. We refine this approach and calculate the eigenmodes and nonlinearities of a Josephson junction intersected transmission line resonator[3](c.f. fig.1a). This spectrum of eigenmodes shows the ultrastrong coupling of the Josephson junction to the resonator modes and nonlinearities are attainable that are significant on the single photon limit. We now proceed one step further and and consider the incorporation of multiple Josephson junctions. A novel transfer matrix technique has to be employed to investigate the eigenmode spectrum of the device.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations

Resolving Vacuum Fluctuations in an Electrical Circuit by Measuring the Lamb Shift

A. Fragner, M. Göppl, J. M. Fink +5 more

Quantum theory predicts that empty space is not truly empty. Even in the absence of any particles or radiation, in pure vacuum, virtual particles are constantly created and annihilated. In an electromagnetic field, the presence of virtual photons manifests itself as a small renormalization of the energy of a quantum system, known as the Lamb shift. We present an experimental observation of the Lamb shift in a solid-state system. The strong dispersive coupling of a superconducting electronic circuit acting as a quantum bit (qubit) to the vacuum field in a transmission-line resonator leads to measurable Lamb shifts of up to 1.4% of the qubit transition frequency. The qubit is also observed to couple more strongly to the vacuum field than to a single photon inside the cavity, an effect that is explained by taking into account the limited anharmonicity of the higher excited qubit states.

Science•Nov 27, 2008•115 citations

Many body physics with coupled transmission line resonators

M Leib, M J Hartmann

We present the Josephson junction intersected superconducting transmission line resonator. In contrast to the Josephson parametric amplifier, Josephson bifurcation amplifier and Josephson parametric converter we consider the regime of few microwave photons. We review the derivation of eigenmode frequencies and zero point fluctuations of the nonlinear transmission line resonator and the derivation of the eigenmode Kerr nonlinearities. Remarkably these nonlinearities can reach values comparable to Transmon qubits rendering the device ideal for accessing the strongly correlated regime. This is particularly interesting for investigation of quantum many-body dynamics of interacting particles under the influence of drive and dissipation. We provide current profiles for the device modes and investigate the coupling between resonators in a network of nonlinear transmission line resonators.

arXiv:1208.0134•Physica Scripta•Mar 1, 2013•5 citations
Electromagnetic fields possess zero point fluctuations which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain, these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by zero point fluctuations in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modeling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about thirty environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits.
Abstract Vacuum fluctuations fundamentally affect an atom by inducing a finite excited state lifetime along with a Lamb shift of its transition frequency. Here we report the reverse effect: modification of vacuum modes by a single atom in circuit quantum electrodynamics. Our one-dimensional vacuum is a long section of a high wave impedance (comparable to resistance quantum) superconducting transmission line. It is directly wired to a transmon qubit circuit. Owing to the combination of high impedance and galvanic connection, the transmon’s spontaneous emission linewidth can greatly exceed the discrete transmission line modes spacing. This condition defines a previously unexplored superstrong coupling regime of quantum electrodynamics where many frequency-resolved vacuum modes hybridize with a single atom. We establish this regime by observing the spontaneous emission line of the transmon, revealed through the mode-by-mode measurement of the vacuum’s density of states. The linewidth as well as the atom-induced dispersive photon−photon interaction are accurately described by a physically transparent Caldeira−Leggett model, with the transmon’s quartic nonlinearity treated as a perturbation. Nonperturbative modification of vacuum, including inelastic scattering of single photons, can be enabled by the superstrong coupling regime upon replacing the transmon by more anharmonic qubits, with broad implications for simulating quantum impurity models of many-body physics.
Abstract The interaction between light and matter remains a central topic in modern physics despite decades of intensive research. Coupling an isolated emitter to a single mode of the electromagnetic field is now routinely achieved in the laboratory, and standard quantum optics provides a complete toolbox for describing such a setup. Current efforts aim to go further and explore the coherent dynamics of systems containing an emitter coupled to several electromagnetic degrees of freedom. Recently, ultrastrong coupling to a transmission line has been achieved where the emitter resonance broadens to a significant fraction of its frequency, and hybridizes with a continuum of electromagnetic (EM) modes. In this work we gain significantly improved control over this regime. We do so by combining the simplicity and robustness 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 many modes (up to ten in the current device) of its environment 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
Inducing interactions between individual photons is key for photonic quantum information and studying many-body photon states. Superconducting circuits are well suited to combine strong interactions with low losses. Typically, microwave photons are stored in an LC oscillator shunted by a Josephson junction, where the zero-point phase fluctuations across the junction determine the strength and order of photon interactions. Most superconducting nonlinear oscillators operate with small phase fluctuations, where two-photon Kerr interactions dominate. In our experiment, we shunt a high-impedance LC oscillator with a dipole element favoring the tunneling of paired Cooper pairs. This leads to large phase fluctuations of 3.4, accessing a regime where transition frequencies shift non-monotonically with excitation number. From spectroscopy, we extract two-, three-, and four-photon interaction energies, all of similar strength and exceeding the photon loss rate. Our results open a new regime of high-order photon interactions in microwave quantum optics. In superconducting circuits, the nonlinearity of Josephson junctions mediates photon interactions, but they are typically dominated by two-photon processes. Here the authors observe multi-photon interactions in a superconducting circuit with Cooper-pair pairing, revealing a new regime of microwave quantum optics.
In its infancy circuit quantum electrodynamics (cQED) has quickly started reproducing fundamental quantum optical experiments, e.g. observation of vacuum rabi oscillations in frequency and time domain, with unprecedented cooperativity. This was possible because of the large coupling of the quasi one-dimensional microwave field of the superconducting transmission line resonators to the macroscopic dipole moment of superconducting qubits. cQED has matured to a discipline of experimental physics capable of performing fundamental quantum information tasks and is currently on the verge of crossing the border between few- to many body physics [1]. This opens up a exciting realm of completely new physical phenomena. Because of the ubiquitous influence of the electromagnetic environment however the number of microwave photons is not conserved which separates cQED systems from other quantum simulators involving atoms, e.g. cold atoms in optical latices. Instead cQED is ideally suited for exploring quantum many-body physics in the driven dissipative regime where the interplay of constantly injecting microwave photons and the unpreventable loss of microwave photons into the electromagnetic environment generates a whole new class of steady- but not equilibrium states. We propose an array of capacitively coupled superconducting resonators each coupled to an superconducting charge qubit and show that this device can be considered as an simulator for Bose Hubbard physics combined with the high flexibility of network topologies unique to cQED systems[2]. We further investigate the driven dissipative dynamics of this device. We refine this approach and calculate the eigenmodes and nonlinearities of a Josephson junction intersected transmission line resonator[3](c.f. fig.1a). This spectrum of eigenmodes shows the ultrastrong coupling of the Josephson junction to the resonator modes and nonlinearities are attainable that are significant on the single photon limit. We now proceed one step further and and consider the incorporation of multiple Josephson junctions. A novel transfer matrix technique has to be employed to investigate the eigenmode spectrum of the device.
Quantum theory predicts that empty space is not truly empty. Even in the absence of any particles or radiation, in pure vacuum, virtual particles are constantly created and annihilated. In an electromagnetic field, the presence of virtual photons manifests itself as a small renormalization of the energy of a quantum system, known as the Lamb shift. We present an experimental observation of the Lamb shift in a solid-state system. The strong dispersive coupling of a superconducting electronic circuit acting as a quantum bit (qubit) to the vacuum field in a transmission-line resonator leads to measurable Lamb shifts of up to 1.4% of the qubit transition frequency. The qubit is also observed to couple more strongly to the vacuum field than to a single photon inside the cavity, an effect that is explained by taking into account the limited anharmonicity of the higher excited qubit states.
We present the Josephson junction intersected superconducting transmission line resonator. In contrast to the Josephson parametric amplifier, Josephson bifurcation amplifier and Josephson parametric converter we consider the regime of few microwave photons. We review the derivation of eigenmode frequencies and zero point fluctuations of the nonlinear transmission line resonator and the derivation of the eigenmode Kerr nonlinearities. Remarkably these nonlinearities can reach values comparable to Transmon qubits rendering the device ideal for accessing the strongly correlated regime. This is particularly interesting for investigation of quantum many-body dynamics of interacting particles under the influence of drive and dissipation. We provide current profiles for the device modes and investigate the coupling between resonators in a network of nonlinear transmission line resonators.