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

Cambridge University Press eBooks

Qubit–Photon Interaction

Juan José García‐Ripoll

Published Jul 31, 2022• 0 citations
Publisher

Abstract

Almost all superconducting quantum technologies are built using a combination of qubits and microwave resonators. In this chapter, we develop the theory to study coherent qubit–photon interaction in such devices. We start with the equivalent of an atom in free space, studying a qubit in an open waveguide. We develop the spin-boson Hamiltonian, with specific methods to solve its dynamics in the limits of few excitations. Using these tools, we can study how an excited qubit can relax to the ground state, producing a photon, and how a propagating photon can interact with a qubit. We then move to closed environments where the photons are confined in cavities or resonators, developing the theory of cavity-QED. Using this theory, we study the Purcell enhancement of interactions, the Jaynes–Cummings model, Rabi oscillations, and vacuum Rabi splitting. We close the chapter illustrating some limits in which cavities can be used to control and measure qubits.

DOI
10.1017/9781316779460.007

Related papers

Quantum Information Processing with Superconducting Qubits and Cavities

Andreas J. Wallraff, David Schuster, Alexandre Blais +10 more

In this paper, the coherent interaction of individual microwave photons with superconducting qubits is presented both for quantum information processing and for novel quantum optics experiments in the circuit quantum electrodynamics (QED) architecture. In the resonant regime we observe the vacuum Rabi mode splitting. In the non-resonant regime we use the dispersive coupling between the qubit and the cavity field to perform high visibility quantum non-demolition (QND) measurements of the qubit state. In the strong dispersive limit we also perform measurements of the cavity state from which the photon number statistics of the field can be extracted. Generally, the circuit QED architecture is attractive for quantum information processing and as an interface in hybrid quantum systems.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2007•2 citations

Propagating microwave photons in superconducting circuits

Juan José García‐Ripoll, J. J. Mazo, E. Solano +1 more

In the last decade, the field of Quantum Optics has been enriched with a completely new platform: superconducting quantum circuits, also known as circuit-QED. This platform builds on the original designs of superconducting qubits, that is few-level systems made of superconducting islands and Josephson junctions, but adds to it a new ingredient, microwave photons. In this talk I will review circuit-QED with a focus on two complementary lines of research: ultrastrong light-matter coupling and strongly correlated propagating photons. The first topic deals with novel designs of superconducting qubits, engineering their coupling to the microwave radiation field to reach Rabi frequencies that approach the qubit and photon frequencies. In this regime, known as ”ultrastrong coupling”, the rotating wave approximation from Quantum Optics is no longer valid, the vacuum may spontaneously polarize, producing photons that get bound to the qubit, and novel physics is expected to emerge. I will review recent experiments on this topic, together with various theoretical proposals to tame this ultrastrong coupling. The second topic revolves around the notion of ”propagating” photons in these circuits. Most experiments in circuit-QED so far adopted the typical configuration of artificial atoms (qubits) interacting with artificial cavities (LC resonators). This proved useful in order to reach the strong coupling regime, demonstrating Rabi oscillations and developing a variety of protocols for quantum information, tomograhy, entanglement, etc. However, recent experiments have shown that it is possible to also work with propagating photons, replacing the LC resonators with open transmission lines, and studying the scattering properties of those artificial atoms. In this context we have worked on developing new technology to detect and control these photons, engineering single-photon detectors, quantum metamaterials and photonic crystals, or even new nonlinear media based on coupled cavities.

•Sep 9, 2012•0 citations

Measurement and control of quantum cavities with electronic atoms

Andrew N. Cleland

This chapter describes a method to control and measure quantum cavities, achieved using a superconducting phase qubit, a type of electronic atom. The phase qubit has been under intensive development for use as a quantum processing element in a quantum computer. It has recently been used to demonstrate the quantum control and measurement of excitations in resonant cavities, including controlling photons in superconducting microwave resonators, as well as phonons in microwave-frequency mechanical resonators. The discussion here focuses on the quantum control of electromagnetic resonators.

Oxford University Press eBooks•Jul 26, 2012•1 citation

Controllable interaction between photons and distant spins via vacuum Rabi oscillations

Xiao Xue, Jurgen Dijkema, Tobias Bonsen +7 more

Vacuum Rabi oscillations between a single photon and a single spin demonstrate the capability of harnessing light-matter interaction at the level of a single quantum of energy. Since the observation of strong spin-photon coupling in gate-defined quantum dots, probing this interaction in the time-domain has been a major objective. Here, we carefully engineer a device composed of two spatially separated double quantum dots hosting single electron spin qubits and a superconducting cavity to accommodate microwave photons. We observe multiple vacuum Rabi oscillations between each spin qubit and the cavity. By concatenating vacuum Rabi oscillations involving the two spins, an energy excitation in one qubit can be emitted as a photon and then transferred to the other qubit. When a single photon is emitted, the cavity is prepared in a Fock state, leading to an accelerated vacuum Rabi frequency. These results serve as building blocks not only in exploring light-matter interactions, but also in interfacing semiconductor spin qubits to photonic links.

cond-mat.mes-hallCross-listedarXiv:2608.03809•Aug 5, 2026

Superconducting Qubits and Quantum Resonators

P. Forn-Díaz

Superconducting qubits are fabricated "loss-free" electrical circuits on a chip with size features of tens of nanometers. If cooled to cryogenic temperatures below -273 °C they behave as quantum elements, similar to atoms and molecules. Such a qubit can be manipulated by fast-oscillating magnetic fields and its resulting quantum state can be measured using a proper magnetic detector. These qubits could be the basic elements for a quantum processor. To that order, multiple qubits have to controllably interact, and to that purpose very high quality resonators are fabricated on the same chip. Effectively the interaction results from the phase-coherent exchange of a single photon between qubit and resonator. In this way it is highly analogous to the so-called cavity QED in atomic physics where single atoms couple to a single trapped photon, all inside a cavity resonator. In this thesis, a superconducting flux qubit has been coupled to an LC resonator and coherent exchange of a single photon between qubit and resonator has been achieved. A striking option in these superconducting circuits, not attainable in "common" atomic cavity-QED, is that the interaction between qubit and photon can be made very large, up to the limit that one no longer can talk about the qubit and resonator as such. This limit requires a fully different description and it leads to novel effects, e.g. in the energy spectrum of the qubit-resonator composite. The Bloch-Siegert spectral shift is experimentally demonstrated in this thesis. As a small but critical technical aside a new type of control line filter has been developed, which allows strong suppression of excess electrical noise that forms a threat for qubit coherence. Having two modes of operation, it shorts all low-frequency noise if control is idle while being transparent if control is active, where short or open is determined by the control line signal level itself.

•Sep 27, 2010•3 citations

Quantum Rabi oscillations of a qubit strongly coupled to a one-dimensional waveguide

Ya. S. Greenberg, A. A. Shtygashev, O. A. Chuikin +2 more

We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.

quant-pharXiv:2608.16077•Aug 18, 2026•0 citations
Almost all superconducting quantum technologies are built using a combination of qubits and microwave resonators. In this chapter, we develop the theory to study coherent qubit–photon interaction in such devices. We start with the equivalent of an atom in free space, studying a qubit in an open waveguide. We develop the spin-boson Hamiltonian, with specific methods to solve its dynamics in the limits of few excitations. Using these tools, we can study how an excited qubit can relax to the ground state, producing a photon, and how a propagating photon can interact with a qubit. We then move to closed environments where the photons are confined in cavities or resonators, developing the theory of cavity-QED. Using this theory, we study the Purcell enhancement of interactions, the Jaynes–Cummings model, Rabi oscillations, and vacuum Rabi splitting. We close the chapter illustrating some limits in which cavities can be used to control and measure qubits.
In this paper, the coherent interaction of individual microwave photons with superconducting qubits is presented both for quantum information processing and for novel quantum optics experiments in the circuit quantum electrodynamics (QED) architecture. In the resonant regime we observe the vacuum Rabi mode splitting. In the non-resonant regime we use the dispersive coupling between the qubit and the cavity field to perform high visibility quantum non-demolition (QND) measurements of the qubit state. In the strong dispersive limit we also perform measurements of the cavity state from which the photon number statistics of the field can be extracted. Generally, the circuit QED architecture is attractive for quantum information processing and as an interface in hybrid quantum systems.
In the last decade, the field of Quantum Optics has been enriched with a completely new platform: superconducting quantum circuits, also known as circuit-QED. This platform builds on the original designs of superconducting qubits, that is few-level systems made of superconducting islands and Josephson junctions, but adds to it a new ingredient, microwave photons. In this talk I will review circuit-QED with a focus on two complementary lines of research: ultrastrong light-matter coupling and strongly correlated propagating photons. The first topic deals with novel designs of superconducting qubits, engineering their coupling to the microwave radiation field to reach Rabi frequencies that approach the qubit and photon frequencies. In this regime, known as ”ultrastrong coupling”, the rotating wave approximation from Quantum Optics is no longer valid, the vacuum may spontaneously polarize, producing photons that get bound to the qubit, and novel physics is expected to emerge. I will review recent experiments on this topic, together with various theoretical proposals to tame this ultrastrong coupling. The second topic revolves around the notion of ”propagating” photons in these circuits. Most experiments in circuit-QED so far adopted the typical configuration of artificial atoms (qubits) interacting with artificial cavities (LC resonators). This proved useful in order to reach the strong coupling regime, demonstrating Rabi oscillations and developing a variety of protocols for quantum information, tomograhy, entanglement, etc. However, recent experiments have shown that it is possible to also work with propagating photons, replacing the LC resonators with open transmission lines, and studying the scattering properties of those artificial atoms. In this context we have worked on developing new technology to detect and control these photons, engineering single-photon detectors, quantum metamaterials and photonic crystals, or even new nonlinear media based on coupled cavities.
This chapter describes a method to control and measure quantum cavities, achieved using a superconducting phase qubit, a type of electronic atom. The phase qubit has been under intensive development for use as a quantum processing element in a quantum computer. It has recently been used to demonstrate the quantum control and measurement of excitations in resonant cavities, including controlling photons in superconducting microwave resonators, as well as phonons in microwave-frequency mechanical resonators. The discussion here focuses on the quantum control of electromagnetic resonators.
Vacuum Rabi oscillations between a single photon and a single spin demonstrate the capability of harnessing light-matter interaction at the level of a single quantum of energy. Since the observation of strong spin-photon coupling in gate-defined quantum dots, probing this interaction in the time-domain has been a major objective. Here, we carefully engineer a device composed of two spatially separated double quantum dots hosting single electron spin qubits and a superconducting cavity to accommodate microwave photons. We observe multiple vacuum Rabi oscillations between each spin qubit and the cavity. By concatenating vacuum Rabi oscillations involving the two spins, an energy excitation in one qubit can be emitted as a photon and then transferred to the other qubit. When a single photon is emitted, the cavity is prepared in a Fock state, leading to an accelerated vacuum Rabi frequency. These results serve as building blocks not only in exploring light-matter interactions, but also in interfacing semiconductor spin qubits to photonic links.
Superconducting qubits are fabricated "loss-free" electrical circuits on a chip with size features of tens of nanometers. If cooled to cryogenic temperatures below -273 °C they behave as quantum elements, similar to atoms and molecules. Such a qubit can be manipulated by fast-oscillating magnetic fields and its resulting quantum state can be measured using a proper magnetic detector. These qubits could be the basic elements for a quantum processor. To that order, multiple qubits have to controllably interact, and to that purpose very high quality resonators are fabricated on the same chip. Effectively the interaction results from the phase-coherent exchange of a single photon between qubit and resonator. In this way it is highly analogous to the so-called cavity QED in atomic physics where single atoms couple to a single trapped photon, all inside a cavity resonator. In this thesis, a superconducting flux qubit has been coupled to an LC resonator and coherent exchange of a single photon between qubit and resonator has been achieved. A striking option in these superconducting circuits, not attainable in "common" atomic cavity-QED, is that the interaction between qubit and photon can be made very large, up to the limit that one no longer can talk about the qubit and resonator as such. This limit requires a fully different description and it leads to novel effects, e.g. in the energy spectrum of the qubit-resonator composite. The Bloch-Siegert spectral shift is experimentally demonstrated in this thesis. As a small but critical technical aside a new type of control line filter has been developed, which allows strong suppression of excess electrical noise that forms a threat for qubit coherence. Having two modes of operation, it shorts all low-frequency noise if control is idle while being transparent if control is active, where short or open is determined by the control line signal level itself.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.