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

Physical Review A

Three-photon resonance and adiabatic passage in the large-detuning Rabi model

Ken K. W., C. K. Law

Published Aug 21, 2015• 77 citations
Publisher

Abstract

We investigate theoretically the quantum Rabi model in the large-detuning regime. When the frequency of the cavity field is near one-third of the atomic transition frequency, we show that there exists a resonant three-photon coupling via intermediate states connected by counter-rotating processes. We derive an effective Hamiltonian of the three-photon coupling, which determines the magnitude of the energy splitting and the position of the resonance analytically. In addition, we present a scheme of three-photon generation based on adiabatic passage across the resonance.

DOI
10.1103/physreva.92.023842

Related papers

Generating three-photon Rabi oscillations without a large-detuning condition

Ke-Xiong Yan, Yuan Qiu, Yang Xiao +2 more

It is well known that in the quantum Rabi model, a three-photon resonance occurs when the cavity field bare frequency is about 1/3 of the atomic transition frequency. In this manuscript, we show that the resonance can also be generated in the absence of the ``1/3 condition'' by employing an artificial atom with tunable transition frequency. To realize the protocol, the modulation frequency should be comparable to the cavity frequency in order to induce a counter-rotating interaction in the effective Hamiltonian. In this way, three-photon Rabi oscillations can be observed in a small-detuning regime, avoiding the excitation of high-energy states of the atom. We derive an effective Hamiltonian (equivalent to the anisotropic Rabi model Hamiltonian) to determine the magnitude of the energy splitting and the resonance position. Numerical simulation results show that the protocol not only generates a three-photon resonance, but also has a detectable output photon flux. We hope the protocol can be exploited for the realization of Fock-state sources and the generation of multiparticle entanglement.

arXiv:2408.00468•Physical Review A•Oct 11, 2024•14 citations

Multiphonon-resonance quantum Rabi model and adiabatic passage in a cavity-optomechanical system

Zhi‐Rong Zhong, Lei Chen, Jianqi Sheng +2 more

In this paper, we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system. In the scheme, when the driving bichromatic laser beam is adjusted to the off-resonant j -order red- and blue-sideband, the interaction between the cavity and mechanical oscillator leads to a j -phonon resonance quantum Rabi model. Moreover, we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system. As a typical example, we theoretically analyze the two-phonon resonance quantum Rabi model, and derive an effective Hamiltonian of the six-phonon coupling. Finally, we present a method of six-phonon generation based on adiabatic passage across the resonance. Numerical simulations confirm the validity of the proposed scheme. Theoretically, the proposed scheme can be extended to the realization of 3 j -phonon state.

Frontiers of Physics•Jul 18, 2021•9 citations

Simultaneous Excitation of Two Atoms with a Single Photon

Luigi Garziano, Roberto Stassi, Vincenzo Macrí +3 more

We consider two separate atoms interacting with a single-mode optical resonator. When the frequency of the resonator field is twice the atomic transition frequency, we show that there exists a resonant coupling between one photon and two atoms, via intermediate virtual states connected by counter-rotating processes. If the resonator is prepared in its one-photon state, the photon can be jointly absorbed by the two atoms in their ground state which will both reach their excited state with probability close to one. Like ordinary quantum Rabi oscillations, this process is coherent and reversible, so that two atoms in their excited state will undergo a downward transition jointly emitting a single cavity photon. This joint absorption and emission processes can also occur with three atoms. The parameters used to investigate this process correspond to experimentally demonstrated values in circuit quantum electrodynamics systems.

•Jan 5, 2016•1 citation

Beyond the Rabi model: Light interactions with polar atomic systems in a cavity

Giovanni Scala, Karolina Słowik, Paolo Facchi A +2 more

The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single-cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasiresonant with the cavity photon energy, and by neglecting the nonresonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one can derive the well-known phenomenology of quasiresonant transitions, including the fluorescence triplets. In this work we consider the most general Rabi model, incorporating the effects of permanent atomic electric dipole moments. Based on a perturbative analysis, we compare the intensities of emission lines induced by rotating terms, counter-rotating terms, and parity-symmetry-breaking terms in order to identify the parameter regimes in which these different contributions play a significant role. The analysis reveals that the emission strength related to the existence of permanent dipoles may surpass the one due to the counter-rotating interaction terms but is usually much weaker than the emission due to the main, resonant coupling. This ratio can be modified in systems with a reduced dimensionality or by engineering the energy spectral density of the continuum.

arXiv:2103.11232•Physical Review A•Jul 27, 2021•14 citations

One Photon Can Simultaneously Excite Two or More Atoms

Luigi Garziano, Vincenzo Macrí, Roberto Stassi +3 more

We consider two separate atoms interacting with a single-mode optical or microwave resonator. When the frequency of the resonator field is twice the atomic transition frequency, we show that there exists a resonant coupling between one photon and two atoms, via intermediate virtual states connected by counterrotating processes. If the resonator is prepared in its one-photon state, the photon can be jointly absorbed by the two atoms in their ground state which will both reach their excited state with a probability close to one. Like ordinary quantum Rabi oscillations, this process is coherent and reversible, so that two atoms in their excited state will undergo a downward transition jointly emitting a single cavity photon. This joint absorption and emission process can also occur with three atoms. The parameters used to investigate this process correspond to experimentally demonstrated values in circuit quantum electrodynamics systems.

arXiv:1601.00886•Physical Review Letters•Jul 22, 2016•171 citations

Quantum dynamics of two-photon quantum Rabi model

Zhiguo Lü, Chunjian Zhao, Hang Zheng

Abstract We apply a simple analytical method based on a unitary transformation to calculate the ground state, its excitation spectrum and quantum dynamic evolution of physical quantities for the double-photon quantum Rabi Hamiltonian over the wide coupling-strength range. The concise analytical method possesses the same mathematical simplicity as the approach of the rotating wave approximation (RWA). By quantitative comparison with the numerically exact result obtained by matrix diagonalization, we confirm that our calculated results obtained by transformed rotating-wave method are not only accurate in the weak coupling regime but also correct in intermediate strong-coupling case. In the intermediate ultrastrong-coupling regime, the calculated values of the ground state and lower lying excited states are nearly the same as the exact ones. It turns out that our calculation for the energy spectrum is beyond the ordinary-RWA. Meanwhile, we demonstrate the signatures resulting from the counter-rotating wave terms by monitoring the population, the coherence, the squeezing of the photon under the ultra-strong conditions. In particular, we find that when the frequency of the photon is much larger than the transition frequency of the system, the lineshape of the time evolution becomes complicated with the increase of the coupling strength, which may be verified experimentally.

Journal of Physics A Mathematical and Theoretical•Dec 21, 2016•27 citations
We investigate theoretically the quantum Rabi model in the large-detuning regime. When the frequency of the cavity field is near one-third of the atomic transition frequency, we show that there exists a resonant three-photon coupling via intermediate states connected by counter-rotating processes. We derive an effective Hamiltonian of the three-photon coupling, which determines the magnitude of the energy splitting and the position of the resonance analytically. In addition, we present a scheme of three-photon generation based on adiabatic passage across the resonance.
It is well known that in the quantum Rabi model, a three-photon resonance occurs when the cavity field bare frequency is about 1/3 of the atomic transition frequency. In this manuscript, we show that the resonance can also be generated in the absence of the ``1/3 condition'' by employing an artificial atom with tunable transition frequency. To realize the protocol, the modulation frequency should be comparable to the cavity frequency in order to induce a counter-rotating interaction in the effective Hamiltonian. In this way, three-photon Rabi oscillations can be observed in a small-detuning regime, avoiding the excitation of high-energy states of the atom. We derive an effective Hamiltonian (equivalent to the anisotropic Rabi model Hamiltonian) to determine the magnitude of the energy splitting and the resonance position. Numerical simulation results show that the protocol not only generates a three-photon resonance, but also has a detectable output photon flux. We hope the protocol can be exploited for the realization of Fock-state sources and the generation of multiparticle entanglement.
In this paper, we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system. In the scheme, when the driving bichromatic laser beam is adjusted to the off-resonant j -order red- and blue-sideband, the interaction between the cavity and mechanical oscillator leads to a j -phonon resonance quantum Rabi model. Moreover, we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system. As a typical example, we theoretically analyze the two-phonon resonance quantum Rabi model, and derive an effective Hamiltonian of the six-phonon coupling. Finally, we present a method of six-phonon generation based on adiabatic passage across the resonance. Numerical simulations confirm the validity of the proposed scheme. Theoretically, the proposed scheme can be extended to the realization of 3 j -phonon state.
We consider two separate atoms interacting with a single-mode optical resonator. When the frequency of the resonator field is twice the atomic transition frequency, we show that there exists a resonant coupling between one photon and two atoms, via intermediate virtual states connected by counter-rotating processes. If the resonator is prepared in its one-photon state, the photon can be jointly absorbed by the two atoms in their ground state which will both reach their excited state with probability close to one. Like ordinary quantum Rabi oscillations, this process is coherent and reversible, so that two atoms in their excited state will undergo a downward transition jointly emitting a single cavity photon. This joint absorption and emission processes can also occur with three atoms. The parameters used to investigate this process correspond to experimentally demonstrated values in circuit quantum electrodynamics systems.
The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single-cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasiresonant with the cavity photon energy, and by neglecting the nonresonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one can derive the well-known phenomenology of quasiresonant transitions, including the fluorescence triplets. In this work we consider the most general Rabi model, incorporating the effects of permanent atomic electric dipole moments. Based on a perturbative analysis, we compare the intensities of emission lines induced by rotating terms, counter-rotating terms, and parity-symmetry-breaking terms in order to identify the parameter regimes in which these different contributions play a significant role. The analysis reveals that the emission strength related to the existence of permanent dipoles may surpass the one due to the counter-rotating interaction terms but is usually much weaker than the emission due to the main, resonant coupling. This ratio can be modified in systems with a reduced dimensionality or by engineering the energy spectral density of the continuum.
We consider two separate atoms interacting with a single-mode optical or microwave resonator. When the frequency of the resonator field is twice the atomic transition frequency, we show that there exists a resonant coupling between one photon and two atoms, via intermediate virtual states connected by counterrotating processes. If the resonator is prepared in its one-photon state, the photon can be jointly absorbed by the two atoms in their ground state which will both reach their excited state with a probability close to one. Like ordinary quantum Rabi oscillations, this process is coherent and reversible, so that two atoms in their excited state will undergo a downward transition jointly emitting a single cavity photon. This joint absorption and emission process can also occur with three atoms. The parameters used to investigate this process correspond to experimentally demonstrated values in circuit quantum electrodynamics systems.
Abstract We apply a simple analytical method based on a unitary transformation to calculate the ground state, its excitation spectrum and quantum dynamic evolution of physical quantities for the double-photon quantum Rabi Hamiltonian over the wide coupling-strength range. The concise analytical method possesses the same mathematical simplicity as the approach of the rotating wave approximation (RWA). By quantitative comparison with the numerically exact result obtained by matrix diagonalization, we confirm that our calculated results obtained by transformed rotating-wave method are not only accurate in the weak coupling regime but also correct in intermediate strong-coupling case. In the intermediate ultrastrong-coupling regime, the calculated values of the ground state and lower lying excited states are nearly the same as the exact ones. It turns out that our calculation for the energy spectrum is beyond the ordinary-RWA. Meanwhile, we demonstrate the signatures resulting from the counter-rotating wave terms by monitoring the population, the coherence, the squeezing of the photon under the ultra-strong conditions. In particular, we find that when the frequency of the photon is much larger than the transition frequency of the system, the lineshape of the time evolution becomes complicated with the increase of the coupling strength, which may be verified experimentally.