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:2304.11103 · Physical Review A

Distance-dependent emission spectrum from two qubits in a strong-coupling regime

Rongzhen Hu, JunYan Luo, Yiying Yan

Published Aug 7, 2023• 3 citations
arXivHTMLPDF

Abstract

We study the emission spectrum of two distant qubits strongly coupled to a waveguide by using the numerical and analytical approaches, which are beyond the Markovian approximation and the rotating-wave approximation. The numerical approach combines the Dirac-Frenkel time-dependent variational principle with the multiple Davydov ${D}_{1}$ ansatz. A transformed rotating-wave approximation (TRWA) treatment and a standard perturbation (SP) are used to analytically calculate the emission spectrum. It is found that the variational approach and the TRWA treatment yield accurate emission spectra of the two distant qubits in certain strong-coupling regimes while the SP breaks down. The emission spectrum is found to be asymmetric irrespective of the two-qubit distance and exhibits a single peak, double peaks, and multiple peaks depending on the two-qubit distance as well as the initial states. In sharp contrast with the single-qubit case, the excited-state populations of the two qubits can ultraslowly decay due to the subradiance even in the presence of a strong qubit-waveguide coupling, which in turn yields an ultranarrow emission line. Our results provide insights into the emission spectral features of the two distant qubits in the strong light-matter coupling regime.

DOI
10.1103/physreva.108.023706

Related papers

Spontaneous emission spectrum from a V-type artificial atom in a strong-coupling regime: Dark lines and line narrowing

Yiying Yan

We employ a time-dependent variational approach with the multiple Davydov ${D}_{2}$ ansatz and two approximate analytical methods to study the spontaneous emission of a V-type artificial atom in the strong-coupling regime, where the decay rate of the emitter becomes a considerable fraction of its transition frequencies, and focus on quantum-interference-induced effects. The variational approach is found to be accurate in certain strong-coupling regimes and is used as the benchmark to address the validity of the analytical methods: the rotating-wave approximation (RWA) and the transformed RWA (TRWA). It is found that the TRWA is fairly accurate in the strong-coupling regime where the RWA breaks down. By using the numerical and analytical methods, we illustrate that there are dark lines and line narrowing in the emission spectra in the strong-coupling regime and in a wide accessible range of the emitter parameters. We also illustrate how the emission spectrum is altered by the counter-rotating couplings. The present results offer insights into the experimental observation of the quantum-interference-induced effect in the strong-coupling regime and in the context of artificial atoms.

Physical Review A•Oct 16, 2023•6 citations

Emission spectral non-Markovianity in qubit–cavity systems in the ultrastrong coupling regime

Chenyi Zhang, Minghong Yu, Yiying Yan +3 more

We study the emission spectra of the dissipative Rabi and Jaynes-Cummings models in the non-Markovian and ultrastrong coupling regimes. We have derived a polaron-transformed Nakajima-Zwanzig master equation (PTNZE) to calculate the emission spectra, which eliminates the well-known limitations of the Markovian approximation and the standard second-order perturbation. Using the time-dependent variational approach with the multiple Davydov ansatz as a benchmark, the PTNZE is found to yield accurate emission spectra in certain ultrastrong coupling regimes where the standard second-order Nakajima-Zwanzig master equation breaks down. It is shown that the emission spectra of the dissipative Rabi and Jaynes-Cummings models are, in general, asymmetric under various initial conditions. Direct comparisons of spectra for the two models illustrate the essential role of the qubit-cavity counter-rotating term and the spectral features under different qubit-cavity coupling strengths and system initial conditions.

arXiv:2304.02675•The Journal of Chemical Physics•Nov 10, 2022•6 citations

Variational approach to time-dependent fluorescence of a driven qubit

Yiying Yan, Lipeng Chen, JunYan Luo +1 more

We employ the Dirac-Frenkel variational principle and the multiple Davydov ansatz to study time-dependent fluorescence spectra of a driven qubit in the weak to strong qubit-reservoir coupling regimes, where both the Rabi frequency and the spontaneous decay rate are comparable to the transition frequency of the qubit. Our method agrees well with the time-local master-equation approach in the weak coupling regime, and offers a flexible way to compute the spectra from the bosonic dynamics instead of two-time correlation functions. While the perturbative master equation breaks down in the strong coupling regime, our method actually becomes more accurate due to the use of bosonic coherent states under certain conditions. We show that the counter-rotating coupling between the qubit and the reservoir has considerable contributions to the photon number dynamics and the spectra under strong driving conditions even when the coupling is moderately weak. The time-dependent spectra are found to be generally asymmetric, a feature that is derived from photon number dynamics. In addition, it is shown that the spectral profiles can be dramatically different from the Mollow triplet due to strong dissipation and/or multiphoton processes associated with the strong driving. Our formalism provides a unique perspective to interpret time-dependent spectra.

arXiv:2008.09726•Physical Review A•Aug 21, 2020•15 citations

Variational quantum dynamics of single-photon scattering in the strong-coupling regime

Yiying Yan, JingGui Tang, Yuguo Su +2 more

Single-photon scattering in waveguide-QED systems plays a pivotal role in quantum information processing and communication. We introduce a time-dependent variational approach employing a modified multiple Davydov Ansatz to simulate single-photon dynamics in one-dimensional waveguide-QED systems within the strong-coupling regime. The method is benchmarked across three configurations: a single qubit, two distant qubits, and a ladder-type qutrit coupled to the waveguide. For the single- and two-qubit cases, the variational results exhibit excellent agreement with those derived from a transformed rotating-wave approximation (TRWA). The accuracy of our approach is further verified by an analysis of the local-in-time error, which remains small even under strong coupling, indicating its potential superiority over TRWA in specific regimes. In addition, by contrasting our results with the rotating-wave approximation, we elucidate the significant influence of counter-rotating couplings on scattering dynamics. Our findings establish this variational method as a reliable and versatile tool for investigating single-photon scattering in diverse waveguide-QED systems, particularly in regimes where traditional approximations falter.

Physical Review A•Nov 25, 2025•0 citations

Distant emitters in ultrastrong waveguide QED: Ground-state properties and non-Markovian dynamics

Carlos A. González-Gutiérrez, Juan Román-Roche, David Zueco

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ans\"atze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.

arXiv:2106.02949•Physical Review A•Nov 1, 2021•27 citations

Distant emitters in ultrastrong waveguide-QED: ground sate properties and non-Markovian dynamics

Carlos A. González-Gutiérrez, Juan Román-Roche, David Zueco

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation (RWA). Employing static and dynamical polaron ansatze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground state magnetization, and entanglement entropy of the two qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting new dynamical effects arising in ultrastrong waveguide-QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also on the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.

•Jun 5, 2021•0 citations
We study the emission spectrum of two distant qubits strongly coupled to a waveguide by using the numerical and analytical approaches, which are beyond the Markovian approximation and the rotating-wave approximation. The numerical approach combines the Dirac-Frenkel time-dependent variational principle with the multiple Davydov D1{D}_{1}D1​ ansatz. A transformed rotating-wave approximation (TRWA) treatment and a standard perturbation (SP) are used to analytically calculate the emission spectrum. It is found that the variational approach and the TRWA treatment yield accurate emission spectra of the two distant qubits in certain strong-coupling regimes while the SP breaks down. The emission spectrum is found to be asymmetric irrespective of the two-qubit distance and exhibits a single peak, double peaks, and multiple peaks depending on the two-qubit distance as well as the initial states. In sharp contrast with the single-qubit case, the excited-state populations of the two qubits can ultraslowly decay due to the subradiance even in the presence of a strong qubit-waveguide coupling, which in turn yields an ultranarrow emission line. Our results provide insights into the emission spectral features of the two distant qubits in the strong light-matter coupling regime.
We employ a time-dependent variational approach with the multiple Davydov D2{D}_{2}D2​ ansatz and two approximate analytical methods to study the spontaneous emission of a V-type artificial atom in the strong-coupling regime, where the decay rate of the emitter becomes a considerable fraction of its transition frequencies, and focus on quantum-interference-induced effects. The variational approach is found to be accurate in certain strong-coupling regimes and is used as the benchmark to address the validity of the analytical methods: the rotating-wave approximation (RWA) and the transformed RWA (TRWA). It is found that the TRWA is fairly accurate in the strong-coupling regime where the RWA breaks down. By using the numerical and analytical methods, we illustrate that there are dark lines and line narrowing in the emission spectra in the strong-coupling regime and in a wide accessible range of the emitter parameters. We also illustrate how the emission spectrum is altered by the counter-rotating couplings. The present results offer insights into the experimental observation of the quantum-interference-induced effect in the strong-coupling regime and in the context of artificial atoms.
We study the emission spectra of the dissipative Rabi and Jaynes-Cummings models in the non-Markovian and ultrastrong coupling regimes. We have derived a polaron-transformed Nakajima-Zwanzig master equation (PTNZE) to calculate the emission spectra, which eliminates the well-known limitations of the Markovian approximation and the standard second-order perturbation. Using the time-dependent variational approach with the multiple Davydov ansatz as a benchmark, the PTNZE is found to yield accurate emission spectra in certain ultrastrong coupling regimes where the standard second-order Nakajima-Zwanzig master equation breaks down. It is shown that the emission spectra of the dissipative Rabi and Jaynes-Cummings models are, in general, asymmetric under various initial conditions. Direct comparisons of spectra for the two models illustrate the essential role of the qubit-cavity counter-rotating term and the spectral features under different qubit-cavity coupling strengths and system initial conditions.
We employ the Dirac-Frenkel variational principle and the multiple Davydov ansatz to study time-dependent fluorescence spectra of a driven qubit in the weak to strong qubit-reservoir coupling regimes, where both the Rabi frequency and the spontaneous decay rate are comparable to the transition frequency of the qubit. Our method agrees well with the time-local master-equation approach in the weak coupling regime, and offers a flexible way to compute the spectra from the bosonic dynamics instead of two-time correlation functions. While the perturbative master equation breaks down in the strong coupling regime, our method actually becomes more accurate due to the use of bosonic coherent states under certain conditions. We show that the counter-rotating coupling between the qubit and the reservoir has considerable contributions to the photon number dynamics and the spectra under strong driving conditions even when the coupling is moderately weak. The time-dependent spectra are found to be generally asymmetric, a feature that is derived from photon number dynamics. In addition, it is shown that the spectral profiles can be dramatically different from the Mollow triplet due to strong dissipation and/or multiphoton processes associated with the strong driving. Our formalism provides a unique perspective to interpret time-dependent spectra.
Single-photon scattering in waveguide-QED systems plays a pivotal role in quantum information processing and communication. We introduce a time-dependent variational approach employing a modified multiple Davydov Ansatz to simulate single-photon dynamics in one-dimensional waveguide-QED systems within the strong-coupling regime. The method is benchmarked across three configurations: a single qubit, two distant qubits, and a ladder-type qutrit coupled to the waveguide. For the single- and two-qubit cases, the variational results exhibit excellent agreement with those derived from a transformed rotating-wave approximation (TRWA). The accuracy of our approach is further verified by an analysis of the local-in-time error, which remains small even under strong coupling, indicating its potential superiority over TRWA in specific regimes. In addition, by contrasting our results with the rotating-wave approximation, we elucidate the significant influence of counter-rotating couplings on scattering dynamics. Our findings establish this variational method as a reliable and versatile tool for investigating single-photon scattering in diverse waveguide-QED systems, particularly in regimes where traditional approximations falter.
Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ans\"atze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.
Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation (RWA). Employing static and dynamical polaron ansatze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground state magnetization, and entanglement entropy of the two qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting new dynamical effects arising in ultrastrong waveguide-QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also on the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.