Variational approach to time-dependent fluorescence of a driven qubit

Yan, Yiying; Chen, Lipeng; Luo, Jun; Zhao, Yue

doi:10.1103/physreva.102.023714

Cited by 12 publications

(15 citation statements)

References 47 publications

(82 reference statements)

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“…In the subsequent sections, we will use j D M 1,2 i to refer to the multiple Davydov Ansätze j Ψ M D 1,2 i. In Figure 1, occupying the top row are the two time-dependent, multiple Davydov Ansätze, namely, the multi-D 1 Ansatz and the multi-D 2 Ansatz, which have been successfully applied to a number of many-body quantum systems, [105][106][107] yielding numerically exact solutions.…”

Section: Multiple Davydov Trial Statesmentioning

confidence: 99%

“…In Figure 7, we display the photon number distribution versus emission frequency and time, which clearly reveals the formation of emission peaks. 107…”

Section: The Driven Sbmmentioning

confidence: 99%

“…The corresponding version for the multi‐

D_{2}

Ansatz is written as 27,104

∣ Ψ_{{normalD}_{2}}^{M} ((), t) true〉 goodbreak= \sum_{m} ∣ m true〉 \sum_{k = 1}^{M} A_{mk} ((), t) e^{(\sum_{l} f_{italickl} (t) b_{l}^{†} - H . c .)} ∣ 0 true〉_{ph} .

In the subsequent sections, we will use

∣ D_{1, 2}^{M} true〉

to refer to the multiple Davydov Ansätze

∣ Ψ_{{normalD}_{1, 2}}^{M} true〉

. In Figure 1, occupying the top row are the two time‐dependent, multiple Davydov Ansätze, namely, the multi‐D 1 Ansatz and the multi‐D 2 Ansatz, which have been successfully applied to a number of many‐body quantum systems, 105–107 yielding numerically exact solutions.…”

Section: Brief History Of Davydov Ansätzementioning

confidence: 99%

“…The multi‐

D_{1}

approach can also be applied to the driven SBM problem 107 :

H ((), t) goodbreak= H_{S} ((), t) goodbreak+ H_{R} goodbreak+ H_{SR},

where

H_{S} ((), t)

describes the driven qubit:

H_{S} ((), t) goodbreak= \frac{1}{2} ω_{0} σ_{z} goodbreak+ normalΩ \cos ((), ω_{x} t) σ_{x},

Here

ω_{0}

is the transition frequency between the two levels of the qubit and

σ_{z, x}

are the Pauli matrices.

normalΩ

is the Rabi frequency and

ω_{x}

is the driving frequency.…”

Section: Applications Of Davydov's Ansätzementioning

confidence: 99%

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The hierarchy of Davydov's Ansätze and its applications

Zhao

Sun

Chen

et al. 2021

WIREs Comput Mol Sci

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This review provides a bird's eye view over the development of the hierarchy of Davydov's Ansätze and its applications in a variety of problems in computational physical chemistry. Davydov's original solitons appeared in the 1970s as a candidate for vibrational energy carriers in proteins, thanks to their association with the Fröhlich Hamiltonian and the Holstein molecular crystal model.Momentum-space projection of those solitary waves emerged to be great approximations to the ground-state wave functions of the extended Holstein Hamiltonian, lending unambiguous evidence to the absence of formal quantum phase transitions in those systems. The multiple Davydov Ansätze are introduced, with increasing multiplicity, as incremental improvements of their corresponding single-Ansatz parents. The time-dependent variational formalism of Davydov's Ansätze is discussed in great detail, and the relative deviation of the Ansätze is constructed to quantify how faithfully they follow the Schrödinger equation, a quantity that is shown to vanish in the limit of large multiplicities. Three approaches to finite-temperature variational dynamics of Davydov's Ansätze are demonstrated, namely, the Monte Carlo importance sampling, the method of thermo-field dynamics, and the method of displaced number states. Applications of Davydov's Ansätze are given to variants of the spin-boson model, the Landau-Zener transition, the Holstein Hamiltonian, energy transfer in light-harvesting, and singlet fission in organic photovoltaics.As an example, simulation of multidimensional spectroscopic signals via Davydov's Ansätze is fully implemented for the finite-temperature fission process in crystalline rubrene.

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Section: Multiple Davydov Trial Statesmentioning

confidence: 99%

“…In Figure 7, we display the photon number distribution versus emission frequency and time, which clearly reveals the formation of emission peaks. 107…”

Section: The Driven Sbmmentioning

confidence: 99%

“…The corresponding version for the multi‐

D_{2}

Ansatz is written as 27,104

∣ Ψ_{{normalD}_{2}}^{M} ((), t) true〉 goodbreak= \sum_{m} ∣ m true〉 \sum_{k = 1}^{M} A_{mk} ((), t) e^{(\sum_{l} f_{italickl} (t) b_{l}^{†} - H . c .)} ∣ 0 true〉_{ph} .

In the subsequent sections, we will use

∣ D_{1, 2}^{M} true〉

to refer to the multiple Davydov Ansätze

∣ Ψ_{{normalD}_{1, 2}}^{M} true〉

Section: Brief History Of Davydov Ansätzementioning

confidence: 99%

“…The multi‐

D_{1}

approach can also be applied to the driven SBM problem 107 :

H ((), t) goodbreak= H_{S} ((), t) goodbreak+ H_{R} goodbreak+ H_{SR},

where

H_{S} ((), t)

describes the driven qubit:

H_{S} ((), t) goodbreak= \frac{1}{2} ω_{0} σ_{z} goodbreak+ normalΩ \cos ((), ω_{x} t) σ_{x},

Here

ω_{0}

is the transition frequency between the two levels of the qubit and

σ_{z, x}

are the Pauli matrices.

normalΩ

is the Rabi frequency and

ω_{x}

is the driving frequency.…”

Section: Applications Of Davydov's Ansätzementioning

confidence: 99%

See 2 more Smart Citations

The hierarchy of Davydov's Ansätze and its applications

Zhao

Sun

Chen

et al. 2021

WIREs Comput Mol Sci

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is fully described by the time-dependent complex displacements, λ mq (t). The time dependent Dirac-Frenkel variational method allows to obtain equations of motion for parameters α n , λ mq [3,6,53,54] dα…”

Section: Fluctuating Exciton Modelmentioning

confidence: 99%

Temperature Controlled Open Quantum System Dynamics using Time-dependent Variational Method

Jakučionis,

Abramavičius

2021

Preprint

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Effects of Counter‐Rotating Couplings on the Dynamics of a Λ System: Long‐Lived Coherence Oscillations

Xiang,

Lü,

Yan

2023

Adv Quantum Tech

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The time evolution of the ground‐state population and coherence of a Λ‐type three‐level emitter strongly coupled to a radiation reservoir is studied by using a transformed rotating‐wave approximation (TRWA) and time‐dependent variational approach with the multiple Davydov ansatz. The study aims at illustrating the role of counter‐rotating couplings in the long‐time evolution of the Λ system. The TRWA and variational approach are found to be consistent with each other and predict that there exist long‐lived oscillatory behaviors of ground‐state populations and coherence, which are robust in the presence of strong dissipation and arise from the counter‐rotating‐coupling‐induced virtual photon processes. The oscillation amplitude and frequency depend on the system‐reservoir coupling strength and the frequency difference between the two ground states, which can be qualitatively and quantitatively captured by the TRWA analytical results. Present results offer insights into the impact of the counter‐rotating couplings on the long‐time evolution of the strongly dissipative multilevel system as well as the protocol of generation of coherent oscillations by relaxation in a strong‐coupling regime.

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Variational approach to time-dependent fluorescence of a driven qubit

Cited by 12 publications

References 47 publications

The hierarchy of Davydov's Ansätze and its applications

The hierarchy of Davydov's Ansätze and its applications

Temperature Controlled Open Quantum System Dynamics using Time-dependent Variational Method

Effects of Counter‐Rotating Couplings on the Dynamics of a Λ System: Long‐Lived Coherence Oscillations

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