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:1703.10775 · Scientific Reports

Dark state with counter-rotating dissipative channels

Zheng-Yang Zhou, Mi Chen, Lian-Ao Wu, Ting Yu, J. Q. You

Published Jul 18, 2017• 7 citations
arXivHTMLPDF

Abstract

Dark state as a consequence of interference between different quantum states has great importance in the fields of chip-scale atomic clock and quantum information. For the Λ-type three-level system, this dark state is generally regarded as being dissipation-free because it is a superposition of two lowest states without dipole transition between them. However, previous studies are based on the rotating-wave approximation (RWA) by neglecting the counter-rotating terms in the system-environment interaction. In this work, we study non-Markovian quantum dynamics of the dark state in a Λ-type three-level system coupled to two bosonic baths and reveal the effect of counter-rotating terms on the dark state. In contrast to the dark state within the RWA, leakage of the dark state occurs even at zero temperature, as a result of these counter-rotating terms. Also, we present a method to restore the quantum coherence of the dark state by applying a leakage elimination operator to the system.

DOI
10.1038/s41598-017-06157-4

Related papers

Quantum interferometric power and non-Markovianity in the decoherence channels

Shao-Jie Xiong, Zhe Sun, Xiaoguang Wang

In quantum open systems, non-Markovianity is an important phenomenon that allows a backflow of information from the environment to the system. In this work, we investigate the non-Markovianity problems in two different types of channels, where the system–environment interactions are treated with and without the rotating-wave approximation (RWA). We employ the quantum interferometric power (QIP) to quantify the non-Markovian dynamics, which is the minimal quantum Fisher information obtained by the local unitary evolution in a bipartite system. By the hierarchy equation method, we calculate the dynamical evolution of the QIP in the non-RWA case. The results show that the dynamical behavior under the non-RWA is significantly different from that under the RWA in both weak and strong coupling. Moreover, in the non-RWA case, we also find the nonmonotonic behavior of the non-Markovianity measure with the variation of coupling strength, which is caused by the competition between the rotating-wave terms and the counterrotating-wave terms. As a result, we highlight the importance of the counterrotating-wave terms for the influence of non-Markovianity.

Chinese Physics B•Apr 7, 2023•5 citations

Discussions of ground state in Lambda-type three-level system

Xiaohong Li Xiaohong Li, Tao Liu Tao Liu, Kelin Wang Kelin Wang

The effects of counter-rotating terms on ground states (GS) of a lambda-type three-level atomic system coupled with two fields are examined. The GS, which are dark states in rotating wave approximation (RWA), can be expressed by a simple formula including the excited states. When the coupling strength is less than 0.2 of the maximum energy splitting in the atomic system, the component coefficients of excited states in the GS can be described by the formula similar as that in a two-level system and have linear relationship with their coupling constant. Further increasing the coupling strength will increase the excited components in the GS more rapidly, very different from the two-level system. OCIS codes: 270.1670. doi: 10.3788/COL201210.S12701.

Chinese Optics Letters•Jan 1, 2012•1 citation

Q.e.d. beyond rotating wave approximation

Andreas Kurcz

This thesis studies counter-rotating terms part of an Hamiltonian usually neglected in the so-called Rotating Wave Approximation. Generalising the usual description of light-matter interactions and open quantum systems it is demonstrated that normally neglected counter-rotating terms have the potential to allocate energy among different system degrees of freedom. It is pointed out in examples that this aspect can affect the energy concentration in quantum systems. Initially, a composite quantum system is considered, i.e. bipartite systems like atom-cavity systems and coupled optical resonators without decay. By resorting to methods from quantum field theory it is shown that for such bosonic systems, the Rotating Wave Approximation cannot be applied far off resonance. In fact, the counter-rotating terms are related to an entropy operator that is capable of generating an irreversible time evolution. The vacuum state of the system is shown to evolve into a generalised coherent state exhibiting entanglement of the modes in which the counter-rotating terms are expressed. Furthermore, it is demonstrated that a non-trivial behaviour of the photon emission rate of such composite quantum system can occur when the counter-rotating terms are not dropped. In such a system, there is a coupling to infinitely many modes with most of them being far off resonance. An energy concentrating mechanism is discussed which cannot be described by the Rotating Wave Approximation. Its result is the continuous leakage of photons from open quantum system, even in the absence of external driving. Finally, a model is proposed to explain the origin of the sudden energy concentration in the intriguing phenomenon of sonoluminescence. The model is based on the quantum dynamics of trapped particles and assumes the presence of a weak but highly inhomogeneous electric field. It is shown that the counter-rotating terms can significantly contribute to the energy focussing mechanism in terms of quantum coherences.

•Sep 1, 2010•0 citations

Interference between driving and dissipation in the spin-boson model: Effect of counter-rotating terms

Chunjian Zhao, Hang Zheng

The quantum dynamics of the dissipative two-level system in the Ohmic bath with Rabi driving is studied by means of a modified Bloch-Redfield approach based on a unitary transformation. The main purpose is to understand the effect of counter-rotating terms of the system-environment interaction on the dynamics of the two-level system and, in particular, if it is possible to control the effective system-environment coupling by their effect on the interference between driving and dissipation. By calculating the nonequilibrium correlation $P(t)$ for a finite driving it is shown that the counter-rotating terms of the system-environment interaction play an important role in the dynamic evolution with a longer coherent time and a weaker amplitude of the long-time driven oscillation.

Physical Review A•Oct 29, 2010•15 citations

Non-Markovianity in experimentally simulated quantum channels: Role of counterrotating-wave terms

Shao-Jie Xiong, Qiwu Hu, Zhe Sun +4 more

We experimentally investigate the non-Markovianity problems in a quantum channel implemented by an all-optical setup. The quantum channel simulates the dynamics of a two-level (qubit) system surrounded by bosonic modes, with the system-environment interaction treated without applying the rotating-wave approximation (RWA). Therefore, it allows us to demonstrate the important role of counterrotating-wave terms in influencing the memory effects of the environment. The experimental and theoretical results are in good agreement and show quite different behaviors of the non-Markovianity measure between RWA and non-RWA channels. One can find the nonmonotonic dependence of the non-Markovianity measure on the coupling and detuning parameters in the non-RWA case, which is attributed to the competing mechanisms caused by the counterrotating-wave terms. We emphasize that the non-RWA channel provides a more clear description of the open-system dynamics and the counterrotating-wave terms are indispensable in the study of non-Markovianity.

Physical Review A•Sep 3, 2019•11 citations

Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems

Wei Wu, Maoxin Liu

We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic or a fermionic environment with a detuned Lorentz spectrum at zero temperature is analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity whether the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.

arXiv:1706.09576•Physical Review A•Sep 29, 2017•18 citations
Dark state as a consequence of interference between different quantum states has great importance in the fields of chip-scale atomic clock and quantum information. For the Λ-type three-level system, this dark state is generally regarded as being dissipation-free because it is a superposition of two lowest states without dipole transition between them. However, previous studies are based on the rotating-wave approximation (RWA) by neglecting the counter-rotating terms in the system-environment interaction. In this work, we study non-Markovian quantum dynamics of the dark state in a Λ-type three-level system coupled to two bosonic baths and reveal the effect of counter-rotating terms on the dark state. In contrast to the dark state within the RWA, leakage of the dark state occurs even at zero temperature, as a result of these counter-rotating terms. Also, we present a method to restore the quantum coherence of the dark state by applying a leakage elimination operator to the system.
In quantum open systems, non-Markovianity is an important phenomenon that allows a backflow of information from the environment to the system. In this work, we investigate the non-Markovianity problems in two different types of channels, where the system–environment interactions are treated with and without the rotating-wave approximation (RWA). We employ the quantum interferometric power (QIP) to quantify the non-Markovian dynamics, which is the minimal quantum Fisher information obtained by the local unitary evolution in a bipartite system. By the hierarchy equation method, we calculate the dynamical evolution of the QIP in the non-RWA case. The results show that the dynamical behavior under the non-RWA is significantly different from that under the RWA in both weak and strong coupling. Moreover, in the non-RWA case, we also find the nonmonotonic behavior of the non-Markovianity measure with the variation of coupling strength, which is caused by the competition between the rotating-wave terms and the counterrotating-wave terms. As a result, we highlight the importance of the counterrotating-wave terms for the influence of non-Markovianity.
The effects of counter-rotating terms on ground states (GS) of a lambda-type three-level atomic system coupled with two fields are examined. The GS, which are dark states in rotating wave approximation (RWA), can be expressed by a simple formula including the excited states. When the coupling strength is less than 0.2 of the maximum energy splitting in the atomic system, the component coefficients of excited states in the GS can be described by the formula similar as that in a two-level system and have linear relationship with their coupling constant. Further increasing the coupling strength will increase the excited components in the GS more rapidly, very different from the two-level system. OCIS codes: 270.1670. doi: 10.3788/COL201210.S12701.
This thesis studies counter-rotating terms part of an Hamiltonian usually neglected in the so-called Rotating Wave Approximation. Generalising the usual description of light-matter interactions and open quantum systems it is demonstrated that normally neglected counter-rotating terms have the potential to allocate energy among different system degrees of freedom. It is pointed out in examples that this aspect can affect the energy concentration in quantum systems. Initially, a composite quantum system is considered, i.e. bipartite systems like atom-cavity systems and coupled optical resonators without decay. By resorting to methods from quantum field theory it is shown that for such bosonic systems, the Rotating Wave Approximation cannot be applied far off resonance. In fact, the counter-rotating terms are related to an entropy operator that is capable of generating an irreversible time evolution. The vacuum state of the system is shown to evolve into a generalised coherent state exhibiting entanglement of the modes in which the counter-rotating terms are expressed. Furthermore, it is demonstrated that a non-trivial behaviour of the photon emission rate of such composite quantum system can occur when the counter-rotating terms are not dropped. In such a system, there is a coupling to infinitely many modes with most of them being far off resonance. An energy concentrating mechanism is discussed which cannot be described by the Rotating Wave Approximation. Its result is the continuous leakage of photons from open quantum system, even in the absence of external driving. Finally, a model is proposed to explain the origin of the sudden energy concentration in the intriguing phenomenon of sonoluminescence. The model is based on the quantum dynamics of trapped particles and assumes the presence of a weak but highly inhomogeneous electric field. It is shown that the counter-rotating terms can significantly contribute to the energy focussing mechanism in terms of quantum coherences.
The quantum dynamics of the dissipative two-level system in the Ohmic bath with Rabi driving is studied by means of a modified Bloch-Redfield approach based on a unitary transformation. The main purpose is to understand the effect of counter-rotating terms of the system-environment interaction on the dynamics of the two-level system and, in particular, if it is possible to control the effective system-environment coupling by their effect on the interference between driving and dissipation. By calculating the nonequilibrium correlation P(t)P(t)P(t) for a finite driving it is shown that the counter-rotating terms of the system-environment interaction play an important role in the dynamic evolution with a longer coherent time and a weaker amplitude of the long-time driven oscillation.
We experimentally investigate the non-Markovianity problems in a quantum channel implemented by an all-optical setup. The quantum channel simulates the dynamics of a two-level (qubit) system surrounded by bosonic modes, with the system-environment interaction treated without applying the rotating-wave approximation (RWA). Therefore, it allows us to demonstrate the important role of counterrotating-wave terms in influencing the memory effects of the environment. The experimental and theoretical results are in good agreement and show quite different behaviors of the non-Markovianity measure between RWA and non-RWA channels. One can find the nonmonotonic dependence of the non-Markovianity measure on the coupling and detuning parameters in the non-RWA case, which is attributed to the competing mechanisms caused by the counterrotating-wave terms. We emphasize that the non-RWA channel provides a more clear description of the open-system dynamics and the counterrotating-wave terms are indispensable in the study of non-Markovianity.
We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic or a fermionic environment with a detuned Lorentz spectrum at zero temperature is analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity whether the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.