Dynamics of the two-spin spin-boson model with a common bath

Deng, Tianrui; Yan, Yiying; Chen, Lipeng; Zhao, Yue

doi:10.1063/1.4945390

Cited by 32 publications

(34 citation statements)

References 40 publications

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“…where P αn ¼ jx αn ihx αn j are projection operators on the eigenstates jx αn i of X α for α ¼ 1, 2. We note that for two coupled systems interacting with a common reservoir [65][66][67], the same expression (9) will follow. Beyond the one-dimensional baths considered here, determining the MFG state for three-dimensional systems, such as a single spin coupled simultaneously to baths in three dimensions [38], require multibath extensions of (3).…”

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confidence: 93%

Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

Cresser

Anders

2021

Phys. Rev. Lett.

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The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature T. However, non-negligible interactions between system and environment can give rise to an altered state. Here, we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reservoir. First, we derive the state in the weak coupling limit and find that, in general, it maintains coherences with respect to the bare system Hamiltonian. Second, we develop a new expansion method suited to investigate the ultrastrong coupling regime. This allows us to derive the explicit form for the mean force Gibbs state, and we find that it becomes diagonal in the basis set by the systemreservoir interaction instead of the system Hamiltonian. Several examples are discussed including a single qubit, a three-level V-system, and two coupled qubits all interacting with bosonic reservoirs. The results shed light on the presence of coherences in the strong coupling regime, and provide key tools for nanoscale thermodynamics investigations.

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confidence: 93%

Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

Cresser

Anders

2021

Phys. Rev. Lett.

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“…On the other hand, such an environmental interaction features also the capability to induce entanglement [5][6][7][8], which can even last for arbitrary long times [9][10][11]. The investigation of these competing environmental effects [11][12][13][14][15][16][17][18][19][20][21][22] adds to the understanding of entanglement and decoherence in the context of open quantum systems which is not only of importance from a fundamental point of view but is also most relevant for fields like quantum computation, communication and metrology.…”

Section: Introductionmentioning

confidence: 99%

Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Hartmann

Strunz

2020

Quantum

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Considering two non-interacting qubits in the context of open quantum systems, it is well known that their common environment may act as an entangling agent. In a perturbative regime the influence of the environment on the system dynamics can effectively be described by a unitary and a dissipative contribution. For the two-spin Boson model with (sub-) Ohmic spectral density considered here, the particular unitary contribution (Lamb shift) easily explains the buildup of entanglement between the two qubits. Furthermore it has been argued that in the adiabatic limit, adding the so-called counterterm to the microscopic model compensates the unitary influence of the environment and, thus, inhibits the generation of entanglement. Investigating this assertion is one of the main objectives of the work presented here. Using the hierarchy of pure states (HOPS) method to numerically calculate the exact reduced dynamics, we find and explain that the degree of inhibition crucially depends on the parameter s determining the low frequency power law behavior of the spectral density J(ω)∼ωse−ω/ωc. Remarkably, we find that for resonant qubits, even in the adiabatic regime (arbitrarily large ωc), the entanglement dynamics is still influenced by an environmentally induced Hamiltonian interaction. Further, we study the model in detail and present the exact entanglement dynamics for a wide range of coupling strengths, distinguish between resonant and detuned qubits, as well as Ohmic and deep sub-Ohmic environments. Notably, we find that in all cases the asymptotic entanglement does not vanish and conjecture a linear relation between the coupling strength and the asymptotic entanglement measured by means of concurrence. Further we discuss the suitability of various perturbative master equations for obtaining approximate entanglement dynamics.

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“…The Bell inequality was tested using a system of two uncoupled qubits interacting with a radiation field in an optical cavity [ 46 ]. Although systems of interacting atoms have been considered as well, but they were only at resonance with the field to avoid the mathematical difficulty caused by the off-resonance condition [ 47 , 48 , 49 , 50 ]. Particularly, ESD was studied in a system of two coupled identical atoms interacting at resonance with a double mode radiation field, where the effects of the coupling as well as the initial state of the system on the system dynamics were investigated [ 51 ].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole–Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning

Sadiek

Al-Dress

Shaglel

et al. 2021

Entropy

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We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole--dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole--dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.

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Dynamics of the two-spin spin-boson model with a common bath

Cited by 32 publications

References 40 publications

Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole–Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning

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