We present a general treatment of a bosonic dissipative network: a chain of coupled dissipative harmonic oscillators whatever its topology---i.e., whichever the way the oscillators are coupled together, the strength of their couplings, and their natural frequencies. Starting with a general more realistic scenario where each oscillator is coupled to its own reservoir, we also discuss the case where all the network oscillators are coupled to a common reservoir. We obtain the master equation governing the dynamic of the network states and the associated evolution equation of the Glauber-Sudarshan $P$ function. With these instruments we briefly show how to analyze the decoherence and the evolution of the linear entropy of general states of the network. We also show how to obtain the master equation for the case of distinct reservoirs from that of a common one.We present a general treatment of a bosonic dissipative network: a chain of coupled dissipative harmonic oscillators whatever its topology---i.e., whichever the way the oscillators are coupled together, the strength of their couplings, and their natural frequencies. Starting with a general more realistic scenario where each oscillator is coupled to its own reservoir, we also discuss the case where all the network oscillators are coupled to a common reservoir. We obtain the master equation governing the dynamic of the network states and the associated evolution equation of the Glauber-Sudarshan $P$ function. With these instruments we briefly show how to analyze the decoherence and the evolution of the linear entropy of general states of the network. We also show how to obtain the master equation for the case of distinct reservoirs from that of a common one.

Physical Review ASep 4, 200726 citations

Quantum Oscillators: General Considerations

Elsevier eBooksJan 1, 19950 citations

Master equation for the quantum Rabi model in the adiabatic regime

Luis Octavio Castaños-Cervantes

A qubit--harmonic-oscillator open system coupled to thermal baths was considered and the master equation describing the evolution of the open system was deduced when the qubit transition frequency is $\ensuremath{\lesssim}0.1$ the oscillator frequency. The master equation is valid in all the qubit-oscillator state space and holds for all values of the qubit-oscillator coupling including the ultrastrong and deep strong coupling regimes. It only requires an oscillator frequency much larger than the relaxation rates. The qubit-oscillator coupling can enhance or decrease both the relaxation rates and the frequency shifts induced by the thermal baths. It was found that weak, sinusoidal qubit driving forces the qubit-oscillator open system to behave like a driven qubit whose evolution is governed by equations similar to those of the Bloch vector in the optical Bloch equations and whose transition frequency decreases with increasing qubit-oscillator coupling strength. Finally, it was shown how one can reach the adiabatic regime by using sinusoidal qubit driving with large driving frequency and the concepts of $\ensuremath{\pi}$ and $\ensuremath{\pi}/2$ pulses were generalized to manipulate transitions between dressed states.A qubit--harmonic-oscillator open system coupled to thermal baths was considered and the master equation describing the evolution of the open system was deduced when the qubit transition frequency is $\ensuremath{\lesssim}0.1$ the oscillator frequency. The master equation is valid in all the qubit-oscillator state space and holds for all values of the qubit-oscillator coupling including the ultrastrong and deep strong coupling regimes. It only requires an oscillator frequency much larger than the relaxation rates. The qubit-oscillator coupling can enhance or decrease both the relaxation rates and the frequency shifts induced by the thermal baths. It was found that weak, sinusoidal qubit driving forces the qubit-oscillator open system to behave like a driven qubit whose evolution is governed by equations similar to those of the Bloch vector in the optical Bloch equations and whose transition frequency decreases with increasing qubit-oscillator coupling strength. Finally, it was shown how one can reach the adiabatic regime by using sinusoidal qubit driving with large driving frequency and the concepts of $\ensuremath{\pi}$ and $\ensuremath{\pi}/2$ pulses were generalized to manipulate transitions between dressed states.

Physical Review AMar 2, 20222 citations

Quantum statistics of reservoir coupled driven oscillators

J. C. Webber

Physics Letters ADec 1, 19681 citation

Master Equation for an Oscillator Coupled to the Electromagnetic Field

G. W. Ford, John T. Lewis, Robert F. O’Connell

Annals of PhysicsDec 1, 199633 citations

Temperature effects on a network of dissipative quantum harmonic oscillators: collective damping and dispersion processes

M. A. de Ponte, Salomon Sylvain Mizrahi, M. H. Y. Moussa

In this article we extend the results presented in Ref. [Phys. Rev. A 76, 032101 (2007)] to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whichever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. We also present a technique to estimate the decoherence time of network states by computing separately the effects of diffusion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the diffusion mechanism is also presented through the evolution of the Wigner function. The interesting collective diffusion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.In this article we extend the results presented in Ref. [Phys. Rev. A 76, 032101 (2007)] to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whichever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. We also present a technique to estimate the decoherence time of network states by computing separately the effects of diffusion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the diffusion mechanism is also presented through the evolution of the Wigner function. The interesting collective diffusion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.

arXiv:0905.1107Journal of Physics A Mathematical and TheoreticalAug 24, 200910 citations

P

function. With these instruments we briefly show how to analyze the decoherence and the evolution of the linear entropy of general states of the network. We also show how to obtain the master equation for the case of distinct reservoirs from that of a common one.