Spontaneous emission from an atom in a nonideal cavity: Application of a generalized master equation

Plank, R.W.F. van der; Suttorp, L.G.

doi:10.1103/physreva.54.2464

Cited by 4 publications

(7 citation statements)

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“…The "generalized" master equation that arises by accounting for these enhanced losses has been established recently [3]. In applying this equation to the time evolution of a decaying atom in a cavity we have found that the effects of increased losses can be quite substantial [4]. These findings are in agreement with the predictions that follow from the solution of delay differential equations for the probability amplitudes [5].…”

Section: Introductionsupporting

confidence: 81%

“…These findings are in agreement with the predictions that follow from the solution of delay differential equations for the probability amplitudes [5]. It may be remarked here that the effects of enhanced losses in cavities with a thin-slab geometry and with infinite mirrors, as treated in [6], are rather different from those discussed in [4,5] . In fact, in the slab configuraa e-mail: suttorp@phys.uva.nl tion the atom-field system is always in the weak-coupling regime, so that Fermi's golden rule can be used.…”

Section: Introductionsupporting

confidence: 81%

“…The "standard" versions of the master equation that have been formulated for systems in nearly-ideal cavities [1,2,7] are not adequate for this purpose. For systems with nonsqueezed baths we have reached this conclusion before [3,4]. In the present paper we have shown that the same holds true for squeezed baths.…”

Section: Degenerate Parametric Oscillator With Localized Interaction supporting

confidence: 67%

“…A strictly rigorous theory for an interacting cavity system with enhanced dissipation is expected to be non-Markovian. Nevertheless, a Markovian master equation can yield quite precise predictions for the time evolution of an interacting system even if the damping is considerable, as we have shown in a previous paper [4]. …”

mentioning

confidence: 94%

“…In [3,4] we assumed that these bath variables are in a vacuum state, so that we could write f (ζ,τ)ρ tot (0) = 0, with ρ tot (0) the density operator at τ = 0 for the total system (including the bath).…”

Section: Generalized Master Equationmentioning

confidence: 99%

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Generalized master equation for systems in nonideal cavities with squeezed baths

Plank

Suttorp

1998

Eur. Phys. J. D

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Generalized master equation for systems in nonideal cavities with squeezed baths van der Plank, R.W.F.; Suttorp, L.G. Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 01 Apr 2019Eur. Phys. J. D 3, 183-193 (1998) Abstract. The master equation for the density operator of a system in a lossy cavity, which is coupled to a squeezed bath, is generalized so as to include the effects of an enhanced loss through a mirror of finite transmittivity. As compared to the standard master equation, which is valid for a nearly-perfect cavity, the generalized master equation is found to contain additional terms that account for an effective squeezed-light mixing at the nonideal mirror and for the interplay of the photon loss and the interaction within the cavity. As an example, the new master equation is used to study the influence of the enhanced losses on the photon statistics of a localized degenerate parametric oscillator. It is found that considerable changes in the photon distribution can occur as soon as the quality of the mirror becomes less than perfect. THE EUROPEAN PHYSICAL JOURNAL D c EDP Sciences Springer-Verlag

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Section: Introductionsupporting

confidence: 81%

Section: Introductionsupporting

confidence: 81%

Section: Degenerate Parametric Oscillator With Localized Interaction supporting

confidence: 67%

mentioning

confidence: 94%

Section: Generalized Master Equationmentioning

confidence: 99%

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Generalized master equation for systems in nonideal cavities with squeezed baths

Plank

Suttorp

1998

Eur. Phys. J. D

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Unification of the Jaynes–Cummings model and Planck’s radiation law

Wonderen

Lendi

2002

Journal of Mathematical Physics

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Articles you may be interested inIntegrability and superintegrability of the generalized n -level many-mode Jaynes-Cummings and Dicke models Decoherence and quantum-classical master equation dynamics A Lorentzian function based spectral filter for calculating the energy of excited bound states in quantum mechanics By combining iterative methods with Laplace transformation, we construct the solution of a dissipative Jaynes-Cummings model. The dissipative part of the model is based on the standard Markovian master equation for a harmonic oscillator that is coupled to a heat bath of nonzero temperature. Besides photon loss, we also take into account frequency detuning between atom and field. Before commencing the iteration, we subject the matrix elements of the density operator to a transformation that depends on temperature. As a result, the pole structure of all Laplace transformed matrix elements is improved. It becomes manifest which poles do not contribute to the asymptotic behavior of the density operator. In proving that our iterative process yields convergent results, we assume upper bounds on: the matrix elements of the density operator, the matrix elements of the initial density operator, the damping parameter of the heat bath, and the temperature of the heat bath. All of these bounds are physically acceptable. The photon field may start from a coherent state or a number state. For experiments in a microwave cavity, temperatures of the order of 0.1 ͓K͔ are allowed. As an application, the evolution of the atomic density matrix is studied. We propose a limit for which this matrix converges to the state of maximum von Neumann entropy. The time, the cubed initial energy density, and the inverse of the damping parameter must tend to infinity equally fast. The photon field is assumed to be in a number state at time zero, whereas the initial state of the atom can be chosen freely.

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Exact solution of the Jaynes-Cummings model with cavity damping

Wonderen

1997

Phys. Rev. A

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Operating in Laplace language and making use of a representation based on photon-number states, we find the exact solution for the density operator that belongs to the Jaynes-Cummings model with cavity damping. The detuning parameter is set equal to zero and the optical resonator does not contain any thermal photons. It is shown that the master equation for the density operator can be replaced by two algebraic recursion relations for vectors of dimension 2 and 4. These vectors are built up from suitably chosen matrix elements of the density operator. By performing an iterative procedure, the exact solution for each matrix element is found in the form of an infinite series. We demonstrate that all series are convergent and discuss how they can be truncated when carrying out numerical work. With the help of techniques from function theory, it is proved that our solutions respect the following conditions on the density operator: conservation of trace, Hermiticity, convergence to the initial state for small times, and convergence to the ground state for large times. We compute some matrix elements of the density operator for the case of weak damping and find that their analytic structure becomes much simpler. Finally, it is shown that the exact atomic density matrix converges to the state of maximum von Neumann entropy if the time, the square of the initial electromagnetic energy density, and the inverse of the cavity-damping parameter tend to infinity equally fast. The initial condition for the atom can be chosen freely, whereas the field may start from either a coherent or a photon-number state.

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Spontaneous emission from an atom in a nonideal cavity: Application of a generalized master equation

Cited by 4 publications

References 8 publications

Generalized master equation for systems in nonideal cavities with squeezed baths

Generalized master equation for systems in nonideal cavities with squeezed baths

Unification of the Jaynes–Cummings model and Planck’s radiation law

Exact solution of the Jaynes-Cummings model with cavity damping

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