Quantum optical master equations: The use of damping bases

Briegel, H.-J.; Englert, Berthold-Georg

doi:10.1103/physreva.47.3311

Cited by 240 publications

(264 citation statements)

References 6 publications

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“…These terms are, of course, of sixth order in (gτ ) 6 and, not really surprisingly, themselves in Lindblad form. All other terms are of lower order in gτ and combine to reproduce Eq.…”

Section: Example: Laguerre Polynomialsmentioning

confidence: 99%

“…[18] and the Appendix) now provides a construction of the operators L λ appearing in Eq. (6). Extract a traceless operator V λ by writing…”

Section: Lindblad From Kraus-stinespringmentioning

confidence: 99%

“…[2,5], the pumping model is based on a dilute stream of excited two-level atoms that cross the laser cavity one by one and interact with the laser mode during some randomly distributed interaction time. This model can be largely handled exactly [6], even in the presence of incoherent effects like cavity damping, imperfect atom preparation, and frequency-shifting collisions. The setup has become known as the 'micromaser' because of its experimental realization with a high-quality cavity [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

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Laser theory in manifest Lindblad form

Henkel

2007

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We discuss the laser theory for a single-mode laser with nonlinear gain. We focus in particular on a micromaser which is pumped with a dilute beam of excited atoms crossing the laser cavity. In the weak-coupling regime, an expansion in the coupling strength is developed that preserves the Lindblad form of the master equation, securing the positivity of the density matrix. This expansion breaks rapidly down above threshold. This can be improved with an alternative approach, not restricted to weak coupling: the Lindblad operators are expanded in orthogonal polynomials adapted to the probability distribution for the atom-laser interaction time. Results for the photon statistics and the laser linewidth illustrate the theory.

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“…These terms are, of course, of sixth order in (gτ ) 6 and, not really surprisingly, themselves in Lindblad form. All other terms are of lower order in gτ and combine to reproduce Eq.…”

Section: Example: Laguerre Polynomialsmentioning

confidence: 99%

“…[18] and the Appendix) now provides a construction of the operators L λ appearing in Eq. (6). Extract a traceless operator V λ by writing…”

Section: Lindblad From Kraus-stinespringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Laser theory in manifest Lindblad form

Henkel

2007

J. Phys. B: At. Mol. Opt. Phys.

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“…Using damping basis methods [48,49] (details can be found in Appendix A) we find, as per (11)- (13), that the affine map representation M of T (θ k ) t is given by…”

Section: Simulation Of Constituent Semigroupsmentioning

confidence: 99%

“…In order to obtain this convex decomposition we proceed via the following steps: Firstly, we utilise the damping basis [48,49] in order to find the affine map representation of T (θ k ) t . From this affine map representation it is then easy to construct the Jamiolkowski state, from which it is possible to obtain the desired convex decomposition [45].…”

Section: Simulation Of Constituent Semigroupsmentioning

confidence: 99%

Simulation of single-qubit open quantum systems

2014

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A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels {Tt} specified by a generator L. This algorithm requires only O (||L|| (1→1) t) 3/2 / 1/2 single qubit and CNOT gates and approximates the channel Tt = e tL up to chosen accuracy . Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilised which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a non-unitary single-qubit quantum channel.

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Entangled Atoms in Micromaser Physics

et al. 1998

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The elements of micromaser physics are reviewed in a tutorial way. The emphasis is on the basic theoretical concepts, not on technical details or experimental subtleties. After a brief treatment of the atom-photon interaction according to the Jaynes-Cummings model, the master equation that governs the dynamics of the one-atom maser is derived. Then the more important properties of the steady states of the one-atom maser are discussed, including the trapped states. The approximations, upon which the standard theoretical model of the one-atom maser is based, are exhibited. The methods by which one calculates statistical properties of the emerging atoms are hinted at.

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Quantum optical master equations: The use of damping bases

Cited by 240 publications

References 6 publications

Laser theory in manifest Lindblad form

Laser theory in manifest Lindblad form

Simulation of single-qubit open quantum systems

Entangled Atoms in Micromaser Physics

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