On the relation between cavity-dressed states, Floquet states, RWA and semiclassical models

Guérin, S.; Monti, Francesca; Dupont, Jean-Marie; Jauslin, H. R.

doi:10.1088/0305-4470/30/20/020

Cited by 60 publications

(75 citation statements)

References 37 publications

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“…Finally, since −i∂/∂θ k,α assumes positive and negative values, N k,α = n − i∂/∂θ k,α , i.e., the photon number, is computed 'around' a large 'mean photon number n' [6], in agreement with the semiclassical limit ( [15], pp 35-37).…”

Section: Mathematical Formalismmentioning

confidence: 88%

“…Since Dirac's 1927 paper [3], this basic role of the phase has not ceased to motivate the search for a unitary phase operator 'e iϕ ' in quantum mechanics [2][3][4][5]. Recent rigorous work [6] on the interaction of N-level atoms with a quantized electromagnetic field has clarified the relationship between the phase operator and the classical limit of the field under which a suitably defined average number of photons tends to infinity while the photon density remains fixed.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper we introduce a phase operator formalism for quantum spins that, through suitable limits, is related to both the work of Guérin et al [6] and classical physics. As an application, we provide a precise mathematical definition of the Villain transform, whose original intuitive definition was flawed by boundary-value problems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Isometric and unitary phase operators: explaining the Villain transform

Hemmen¹,

Wreszinski²

2007

J. Phys. A: Math. Theor.

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The Villain transform plays a key role in spin-wave theory, a bosonization of elementary excitations in a system of extensively many Heisenberg spins. Intuitively, it is a representation of the spin operators in terms of an angle and its canonically conjugate angular momentum operator and, as such, has a few nasty boundary-condition twists. We construct an isometric phase representation of spin operators that conveys a precise mathematical meaning to the Villain transform and is related to both classical mechanics and the Pegg-Barnett-Bialynicki-Birula boson (photon) phase operators by means of suitable limits. In contrast to the photon case, unitary extensions are inadequate because they describe the wrong physics. We also discuss in some detail the application to spin-wave theory, pointing out some examples in which the isometric representation is indispensable.

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Section: Mathematical Formalismmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Isometric and unitary phase operators: explaining the Villain transform

Hemmen¹,

Wreszinski²

2007

J. Phys. A: Math. Theor.

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“…It has been proved in [14] that (16) is integrable according to 1) for both large and small coupling g. In reference [15] it has been remarked thatH…”

Section: Integrabilitymentioning

confidence: 99%

Quantum NOT operation and integrability in two-level systems

Angelo

Wreszinski

2007

Annals of Physics

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We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different "average" systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps.

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“…These problems are modeled in terms of an n-level (often 3-level) atom interacting with a strong external field [19,20,21,22,23,24]. In this paper we consider population control in a nearly degenerate 3-level atom.…”

Section: Introductionmentioning

confidence: 99%

Complete population transfer in a degenerate three-state atom

Rakhimov¹,

Shakov²,

McGuire³

2004

Phys. Rev. A

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We find conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate 3-level atom, where transitions are caused by an external interaction. Complete population transfer from an initially occupied state 1 to a designated state 2 occurs under two conditions. First, there is a constraint on the ratios of the transition matrix elements of the external interaction. Second, there is a constraint on the action integral over the interaction, or "area", corresponding to the phase shift induced by the external interaction. Both conditions may be expressed in terms of simple odd integers.

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On the relation between cavity-dressed states, Floquet states, RWA and semiclassical models

Cited by 60 publications

References 37 publications

Isometric and unitary phase operators: explaining the Villain transform

Isometric and unitary phase operators: explaining the Villain transform

Quantum NOT operation and integrability in two-level systems

Complete population transfer in a degenerate three-state atom

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