Stationary states of the Jaynes Cummings model with atomic centre-of-mass quantum motion: analytical approximation to transfer counterpropagating waves into a standing wave in a large photon number limit

Muradyan, A. Zh.; Muradyan, G. A.

doi:10.1088/0953-4075/35/19/304

Cited by 5 publications

(3 citation statements)

References 37 publications

(23 reference statements)

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“…Hence, it is possible to ana-lyze these systems without destroying them, in contrast to the time-of-flight imaging technique used for ultracold quantum gases. Since the atoms are trapped inside the cavities right from the start and their thermal motion does not quantitatively disturb the polariton dynamics [52], BEC experiments with cavity QED setups can thus be performed even at room temperatures [53]. However, in order to facilitate stable experiments with this setup, one needs a strong coupling between light and matter in order to reduce the losses induced by the spontaneous emission.…”

Section: B Cavity Qed Latticesmentioning

confidence: 99%

Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model

Nietner¹,

Pelster²

2012

Phys. Rev. A

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We develop a Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model which effectively describes both static and dynamic properties of photons evolving in a cubic lattice of cavities, each filled with a two-level atom. To this end we calculate the effective action to first-order in the hopping parameter. Within a Landau description of a spatially and temporally constant order parameter we calculate the finite-temperature mean-field quantum phase boundary between a Mott insulating and a superfluid phase of polaritons. Furthermore, within the Ginzburg-Landau description of a spatio-temporal varying order parameter we determine the excitation spectra in both phases and, in particular, the sound velocity of light in the superfluid phase.

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Section: B Cavity Qed Latticesmentioning

confidence: 99%

Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model

Nietner¹,

Pelster²

2012

Phys. Rev. A

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“…The eigenvalues and eigenvectors of this infinite Hamiltonian are not known in the general case but approximate analytical results may be found, see Refs. [30,31,32,33]. For example, one interesting approximation, related to the Raman-Nath limit, is when the q 2 -terms are neglected and it may be solved analytically.…”

Section: B Energy Band Structurementioning

confidence: 99%

“…For such a system, an extended JC model including atomic centre of mass motion and a standing wave coupling has been studied in a large number of papers, here we just mention a few. The dynamics has been analysed in, for example, [24,25,26,27,28,29,30,31,32,33], while in [30,31,32,33], approximation methods are used, such as Raman-Nath, Bragg, tight-binding or large detuning. In the Raman-Nath approximation, the kinetic energy term is neglected, and this has been assumed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Effective mass in cavity QED

Larson¹,

Salo²,

Stenholm³

2005

Phys. Rev. A

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We consider propagation of a two-level atom coupled to one electro-magnetic mode of a high-Q cavity. The atomic center-of-mass motion is treated quantum mechanically and we use a standing wave shape for the mode. The periodicity of the Hamiltonian leads to a spectrum consisting of bands and gaps, which is studied from a Floquet point of view. Based on the band theory we introduce a set of effective mass parameters that approximately describe the effect of the cavity on the atomic motion, with the emphasis on one associated with the group velocity and on another one that coincides with the conventional effective mass. Propagation of initially Gaussian wave packets is also studied using numerical simulations and the mass parameters extracted thereof are compared with those predicted by the Floquet theory. Scattering and transmission of the wave packet against the cavity are further analyzed, and the constraints for the effective mass approach to be valid are discussed in detail.Comment: 16 pages, 15 figures, accepted in Phys Rev

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A unified approach to -, - and V-type systems with one continuum

Sen¹,

Dey²,

Deb

2017

Journal of Modern Optics

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We present a systematic approach to classify the three-level-like models with two bound states coupled to a continuum. It is shown that, when one of the discrete levels of usual three-level Lambda-(Λ), cascade (Ξ) or Vee (V )-type systems is replaced by a continuum of states, the resulting each model can be classified into three distinct categories with nine possible configurations. We show that all these models are exactly solvable. We obtain and compare the asymmetric Fano line shapes of the spectra for all the models. Our results are important for exploring new coherent effects in a variety of physical systems involving continuum-bound coupling such as photoassociation of cold atoms, plasmonics, quantum dots, photonic crystals, electromagnetic metamaterials and so on.

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Stationary states of the Jaynes Cummings model with atomic centre-of-mass quantum motion: analytical approximation to transfer counterpropagating waves into a standing wave in a large photon number limit

Cited by 5 publications

References 37 publications

Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model

Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model

Effective mass in cavity QED

A unified approach to -, - and V-type systems with one continuum

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