Scattering and Bound States of two Polaritons in an Array of Coupled Cavities

Zhu, Chuanzhou; Endo, Shiro; Naidon, Pascal; Zhang, Peng

doi:10.1007/s00601-012-0562-4

Cited by 12 publications

(6 citation statements)

References 25 publications

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“…The scattering theory also provides the way to explore some non-Markovian effects of emitters coupled to the waveguide with nonlinear spectrum, where the multiphoton bound states [54,55] may form. The general result of the transition amplitude and the generalized master equation enable us to study the photon transmission in more complicated quantum optics systems and the dissipative many-body systems.…”

Section: Discussionmentioning

confidence: 99%

Multiphoton-scattering theory and generalized master equations

2015

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We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time-evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S-matrix of the asymptotic in-and out-states. For the case of few incident photons in the waveguide, we also re-derive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the forth one, we show how a quantum emitter can generate entanglement of out-going photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.

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Section: Discussionmentioning

confidence: 99%

Multiphoton-scattering theory and generalized master equations

2015

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“…(24) Figure 3 provides some results obtained from the ansatz in Eq. (23). Since the dissipator scales with the dissipation strength α 2 − δ 2 , in the top left panel we have plotted the normalized quantity I η /|α 2 − δ 2 |.…”

Section: A Mean-field Treatmentmentioning

confidence: 99%

“…One of them deals with the investigation of driven-dissipative many-body systems [13][14][15][16]. Available platforms include coupled QED cavities [17][18][19][20] or optomechanical arrays [21][22][23], as well as atomic and molecular optical systems such as Rydberg atoms [24] or trapped ions [25]. Dissipation however is not necessarily detrimental.…”

Section: Introductionmentioning

confidence: 99%

Persistent currents by reservoir engineering

2018

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We demonstrate that persistent currents can be induced in a quantum system in contact with a structured reservoir, without the need of any applied gauge field. The working principle of the mechanism leading to their presence is based on the extension to the many-body scenario of nonreciprocal Lindblad dynamics, recently put forward by Metelmann and Clerk in Phys. Rev. X 5, 021025 (2015): Non-reciprocity can be generated by suitably balancing coherent interactions with their corresponding dissipative version, induced by the coupling to a common structured environment, such to make total interactions directional. Specifically, we consider an interacting spin/boson model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing a combination of cluster mean-field, exact diagonalization and matrix-product-operator techniques, we show that solely dissipative effects suffice to engineer steady states with a persistent current that survives in the limit of large systems. We also verify the robustness of such current in the presence of additional dissipative or Hamiltonian perturbation terms. arXiv:1809.02964v2 [quant-ph]

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“…Photonic non-linearities are often induced by coupling photons to two-level emitters, as achieved in atomic and molecular setups with single emitters in a cavity configuration 18 19 . Alternatively, photonic non-linearities can result, e.g., from the anharmonicity of the multi-excitation spectra in the Jaynes-Cummings Hamiltonian 20 21 22 23 24 , or from dipolar or van-der-Waals interactions between atoms, such as in Rydberg atoms under condition of electromagnetically induced transparency (EIT) 25 26 27 28 29 . Recent groundbreaking experiments 28 29 , in particular, have demonstrated attraction of photons caused by formation of bound bipolariton states 30 31 .…”

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confidence: 99%

Broadband photon-photon interactions mediated by cold atoms in a photonic crystal fiber

Litinskaya

Tignone

Pupillo

2016

Sci Rep

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We demonstrate theoretically that photon-photon attraction can be engineered in the continuum of scattering states for pairs of photons propagating in a hollow-core photonic crystal fiber filled with cold atoms. The atoms are regularly spaced in an optical lattice configuration and the photons are resonantly tuned to an internal atomic transition. We show that the hard-core repulsion resulting from saturation of the atomic transitions induces bunching in the photonic component of the collective atom-photon modes (polaritons). Bunching is obtained in a frequency range as large as tens of GHz, and can be controlled by the inter-atomic separation. We provide a fully analytical explanation for this phenomenon by proving that correlations result from a mismatch of the quantization volumes for atomic excitations and photons in the continuum. Even stronger correlations can be observed for in-gap two-polariton bound states. Our theoretical results use parameters relevant for current experiments and suggest a simple and feasible way to induce interactions between photons.

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Scattering and Bound States of two Polaritons in an Array of Coupled Cavities

Cited by 12 publications

References 25 publications

Multiphoton-scattering theory and generalized master equations

Multiphoton-scattering theory and generalized master equations

Persistent currents by reservoir engineering

Broadband photon-photon interactions mediated by cold atoms in a photonic crystal fiber

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