Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Dark-polariton bound pairs in the modified Jaynes-Cummings-Hubbard model

Angelo Maggitti, Milan Radonjić, B. M. Jelenković

Published Jan 19, 2016• 9 citations
Publisher

Abstract

We investigate a one-dimensional modified Jaynes-Cummings-Hubbard chain of $N$ identical QED cavities with nearest-neighbor photon tunneling and periodic boundary conditions. Each cavity contains an embedded three-level atom which is coupled to a cavity mode and an external classical control field. In the case of two excitations and common large detuning of two Raman-resonant fields, we show the emergence of two different species of dark-polariton bound pairs (DPBPs) that are mutually localized in their relative spatial coordinates. Due to the high degree of controllability, we show the appearance of either one or two DPBPs, having the energies within the energy gaps between three bands of mutually delocalized eigenstates. Interestingly, in a different parameter regime with negatively detuned Raman fields, we find that the ground state of the system is a DPBP which can be utilized for the photon storage, retrieval, and controllable state preparation. Moreover, we propose an experimental realization of our model system.

DOI
10.1103/physreva.93.013835

Related papers

Formation of dark-state polaritons and two-polariton bound states in arrays of atoms and optical cavities

Angelo Maggitti

This thesis covers a theoretical analysis of non-interacting and interacting quasi\nparticles, called polaritons. Polaritons are composites, based on photonic and atomic\nexcitations in a tunable and controlled manner. Dark-state polaritons, as a subclass\nof polaritons, are very curious objects, as they can act as a quantum memory of\nphotons within an ensemble of alkali-metal atoms in -type conguration which\nadmit electromagnetically induced transparency (EIT). This thesis focus on the\nformation of dark-state polaritons in degenerate two-level systems, where two light\nelds, a quantum probe and a classical driving eld, couple the same transition\nbetween the ground state and excited state manifold. An algorithm is going to\nbe derived in order to determine the dispersion relation and inherent composition\nof the dark-state polaritons in the degenerate two-level system. The algorithm is\nbased on a microscopic equation of motion technique and provides an extension of\nthe non-degenerate case. Depending on the polarization of the light elds, it will be\nshown that either one or two dark-state polaritons can exist. Further, the calculated\ndark-state polaritons can be used in order to perform a frequency conversion and\neven a conversion of linear light polarization.\nIn the second part of the thesis, interacting polaritons in arrays of coupled QED\ncavities will be discussed. In rst place, the standard Jaynes-Cummings model is\ndiscussed in order to provide a better insight to polaritons in QED cavities. Then,\na modied Jaynes-Cummings model is introduced and derived in order to study\ndark-polaritons and their interaction. It will be shown that dark-polaritons directly\ndepend on the common single photon detuning of the two coupling elds, quantum\nprobe and classical driving eld. The interaction between dark-polaritons will be\ndiscussed where the emergence of dark-polariton bound pairs will be shown. By\ntuning the Stark-shift due to the classical control eld, the number and the composition\nof dark-polariton bound pairs can be controlled. It will be demonstrated\nthat there exists a dark-polariton bound pair which diers from the aforementioned\nones, because it represents a ground state of the system. Using that kind of a darkpolariton\nbound pair, storage and retrieval of a single photon can be performed,\neven though that the photons are in a two-photon bound state.\nIn the last part of the thesis, disorder between QED cavities will be introduced\nin a controlled manner through staggered inter-cavity photon hopping strengths J1\nand J2. Further, the appearance of a dark-polariton bound pair of a completely\ndierent type will be presented.

•Apr 7, 2016•0 citations

Quantum communication through Jaynes-Cummings-Hubbard arrays

R. Chakrabarti, G Sreekumari

We study the dynamics of an one dimensional array of Jaynes-Cummings-Hubbard system of arbitrary number of coupled cavities, each containing a two level atom that interacts with a field mode. In particular, we consider propagation of a single excitation quantum state for two different couplings of the photonic modes of the adjacent cavities, namely, a translation invariant closed chain of uniformly coupled cavities, and also a linear chain with nonuniform parabolically varying intercavity coupling where the interaction Hamiltonian is associated with the Jacobi matrix of the Krawtchouk polynomials. Using a description via the delocalized atomic and field modes we observe that for a large detuning of these two degrees of freedom atomic excitations propagate without populating the field modes, and vice versa. For the near-resonance scenario between these modes the atomic excitations, say, while propagating mix with the photonic states. In the context of the parabolic coupling between photons of adjacent cavities an arbitrary element of the time-dependent correlation function between two arbitrary cavities may be expressed in closed form for dominant values of the detuning parameter, when an exact transmission of the quantum state at pre-specified times is realized.

arXiv:1103.0640•Mar 3, 2011•0 citations

Two-polariton bound states in the Jaynes-Cummings-Hubbard model

Max T. C. Wong, C. K. Law

We examine the eigenstates of the one-dimensional Jaynes-Cummings-Hubbard model in the two-excitation subspace. We discover that two-excitation bound states emerge when the ratio of vacuum Rabi frequency to the tunneling rate between cavities exceeds a critical value. We determine the critical value as a function of the quasimomentum quantum number, and indicate that the bound states carry a strong correlation in which the two polaritons appear to be spatially confined together.

arXiv:1101.1366•Physical Review A•May 16, 2011•14 citations

Propagation of single-excitation quantum states through Jaynes–Cummings–Hubbard arrays

R. Chakrabarti, G Sreekumari

We study the dynamics of a one-dimensional array of the Jaynes–Cummings–Hubbard system of arbitrary number of coupled cavities, each containing a two-level atom that interacts with a field mode. In particular, we consider the propagation of a single-excitation quantum state for two different couplings between the localized photonic modes of the adjacent cavities, namely a translation invariant uniform coupling on a closed chain of cavities, and also a nonuniform parabolically varying intercavity coupling on a linear chain where the interaction Hamiltonian is associated with the Jacobi matrix of the relevant Krawtchouk polynomial. Using a description via the delocalized atomic and field modes, we observe that for a large detuning of these two degrees of freedom, atomic excitations propagate without populating the field modes, and vice versa. For the near-resonance scenario between these modes, the atomic excitations, say, while propagating mix with the photonic states. In the context of the parabolic coupling between photons of adjacent cavities, the time-dependent correlation function describing the propagation of the quantum state between two arbitrary sites may be expressed in closed form for dominant values of the detuning parameter, when an exact transmission of the quantum state at pre-specified times is realized.

Journal of Physics B Atomic Molecular and Optical Physics•May 19, 2011•4 citations

Effective Three-Body Interactions in Jaynes-Cummings-Hubbard Systems

Srivatsa Badariprasad, AM Martin

A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.

•Nov 2, 2018•0 citations

Effective Three-Body Interactions in Jaynes-Cummings-Hubbard Systems

Srivatsa B. Prasad, A. Martin

A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.

arXiv:1710.02424•Scientific Reports•Oct 29, 2018•16 citations
We investigate a one-dimensional modified Jaynes-Cummings-Hubbard chain of NNN identical QED cavities with nearest-neighbor photon tunneling and periodic boundary conditions. Each cavity contains an embedded three-level atom which is coupled to a cavity mode and an external classical control field. In the case of two excitations and common large detuning of two Raman-resonant fields, we show the emergence of two different species of dark-polariton bound pairs (DPBPs) that are mutually localized in their relative spatial coordinates. Due to the high degree of controllability, we show the appearance of either one or two DPBPs, having the energies within the energy gaps between three bands of mutually delocalized eigenstates. Interestingly, in a different parameter regime with negatively detuned Raman fields, we find that the ground state of the system is a DPBP which can be utilized for the photon storage, retrieval, and controllable state preparation. Moreover, we propose an experimental realization of our model system.
This thesis covers a theoretical analysis of non-interacting and interacting quasi\nparticles, called polaritons. Polaritons are composites, based on photonic and atomic\nexcitations in a tunable and controlled manner. Dark-state polaritons, as a subclass\nof polaritons, are very curious objects, as they can act as a quantum memory of\nphotons within an ensemble of alkali-metal atoms in -type conguration which\nadmit electromagnetically induced transparency (EIT). This thesis focus on the\nformation of dark-state polaritons in degenerate two-level systems, where two light\nelds, a quantum probe and a classical driving eld, couple the same transition\nbetween the ground state and excited state manifold. An algorithm is going to\nbe derived in order to determine the dispersion relation and inherent composition\nof the dark-state polaritons in the degenerate two-level system. The algorithm is\nbased on a microscopic equation of motion technique and provides an extension of\nthe non-degenerate case. Depending on the polarization of the light elds, it will be\nshown that either one or two dark-state polaritons can exist. Further, the calculated\ndark-state polaritons can be used in order to perform a frequency conversion and\neven a conversion of linear light polarization.\nIn the second part of the thesis, interacting polaritons in arrays of coupled QED\ncavities will be discussed. In rst place, the standard Jaynes-Cummings model is\ndiscussed in order to provide a better insight to polaritons in QED cavities. Then,\na modied Jaynes-Cummings model is introduced and derived in order to study\ndark-polaritons and their interaction. It will be shown that dark-polaritons directly\ndepend on the common single photon detuning of the two coupling elds, quantum\nprobe and classical driving eld. The interaction between dark-polaritons will be\ndiscussed where the emergence of dark-polariton bound pairs will be shown. By\ntuning the Stark-shift due to the classical control eld, the number and the composition\nof dark-polariton bound pairs can be controlled. It will be demonstrated\nthat there exists a dark-polariton bound pair which diers from the aforementioned\nones, because it represents a ground state of the system. Using that kind of a darkpolariton\nbound pair, storage and retrieval of a single photon can be performed,\neven though that the photons are in a two-photon bound state.\nIn the last part of the thesis, disorder between QED cavities will be introduced\nin a controlled manner through staggered inter-cavity photon hopping strengths J1\nand J2. Further, the appearance of a dark-polariton bound pair of a completely\ndierent type will be presented.
We study the dynamics of an one dimensional array of Jaynes-Cummings-Hubbard system of arbitrary number of coupled cavities, each containing a two level atom that interacts with a field mode. In particular, we consider propagation of a single excitation quantum state for two different couplings of the photonic modes of the adjacent cavities, namely, a translation invariant closed chain of uniformly coupled cavities, and also a linear chain with nonuniform parabolically varying intercavity coupling where the interaction Hamiltonian is associated with the Jacobi matrix of the Krawtchouk polynomials. Using a description via the delocalized atomic and field modes we observe that for a large detuning of these two degrees of freedom atomic excitations propagate without populating the field modes, and vice versa. For the near-resonance scenario between these modes the atomic excitations, say, while propagating mix with the photonic states. In the context of the parabolic coupling between photons of adjacent cavities an arbitrary element of the time-dependent correlation function between two arbitrary cavities may be expressed in closed form for dominant values of the detuning parameter, when an exact transmission of the quantum state at pre-specified times is realized.
We study the dynamics of a one-dimensional array of the Jaynes–Cummings–Hubbard system of arbitrary number of coupled cavities, each containing a two-level atom that interacts with a field mode. In particular, we consider the propagation of a single-excitation quantum state for two different couplings between the localized photonic modes of the adjacent cavities, namely a translation invariant uniform coupling on a closed chain of cavities, and also a nonuniform parabolically varying intercavity coupling on a linear chain where the interaction Hamiltonian is associated with the Jacobi matrix of the relevant Krawtchouk polynomial. Using a description via the delocalized atomic and field modes, we observe that for a large detuning of these two degrees of freedom, atomic excitations propagate without populating the field modes, and vice versa. For the near-resonance scenario between these modes, the atomic excitations, say, while propagating mix with the photonic states. In the context of the parabolic coupling between photons of adjacent cavities, the time-dependent correlation function describing the propagation of the quantum state between two arbitrary sites may be expressed in closed form for dominant values of the detuning parameter, when an exact transmission of the quantum state at pre-specified times is realized.
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.