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arXiv:1101.1366 · Physical Review A

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

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

Published May 16, 2011• 14 citations
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Abstract

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.

DOI
10.1103/physreva.83.055802

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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.
A cavity quantum electrodynamics (cavity-QED) system combines two or more distinct quantum components, exhibiting features not seen in the individual systems. In this work, we study the one-dimensional Jaynes-Cummings-Hubbard model in the two-excitation (two-polariton) subspace. We find that the centre momentum of two-excitation induces a magnetic flux piercing the equivalent Hamiltonian Hk in the invariant subspace with momentum k, which can be described as a 4-leg ladder in the auxiliary space. Furthermore, it is shown that the system in π-centre-momentum subspace is equivalent to a lattice system for spin-1 particle with spin-orbit coupling. On the basis of this concise description, a series of bound-pair eigenstates which display long-range polaritonic entanglement is presented as a simple application.
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.
Abstract We present a scheme for generating polaritons which are maximally entangled qubit states in the Jaynes-Cummings interaction mechanism. Considering a specific case of an atom initially in an excited state entering a cavity mode initially in vacuum state and in a non-resonant atom-field Jaynes-Cummings interaction, we demonstrate using graphical representation on the Bloch sphere that an increase in frequency detuning leads to an increase in Rabi oscillations. Analysis of the dynamical behaviour of quantum entanglement in the general Jaynes-Cummings atom-field interactions measured by concurrence show that frequency detuning and photon number parameters are vital in enhancing entanglement.
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 discuss the Jaynes–Cummings–Hubbard model describing the superfluid–Mott insulator transition of polaritons (i.e., dressed photon–qubit states) in coupled qubit–cavity arrays in the crossover from strong to weak correlations. In the strongly correlated regime the phase diagram and the elementary excitations of lattice polaritons near the Mott lobes are calculated analytically using a slave-boson theory (SBT). The opposite regime of weakly interacting polariton superfluids is described by a weak-coupling mean-field theory for a generalized multi-mode Dicke model. We show that a remarkable relation between the two theories exists in the limit of large photon bandwidth and large negative detuning, i.e., when the nature of polariton quasiparticles becomes qubit-like. In this regime, the weak-coupling theory predicts the existence of a single Mott lobe with a change of the universality class of the phase transition at the tip of the lobe, in perfect agreement with the SBT. Moreover, the spectra of low energy excitations, i.e., the sound velocity of the Goldstone mode and the gap of the amplitude mode match exactly as calculated from both theories.
We present a method to study the semiclassical dynamics of the Jaynes-Cummings dimer model, describing two coupled cavities, each containing a two-level system (qubit). We develop a Fock-space WKB approach in the polariton basis where each site is treated exactly while the intersite polariton hopping is treated semiclassically. We show that the self-trapped states can be viewed as Fock-space localized states. We find that this picture yields the correct critical value of interaction strength at which the delocalization-localization transition occurs. Moreover, the validity of our WKB approach is supported by showing that the quantum spectrum can be derived from a set of Bohr-Sommerfeld quantization conditions and by confirming that the quantum eigenstates are consistent with the classical orbital motion in the polariton band picture. The underlying idea of our method is quite general and can be applied to other interacting spin-boson models.