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Studies of interacting two level atoms in cavity-Quantum ElectroDynamics arrays

賴奕志

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Nowadays the light-matter interaction phenomena in spatially periodic structure have been studied extensive, i.e. photonic crystals, cavity array. In this thesis, we consider coherent properties of coupled atom-field systems with adding the interaction between atoms and discuss the quantum phase transition and envelope function method for this system. We further show that beyond widely used low excitation density limit and Holstein-Primakoff transformation. We have shown that the phase transition diagram of the normal to superfluid (BEC) state of low branch polaritons in the critical temperature domain. Finally, a multiple-scale technique has been used to analyze the electromagnetic properties of the nonlinear dielectric periodic thin-film stacks. We have found a solitary–wave equation behavior in the array which includes the atom-atom interaction.

DOI
10.6843/nthu.2011.00368

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Nowadays the light-matter interaction phenomena in spatially periodic structure have been studied extensive, i.e. photonic crystals, cavity array. In this thesis, we consider coherent properties of coupled atom-field systems with adding the interaction between atoms and discuss the quantum phase transition and envelope function method for this system. We further show that beyond widely used low excitation density limit and Holstein-Primakoff transformation. We have shown that the phase transition diagram of the normal to superfluid (BEC) state of low branch polaritons in the critical temperature domain. Finally, a multiple-scale technique has been used to analyze the electromagnetic properties of the nonlinear dielectric periodic thin-film stacks. We have found a solitary–wave equation behavior in the array which includes the atom-atom interaction.
Coherent properties of a two-dimensional spatially periodic structure, polaritonic crystal (PolC) formed by trapped two-level atoms in an optical cavity array interacting with a light field, are analyzed. By considering the wave function overlapping for both photonic and atomic states, a cubic-quintic complex nonlinear Schr\"odinger equation is derived for the dynamics of coupled atom-light states, wave function of low-branch polaritons, associated with PolC in the continuous limit. A variational approach predicts that a stable ground-state wave function of PolC exists but is accompanied by an oscillating width. For a negative scattering length, the wave function collapses in the presence of a small quintic nonlinearity appearing due to a three-body polariton interaction. By studying the nonequilibrium (dissipative) dynamics of polaritons with adiabatic approximation, we have shown that the collapse of PolC wave function can be prevented even in the presence of small decaying of a number of polariton particles.
The coherent and nonlinear properties of a polaritonic crystal (PolC), formed by trapped two-level atoms in an optical cavity array and interacting with an optical field, are analyzed. The nonlinear Schrödinger equation is considered for the dynamics of coupled atom-light states and low-branch polaritons associated with PolCs in the continuous medium limit. The existence of a stable ground-state PolC wave function is predicted using the variational approach. For negative scattering lengths, the wave function collapses in the presence of small quintic nonlinearity.
The enormous progress in controlling quantum optical and atomic systems has prompted ideas for new experimental realizations of strongly correlated many-body systems operating with light. These systems consist of photons confined in optical cavities, which interact strongly with atoms or atomiclike structures. Due to the interaction between the two particle species optical nonlinearities appear, leading to a quantum phase transition from Mott to superfluid phase. Here, we address the Tavis-Cummings lattice model, which describes light-matter systems containing multiple atomiclike structures in each cavity. In particular, we investigate the phase boundary delimiting Mott from superfluid phase and the elementary excitations of the two-dimensional Tavis-Cummings lattice model in dependence of the number of atomiclike structures per cavity. In order to obtain the results we employ the variational cluster approach. We evaluate spectral functions and densities of states of both particle species, which allows us to characterize the fundamental excitations of light-matter systems. These excitations are termed polaritons and are superpositions of photons and atomic excitations. We introduce polariton quasiparticles as appropriate linear combinations of both particle species and analyze the weights of their constituents. Our results demonstrate the dependence of the quantum phase transition and the elementary excitations on the number of atomiclike structures per cavity and provide thus valuable insight into the physics of light-matter systems.
We propose a new type of spatially periodic structure, i.e. polaritonic crystal (PolC), to observe a "slow"/"stopped" light phenomenon due to coupled atom-field states (polaritons) in a lattice. Under the tightbinding approximation, such a system realizes an array of weakly coupled trapped two-component atomic ensembles interacting with optical field in a tunnel-coupled one dimensional cavity array. We have shown that the phase transition to the superfluid Bardeen-Cooper-Schrieffer state, a so-called (BCS)-type state of low branch polaritons, occurs under the strong coupling condition. Such a transition results in the appearance of a macroscopic polarization of the atomic medium at non-zero frequency. The principal result is that the group velocity of polaritons depends essentially on the order parameter of the system, i.e. on the average photon number in the cavity array.
Coupling between quantum emitters and modes of light is foundational to studies of quantum systems. Coherent interactions between matter and light have greatly advanced the development of quantum technologies. When an ensemble of atoms interacts with light that is confined within a cavity---a resonator for photons---light also mediates atom-atom interactions, leading to collective phenomena that cannot be extrapolated from microscopic behaviors. Understanding how interactions among quantum particles lead to macroscopic phenomena, such as phase transitions and breaking of symmetries, remains a challenge in modern physics. In this dissertation, I present results addressing this challenge in the context of mesoscopic arrays of optical-tweezer-trapped atoms interfaced with a high-finesse optical cavity. In particular, the physics we investigate arises from the collective scattering of light. Utilizing the ability to place atoms with nanometer-scale precision, we engineer superradiant and subradiant states, where control over interference of the emission from multiple atoms leads to collectively enhanced or suppressed amounts of scattered light. Building on this work, we investigate the emergence of optomechanical self-organization, mediated by superradiance in the cavity electromagnetic field. By coupling atoms to the same cavity mode, the atoms exert forces on one another through the exchange of photons, leading them to autonomously order themselves spatially. We characterize mesoscopic fluctuations and their effect on symmetry-breaking dynamics associated with self-organization. Finally, we extend this framework to theoretically investigate how the phase of the atom-cavity coupling can be altered to generate higher symmetries. Our analysis reveals first-order phase transitions and instabilities induced by non-reciprocal forces. Altogether, this work establishes a path towards realizing mesoscopic systems of complex phases of matter in cavity quantum electrodynamics with unprecedented programmability.
A new developed for storing quantum information on atomic polaritons being at thermal equilibrium is developed for the first time. We propose a new type of spatially periodic structure - polaritonic crystal (PolC) formed by trapped two-level atoms interacting with quantum electromagnetic field in one-dimensional array of tunnelcoupled microcavities, which allows polaritons to be fully localized. The quantum degeneracy and phase transition to superfluid (Bardeen-Cooper-Schrieffer-type) state for low branch polaritons is discussed. The principal result is that the group velocity of polaritons depends essentially on the order parameter of the system, i.e. on the average photon number in the cavity array. An algorithm for the spatially distributed writing, storing, and retrieving of quantum optical information using polariton wave packet propagated in the cavity array is examined. To take into account decoherence processes in polaritonic system the quantum Brownian particle model is discussed as well.