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arXiv:1103.4856 · Physical Review A

Sine-Gordon and Bose-Hubbard dynamics with photons in a hollow-core fiber

Ming-Xia Huo, Dimitris G. Angelakis

Published Feb 17, 2012• 10 citations
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Abstract

We show that sine-Gordon and Bose-Hubbard dynamics with stationary polaritons could be observed in a hollow-core one-dimensional fiber loaded with a cold atomic gas. Utilizing the strong light confinement in the fiber, a range of different strongly correlated polaritonic and photonic states corresponding to both strong and weak interactions can be created and probed. The key ingredient is the creation of a tunable effective lattice potential acting on the interacting polaritonic gas, which is possible by slightly modulating the atomic density. We analyze the relevant phase diagram corresponding to the realizable Bose-Hubbard (weak) and sine-Gordon (strong) interacting regimes and conclude by describing the measurement process. The latter consists of mapping the stationary excitations to propagating light pulses whose correlations can be efficiently probed once they exit the fiber using available optical technologies.

DOI
10.1103/physreva.85.023821

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We show that sine-Gordon and Bose-Hubbard dynamics with stationary polaritons could be observed in a hollow-core one-dimensional fiber loaded with a cold atomic gas. Utilizing the strong light confinement in the fiber, a range of different strongly correlated polaritonic and photonic states corresponding to both strong and weak interactions can be created and probed. The key ingredient is the creation of a tunable effective lattice potential acting on the interacting polaritonic gas, which is possible by slightly modulating the atomic density. We analyze the relevant phase diagram corresponding to the realizable Bose-Hubbard (weak) and sine-Gordon (strong) interacting regimes and conclude by describing the measurement process. The latter consists of mapping the stationary excitations to propagating light pulses whose correlations can be efficiently probed once they exit the fiber using available optical technologies.
In this work we show that light-matter excitations (polaritons) generated inside a hollow-core one-dimensional fiber filled with two types of atoms, can exhibit Luttinger liquid behavior. We first explain how to prepare and drive this quantum-optical system to a strongly interacting regime, described by a bosonic two-component Lieb-Liniger model. Utilizing the connection between strongly interacting bosonic and fermionic systems, we then show how spin-charge separation could be observed by probing the correlations in the polaritons. This is performed by first mapping the polaritons to propagating photon pulses and then measuring the effective photonic spin and charge densities and velocities by analyzing the correlations in the emitted photon spectrum. The necessary regime of interactions is achievable with current quantum-optical technology.
In this work we show that light-matter excitations (polaritons) generated inside a hollow-core onedimensional fiber filled with two types of atoms, can exhibit Luttinger liquid behavior.We first explain how to prepare and drive this quantum-optical system to a strongly interacting regime, described by a bosonic two-component Lieb-Liniger model.Utilizing the connection between strongly interacting bosonic and fermionic systems, we then show how spin-charge separation could be observed by probing the correlations in the polaritons.This is performed by first mapping the polaritons to propagating photon pulses and then measuring the effective photonic spin and charge densities and velocities by analyzing the correlations in the emitted photon spectrum.The necessary regime of interactions is achievable with current quantum-optical technology.
We investigate the dynamics of one-dimensional interacting bosons in an optical lattice after a sudden quench in the weakly interacting (Bose-Hubbard) and strongly interacting (sine-Gordon) regimes. While in a higher dimension, the Mott-superfluid phase transition is observed for weakly interacting bosons in deep lattices, in one dimension an instability is generated also for shallow lattices with a commensurate periodic potential pinning the atoms to the Mott state through a transition described by the sine-Gordon model. The present work aims at identifying the quench dynamics in both the Bose-Hubbard and sine-Gordon interaction regimes. We numerically exactly solve the time-dependent Schr\"odinger equation for a small number of atoms and obtain dynamical measures of several key quantities. We investigate the correlation dynamics of first and second order; both exhibit rich many-body features in the dynamics. We conclude that in both cases, dynamics exhibits collapse-revival phenomena, though with different timescales. We argue that the dynamical fragmentation is a convenient quantity to distinguish the dynamics especially near the pinning zone. To understand the relaxation process we measure the many-body information entropy. Bose-Hubbard dynamics clearly establishes the possible relaxation to the maximum entropy state. In contrast, the sine-Gordon dynamics is so fast that it does not exhibit any signature of relaxation in the present timescale of computation.
We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the sine-Gordon regime of weak lattices, to the complete absence of a lattice. Using the Bose-Fermi mapping between strongly interacting bosons and weakly interacting fermions, we derive the phase diagram in the parameter space of lattice depth and chemical potential. This extends previous knowledge from tight-binding (Bose-Hubbard) studies in a direction which is important because the lattice depth is a readily adjustable experimental parameter. Several other results (equations of state, energy gaps, profiles in harmonic trap) are presented as corollaries to the physics contained in this phase diagram. Generically, both incompressible (gapped) and compressible phases coexist in a trap; this has implications for experimental measurements.
We report on the first observation of stationary light pulses and narrowband light storage inside a hollow-core photonic crystal fiber. Laser-cooled atoms were first loaded into the fiber core providing strong light-matter coupling. Light pulses were then stored in a collective atomic excitation using a single control laser beam. By applying a second counterpropagating control beam, a light pulse could be brought to a standstill. Our work paves the way towards the creation of strongly-correlated many-body systems with photons and applications in the field of quantum information processing.
We propose a scheme to observe the crossover from weakly to strongly bound pairs with stationary polaritons. We first show how stationary light-matter excitations (polaritons) can realize an optically tunable two-component Bose-Hubbard model with repulsive intraspecies interactions and attractive interspecies interactions. We then discuss the feasibility of generating an effective Fermi-Hubbard model of polaritons exhibiting the crossover behavior. The predicted behavior of the system characterized by a crossover from short- to long-range spatial correlations as interactions are tuned can be efficiently observed by measuring correlation functions on the light exiting the waveguide.