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Register a new userMultiband and array effects in matter-wave-based waveguide QED
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Recent experiments on spontaneous emission of atomic matter waves open a new window into the behavior of quantum emitters coupled to a waveguide. Here we develop an approach based on infinite products to study this system theoretically, without the need to approximate the band dispersion relation of the waveguide. We solve the system for a one-dimensional array of one, multiple and an infinite number of quantum emitters and compare with the experiments. This leads to a detailed characterization of the decay spectrum, with a family of in-gap bound states, new mechanisms for enhanced Markovian emission different from superradiance, and the emergence of matter-wave polaritons.
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We calculate the band structure of ultracold atoms located inside a laser-driven optical cavity. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (non-cavity) optical lattices. However, in our case the nonlinearity derives from the cavity back-action rather than from direct interatomic interactions. We find both bi- and tri-stable regimes associated with the lowest band, and show that the multistability we observe can be analyzed in terms of swallowtail catastrophes. Dynamic and energetic stability of the mean-field solutions is also discussed, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the atomic band structure has important implications for proposals concerning Bloch oscillations of atoms inside optical cavities [Peden et al., Phys. Rev. A 80, 043803 (2009), Prasanna Venkatesh et al., Phys. Rev. A 80, 063834 (2009)].
We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and superradiant collective excitation eigenmodes, direct numerical solutions, and analytical transfer-matrix methods. We illustrate how the spectrum of transmitted light through the waveguide including the emergence of narrow Fano resonances can be understood by the resonance features of the eigenmodes. We describe a method based on superradiant and subradiant modes to engineer the optical response of the waveguide and to store light. The stopping of light is obtained by transferring an atomic excitation to a subradiant collective mode with the zero radiative resonance linewidth by controlling the level shift of an atom in the waveguide. Moreover, we obtain an exact analytic solution for the transmitted light through the waveguide for the case of a regular lattice of atoms and provide a simple description how the light transmission may present large resonance shifts when the lattice spacing is close, but not exactly equal, to half of the wavelength of the light. Experimental imperfections such as fluctuations of the positions of the atoms and loss of light from the waveguide are easily quantified in the numerical simulations, which produce the natural result that the optical response of the atomic array tends toward the response of a gas with random atomic positions.
We study the time evolution of ultra-cold atoms in an accelerated optical lattice. For a Bose- Einstein condensate with a narrow quasi-momentum distribution in a shallow optical lattice the decay of the survival probability in the ground band has a step-like structure. In this regime we establish a connection between the wave function renormalization parameter Z introduced in [Phys. Rev. Lett. 86, 2699 (2001)] to characterize non-exponential decay and the phenomenon of resonantly enhanced tunneling, where the decay rate is peaked for particular values of the lattice depth and the accelerating force.
We present the first realisation of a solitonic atom interferometer. A Bose-Einstein condensate of $1times10^4$ atoms of rubidium-85 is loaded into a horizontal optical waveguide. Through the use of a Feshbach resonance, the $s$-wave scattering length of the $^{85}$Rb atoms is tuned to a small negative value. This attractive atomic interaction then balances the inherent matter-wave dispersion, creating a bright solitonic matter wave. A Mach-Zehnder interferometer is constructed by driving Bragg transitions with the use of an optical lattice co-linear with the waveguide. Matter wave propagation and interferometric fringe visibility are compared across a range of $s$-wave scattering values including repulsive, attractive and non-interacting values. The solitonic matter wave is found to significantly increase fringe visibility even compared with a non-interacting cloud.
We study the scattering of matter-waves from interacting bosons in a one-dimensional optical lattice, described by the Bose-Hubbard Hamiltonian. We derive analytically a formula for the inelastic cross section as a function of the atomic interaction in the lattice, employing Bogoliubovs formalism for small condensate depletion. A linear decay of the inelastic cross section for weak interaction, independent of number of particles, condensate depletion and system size, is found.
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