Cooperative ordering in lattices of interacting two-level dipoles

Bettles, Robert J.; Gardiner, S. A.; Adams, Charles S.

doi:10.1103/physreva.92.063822

Cited by 90 publications

(85 citation statements)

References 70 publications

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“…(20). We first carry out the angular integral, and in the remaining integral over make the substitution x = ξ 2 + 2 .…”

Section: B Numerical Simulationsmentioning

confidence: 99%

“…The growing throughput of computers available to researchers is making such a plan practical. These methods, whether called classicalelectrodynamics simulations or coupled-dipole simulations, are now a routine theoretical tool [2,4,7,8,[14][15][16][17][18][19][20][21][22][23][24][25][26]. Closely related numerical techniques based on the analysis of the eigenstates of the coupled system of the light and the atoms [15,[27][28][29][30][31][32] or density matrices and quantum trajectories [33][34][35] are also widely used today.…”

Section: Introductionmentioning

confidence: 99%

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Exact electrodynamics versus standard optics for a slab of cold dense gas

Javanainen

Ruostekoski

et al. 2017

Phys. Rev. A

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We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample ρ and the wave number of resonant light k satisfy ρk −3 1. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes strongly correlated. The deviations from mean-field theory appear to scale with the parameter ρk −3 , and we demonstrate noticeable effects already at ρk −3 10 −2 . In dilute gases and in gases with an added inhomogeneous broadening the simulations show shifts of the resonance lines in qualitative agreement with the predicted Lorentz-Lorenz shift and "cooperative Lamb shift," but the quantitative agreement is unsatisfactory. Our interpretation is that the microscopic basis for the local-field corrections in electrodynamics is not fully understood.

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“…(20). We first carry out the angular integral, and in the remaining integral over make the substitution x = ξ 2 + 2 .…”

Section: B Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact electrodynamics versus standard optics for a slab of cold dense gas

Javanainen

Ruostekoski

et al. 2017

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…We first formulated quantum field-theoretical equations of motion describing the optical response [Eqs. (24)] that systematically include the atomic saturation effects and the internal-level structure. In order to solve the resultant dynamics, we then introduced a simple procedure to derive stochastic electrodynamics equations that can be used to study recurrent, or dependent, scattering between the atoms in the presence of strong light-atom coupling.…”

Section: Discussionmentioning

confidence: 99%

“…(24) can be significantly further simplified, particularly so for atoms of isotropic polarizability or two-level atoms. We discuss these simplifications below, before considering the stochastic solution of the resultant equations in Sec.…”

Section: Evolution Of Atomic Fieldsmentioning

confidence: 99%

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Stochastic methods for light propagation and recurrent scattering in saturated and nonsaturated atomic ensembles

2016

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We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal-level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low-light-intensity limit for atoms with a single electronic ground state, the full quantum field-theoretical representation of the model can be solved exactly by means of classical stochastic electrodynamics simulations for stationary atoms that represent cold atomic ensembles. Simulations for the optical response of atoms in a quantum degenerate regime require one to synthesize a stochastic ensemble of atomic positions that generates the corresponding quantum statistical position correlations between the atoms. In the case of multiple ground levels or at light intensities where saturation becomes important, the classical simulations require approximations that neglect quantum fluctuations between the levels. We show how the model is extended to incorporate corrections due to quantum fluctuations that result from virtual scattering processes. In the low-light-intensity limit, we illustrate the simulations in a system of atoms in a Mott-insulator state in a two-dimensional optical lattice, where recurrent scattering of light induces strong interatomic correlations. These correlations result in collective many-atom subradiant and superradiant states and a strong dependence of the response on the spatial confinement within the lattice sites.

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Cooperative Interactions in Lattices of Atomic Dipoles

Bettles

2017

Springer Theses

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Coherent radiation by an ensemble of scatterers can dramatically modify the ensemble's optical response. This can include, for example, enhanced and suppressed decay rates (superradiance and subradiance respectively), energy level shifts, and highly directional scattering. This behaviour is referred to as cooperative, since the scatterers in the ensemble behave as a collective rather than independently. In this Thesis, we investigate the cooperative behaviour of one-and two-dimensional arrays of interacting atoms.We calculate the extinction cross-section of these arrays, analysing how the cooperative eigenmodes of the ensemble contribute to the overall extinction. Typically, the dominant eigenmode if the atoms are driven by a uniform or Gaussian light beam is the mode in which the atomic dipoles oscillate in phase together and with the same polarisation as the driving field. The eigenvalues of this mode become strongly resonant as the atom number is increased. For a one-dimensional array, the location of these resonances occurs when the atomic spacing is an integer or half integer multiple of the wavelength, thus behaving analogously to a single atom in a cavity. The interference between this mode and additional eigenmodes can result in Fano-like asymmetric lineshapes in the extinction.We find that the kagome lattice in particular exhibits an exceptionally strong interference lineshape, like a cooperative analog of electromagnetically induced transparency.Triangular, square and hexagonal lattices however are typically dominated by one single mode which, for lattice spacings of the order of a wavelength, can be highly subradiant.This can result in near-perfect extinction of a resonant driving field, signifying a significant increase in the atom-light coupling efficiency. We show that this extinction is robust to possible experimental imperfections.

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Cooperative ordering in lattices of interacting two-level dipoles

Cited by 90 publications

References 70 publications

Exact electrodynamics versus standard optics for a slab of cold dense gas

Exact electrodynamics versus standard optics for a slab of cold dense gas

Stochastic methods for light propagation and recurrent scattering in saturated and nonsaturated atomic ensembles

Cooperative Interactions in Lattices of Atomic Dipoles

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