Spatial and temporal localization of light in two dimensions

Máximo, Carlos Eduardo; Piovella, N.; Courteille, Ph. W.; Kaiser, Robin; Bachelard, Romain

doi:10.1103/physreva.92.062702

Cited by 41 publications

(55 citation statements)

References 17 publications

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“…In this case, J = 0, 1 and the decomposition (20) of the internal Hilbert space of the atomic system reads…”

Section: Appendix C : General Solution For 2 Atomsmentioning

confidence: 99%

“…The total Hilbert space H is therefore spanned by the states N basis states {|J, M, k J } form the coupled spin basis [45]. By construction, |J, M, k J are spin-J states satisfying According to the Schur-Weyl duality [52,53], any permutation P π acts only on the multiplicity subspaces K J [see decomposition (20)] and thus has the form…”

Section: A Coupled Spin Basismentioning

confidence: 99%

“…They can also be observed in dilute atomic systems for which the near-field contributions of the dipole-dipole interactions are insignificant. Recent studies concern single-photon superradiance [11][12][13][14], subradiance in cold atomic gases [15,16], collective Lambshift [17,18] and localization of light [19,20]. Moreover, super-and subradiance can be explained using a quantum multipath interference approach and can be simulated from the measurement of higher-order-intensitycorrelation functions on atoms separated by a distance larger than the emission wavelength [21,22].…”

Section: Introductionmentioning

confidence: 99%

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Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states

2016

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We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates γ and γ0 and a single parameter ∆ dd describing the dipole-dipole shifts. We solve the dynamics exactly for N = 2 atoms, numerically for up to 30 atoms, and obtain the large-N -limit by a mean-field approach. We find that there is a critical difference γ0 − γ that depends on N beyond which superradiance is lost. We show that exact non-trivial dark states (i.e. states other than the ground state with vanishing spontaneous emission) only exist for γ = γ0, and that those states (dark when γ = γ0) are subradiant when γ < γ0.

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“…In this case, J = 0, 1 and the decomposition (20) of the internal Hilbert space of the atomic system reads…”

Section: Appendix C : General Solution For 2 Atomsmentioning

confidence: 99%

Section: A Coupled Spin Basismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states

2016

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“…In particular, the study of the spectra of Green's matrices unveiled important information about structural resonances in disordered systems. Indeed, the numerical analysis of Green's matrices has been successfully employed to address different aspects of light propagation in open random media, such as Anderson localization of light [55,[86][87][88][89] and matter waves [90], random lasing [91][92][93], light transport in nonlinear media [94], and superradiance in atomic random systems [95][96][97][98]. An analytical theory has also been developed for the eigenvalue density of random Green's matrices, providing fundamental insights into light-matter interactions in disordered media [93,99,100].…”

Section: The Green's Matrix Methodsmentioning

confidence: 99%

Structural and Spectral Properties of Deterministic Aperiodic Optical Structures

2016

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Abstract:In this comprehensive paper we have addressed structure-property relationships in a number of representative systems with periodic, random, quasi-periodic and deterministic aperiodic geometry using the interdisciplinary methods of spatial point pattern analysis and spectral graph theory as well as the rigorous Green's matrix method, which provides access to the electromagnetic scattering behavior and spectral fluctuations (distributions of complex eigenvalues as well as of their level spacing) of deterministic aperiodic optical media for the first time.

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“…Similarly, recent numerical simulations considering pointdipole resonant scatterers study the collective modes of the effective Hamiltonian of the system and, in particular, their lifetimes [45][46][47][48][49]. Our work shows that Dicke subradiance can also be at the origin of very long lifetimes and that a careful analysis is required to distinguish subradiant from localized modes [49]. Finally, the combination of subradiance with disorder acting on the atomic transitions might provide an alternative route to strong localization of light, as was recently suggested [50].…”

Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Storing Light in the Dark

Carmele

2016

Physics

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Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes. Here, we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model. DOI: 10.1103/PhysRevLett.116.083601 Despite its many applications, ranging from astrophysics [1] to mesoscopic physics [2,3] and quantum information technology [4], light interacting with a large ensemble of N scatterers still bears many surprising features and is at the focus of intense research. For N ¼ 2 atoms placed close together, the in-phase oscillation of the induced dipoles produces a large, superradiant dipole, whereas the out-ofphase oscillation corresponds to a subradiant quadrupole. Generalizing for N ≫ 2, Dicke has shown that, for samples of a small size compared to the wavelength of the atomic transition, the symmetric superposition of atomic states induces superradiant emission, scaling with the number of particles N, whereas the antisymmetric superpositions are decoupled from the environment, with vanishing emission rates, which corresponds to subradiance [5].Dicke superradiance has been extensively studied in the 1970s [6][7][8] but the observation of its counterpart, subradiance, has been restricted to indirect evidence of modified decay rates in one particular direction [9] or in systems of two particles at very short distance [10][11][12]. One challenge for the observation of subradiance by a large number of particles is the fragile nature of these states, which require protection from any local nonradiative decay mechanism [13]. Furthermore, contrary to the two-atom case, for which the distance between atoms has to be small compared to the wavelength, for N ≫ 2, the retarded, long-range resonant dipole-dipole interaction [14] gives rise to super-and subradiant effects ("cooperative scattering") also in dilute samples, with interatomic distances much larger than the wavelength, and corresponding large system sizes. Since, for N > 2, the Hamiltonians for short and long-range interactions do not commute, the collective eigenstates due to the long-range interactions are suppressed by short-range interactions [8]. These short-range or near-field effects (or "van der Waals dephasing") thus need to be avoided in t...

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Spatial and temporal localization of light in two dimensions

Cited by 41 publications

References 17 publications

Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states

Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states

Structural and Spectral Properties of Deterministic Aperiodic Optical Structures

Storing Light in the Dark

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