Markovian and non-Markovian dynamics of quantum emitters coupled to two-dimensional structured reservoirs

González-Tudela, Alejandro; Cirac, J. I.

doi:10.1103/physreva.96.043811

Cited by 131 publications

(216 citation statements)

References 88 publications

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“…For ∆ = 0, their imaginary part coincides and is given by [36] Γ e ≈ g 2 πJ log 32πJ 2 g 2 (4) obtained in the limit . This explains both the finite time scale observed in Fig.…”

mentioning

confidence: 67%

“…From now on we focus on what happens for energies, E, around the middle of the band (|E| J) where the selfenergy can be expanded as [36][37][38] Σ e (E + i0…”

mentioning

confidence: 99%

“…z−ω(k) is the collective QE interaction induced by the environment, which can be obtained recursively [36][37][38]. Along this manuscript, we focus on a situation when the two QEs lie along a diagonal, n 12 = (n, n), as this is where most of the emission occurs [see Fig.…”

mentioning

confidence: 99%

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Quantum Emitters in Two-Dimensional Structured Reservoirs in the Nonperturbative Regime

2017

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We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which can not be captured by standard perturbative treatments. In particular, for a single quantum emitter with its transition frequency in the middle of the band we predict an exponential relaxation at a rate different from that predicted by the Fermi's Golden rule, followed by overdamped oscillations and slow relaxation decay dynamics. This is accompanied by directional emission into the reservoir. This directionality leads to a modification of the emission rate for few emitters and even perfect subradiance, i.e., suppression of spontaneous emission, for four quantum emitters.The interaction of quantum emitters (QEs) with propagating bosonic particles, e.g., photons, lies at the core of Quantum Optics [1]. This interaction leads, for example, to collective interactions between QEs [2, 3] which can be harnessed for both quantum information and simulation applications. New avenues in the integration of QEs with nanophotonic structures [4][5][6][7][8][9][10][11][12][13][14] provide us with systems in which the QEs interact with low dimensional bosonic modes, with complicated energy dispersions in the case of engineered dielectrics [6][7][8][9][10][11][12]. Despite originally the main motivation of such implementations was to exploit the small sizes to enhance light-matter interactions, it was soon realized that intriguing phenomena arise because of the reduced dimensionality. One particular aspect is the possibility of realizing chiral emission [15][16][17], which can display very uncommon features [18,19]. Another one is the possibility of exploiting the phenomena of sub and superradiance [11,12,[20][21][22], e.g., to enhance the coupling to the emitter [23], to generate QE entanglement [18,24], to produce non-classical light [25,26], or even to perform quantum computation [27].The dynamics of QEs in 1D reservoirs is relatively simple, specially when their transition frequency, ω e , lies within a band. Perturbative treatments predict that a single QE initially excited decays at a rate, Γ, given by the Fermi's Golden Rule (FGR), i.e. proportional to the density of states of the bath at ω e . The emission mostly occurs in the bath modes that are resonant with that frequency. Typically, there are two such modes of associated momentum ±k e , leading to a symmetric left/right emission. When two (or more) QEs are present, the existence of only two such modes leads to super/subradiant states, where the emission is enhanced or suppressed by interference. In higher dimensions for structureless baths, a single QE will also decay at a rate given by the FGR. However, the emission takes place in different directions as there are many resonant modes in the bath. For two QEs, the interference in the emission cannot occur in all those modes at the same time [28] and thus, the phenomena of sub and superradiance are generically absent.In this manus...

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“…For ∆ = 0, their imaginary part coincides and is given by [36] Γ e ≈ g 2 πJ log 32πJ 2 g 2 (4) obtained in the limit . This explains both the finite time scale observed in Fig.…”

mentioning

confidence: 67%

“…From now on we focus on what happens for energies, E, around the middle of the band (|E| J) where the selfenergy can be expanded as [36][37][38] Σ e (E + i0…”

mentioning

confidence: 99%

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Quantum Emitters in Two-Dimensional Structured Reservoirs in the Nonperturbative Regime

2017

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“…In this case, with at most one excitation present in the whole system, the fermionic chain we consider is completely equivalent to the bosonic one studied in reference, 37 and the analytical calculation of C e in the thermodynamic limit presented in that work is also applicable to our setup. We used this result to obtain the non-Markovianity degree N , which we plot for a wide range of Hamiltonian parameters in Fig.…”

Section: Vacuum Initial Statementioning

confidence: 99%

“…The magnitudes of the contributions decay exponentially (RS), with a power law (UE,LE) or are constant (UBS,LBS). 37 Strictly, the resonance and bound state contributions stem from singularities in G e (z). In 70 it was proven that if Im Σ e (z) diverges at the band edge, where it is proportional to the spectral density D(E), 37 there always exists a pole associated to a bound state.…”

Section: Appendix Amentioning

confidence: 99%

Markovianity of an emitter coupled to a structured spin-chain bath

2020

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We analyze the dynamics of a spin 1/2 subsystem coupled to a spin chain. We simulate numerically the full quantum many-body system for various sets of parameters and initial states of the chain, and characterize the divisibility of the subsystem dynamics, i.e. whether it is Markovian and can be described by a (time dependent) master equation. We identify regimes in which the subsystem admits such Markovian description, despite the many-body setting, and provide insight about why the same is not possible in other regimes. Interestingly, coupling the subsystem at the edge, instead of the center, of the chain gives rise to qualitatively distinct behavior.

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Completely Subradiant Multi‐Atom Architectures Through 2D Photonic Crystals

Galve

Zambrini

2018

Annalen der Physik

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Following recent advances in the manipulation of atoms trapped near 1D waveguides and proposals to use surface acoustic waves on piezoelectric substrates for the same purpose, the potential of two-dimensional platforms is shown. Directional emission of atoms near photonic crystal slabs with square symmetry is used, in the ideal case, to build perfect subradiant states of 2 distant atoms, possible in 2D only for finite lattices with perfectly reflecting boundaries. These allow the design of massively parallel 1D arrays of atoms above a single crystal, useful for multi-port output of nonclassical light, by exploiting destructive interference of guided resonance modes. Directionality of the emission is shown to be present whenever a linear iso-frequency manifold is present in the dispersion relation of the crystal.Multi-atom radiance properties can be predicted from a simple cross-talk coefficient of a master equation, in good agreement with exact atom-crystal dynamics, showing its predictive power. Departing from the ideal theoretical case, possible experimental issues in photonic crystal implementations are also discussed, and an outlook of other relevant modern platforms for 2D propagation of excitations is given.

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Markovian and non-Markovian dynamics of quantum emitters coupled to two-dimensional structured reservoirs

Cited by 131 publications

References 88 publications

Quantum Emitters in Two-Dimensional Structured Reservoirs in the Nonperturbative Regime

Quantum Emitters in Two-Dimensional Structured Reservoirs in the Nonperturbative Regime

Markovianity of an emitter coupled to a structured spin-chain bath

Completely Subradiant Multi‐Atom Architectures Through 2D Photonic Crystals

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