Classical analogues to quantum nonlinear coherent states in photonic lattices

Pérez-Leija, Armando; Moya‐Cessa, H.; Soto‐Eguibar, Francisco; Aguilar-Loreto, O.; Christodoulides, Demetrios N.

doi:10.1016/j.optcom.2010.12.005

Cited by 8 publications

(9 citation statements)

References 17 publications

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“…where T = −Z corresponds to the final distance, then from Eqs. (25), (22) and (10) we find that the initial and final states coincide with those in (14), except an unimportant phase factor e iθ0(T ) for the final state. We additionally require that the initial and fi-…”

Section: Engineering the Lattice Output Using Shortcuts To Adiabmentioning

confidence: 62%

“…Note that the relation between the specific photonic lattice and Lewis-Riesenfeld invariants has been pointed out in [14], but here we use an invariant different than the one used there. The time-dependent eigenfunctions of Î are [29,30] where φ n (q) = |n are given in (10). They satisfy…”

Section: Engineering the Lattice Output Using Shortcuts To Adiabaticitymentioning

confidence: 99%

“…Many recent studies have demonstrated that a family of photonic lattices, implemented in arrays of evenescently coupled waveguides [1], provides the ideal testbed for a large variety of quantum phenomena [2]. We mention the observation in these lattices of Bloch-like revivals [3][4][5], Anderson localization of light [6][7][8], and the classical analog of coherent states and quantum correlations [9,10], to name a few. On the other hand, ideas from quantum mechanics have inspired the design of optical structures with desired properties.…”

Section: Introductionmentioning

confidence: 99%

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Design of a photonic lattice using shortcuts to adiabaticity

Stefanatos¹

2014

Phys. Rev. A

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In this article we use the method of shortcuts to adiabaticity to design a photonic lattice (array of waveguides) which can drive the input light to a controlled location at the output. The output position in the array is determined by functions of the propagation distance along the waveguides, which modulate the lattice characteristics (index of refraction, first and second neighbor couplings). The proposed coupler is expected to posses the robustness properties of the design method, coming from its adiabatic nature, and also to have a smaller footprint than purely adiabatic couplers. The present work provides a very interesting example where methods from quantum control can be exploited to design lattices with desired input-output properties.

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Section: Engineering the Lattice Output Using Shortcuts To Adiabmentioning

confidence: 62%

Section: Engineering the Lattice Output Using Shortcuts To Adiabaticitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Design of a photonic lattice using shortcuts to adiabaticity

Stefanatos¹

2014

Phys. Rev. A

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“…This system is equivalent to that studied in [50] with parameter χ = 1 and it is straightforward to show that this is equivalent to the Schrödinger-like equation with |E = j E j |k, j and Bargmann…”

Section: Classical Optics Examplesmentioning

confidence: 99%

Phase state and related nonlinear coherent states

2014

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We cast the phase state as a SU (1, 1) nonlinear coherent state to support the idea that the SU (1, 1) representation of the electromagnetic field may be helpful in some instances and to bring forward that it may relate to the phase state problem. We also construct nonlinear coherent states related to the exponential phase operator and provide their corresponding nonlinear annihilation operators. Finally, we discuss the propagation of classical fields through arrays of coupled waveguides that are solved through the use of nonlinear coherent states of SU (1, 1) or the exponential phase operator.

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“…10 Due to such character, the generation of Glauber-Fock states, coherent states, su(1, 1) and su(2) coherent states, by using the photonic lattices, have been studied. [11][12][13][14][15][16][17] In these cases, by considering the edge channel in the exited state, a displacement type su(1, 1) coherent states are realized in waveguide lattices. Also, the field distribution of any channel corresponds to number state and deformed number state, with regard to coupling coefficients among neighbouring channels of waveguide lattices.…”

Section: Introductionmentioning

confidence: 99%