Arbitrary orbital angular momentum addition in second harmonic generation

Buono, Wagner Tavares; Moraes, L F C; Huguenin, J. A. O.; Souza, C. E. R.; Khoury, A. Z.

doi:10.1088/1367-2630/16/9/093041

Cited by 51 publications

(26 citation statements)

References 48 publications

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“…In appendix A, the calculation of the corresponding overlap integral is detailed and two selection rules are derived. The first one leads to the expected OAM conservation, already discussed in previous works [40,41,43,48,49]. The second one is less obvious and predicts that higher radial orders are generated in the second harmonic field when opposite helicities are combined in the nonlinear process.…”

Section: A Effective Nonlinear Mode Couplingmentioning

confidence: 58%

Orbital angular momentum mixing in type II second harmonic generation

Khoury¹,

Pereira²,

Buono³

et al. 2017

Nonlinear Optics

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We investigate the non linear mixing of orbital angular momentum in type II second harmonic generation with arbitrary topological charges imprinted on two orthogonally polarized beams. Starting from the basic nonlinear equations for the interacting fields, we derive the selection rules determining the set of paraxial modes taking part in the interaction. Conservation of orbital angular momentum naturally appears as the topological charge selection rule. However, a less intuitive rule applies to the radial orders when modes carrying opposite helicities are combined in the nonlinear crystal, an intriguing feature confirmed by experimental measurements.

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Section: A Effective Nonlinear Mode Couplingmentioning

confidence: 58%

Orbital angular momentum mixing in type II second harmonic generation

Khoury¹,

Pereira²,

Buono³

et al. 2017

Nonlinear Optics

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“…This analogy was used to demonstrate the topological phase acquired by entangled states evolving under local unitary operations [12]. Recently, it has attracted a growing interest due both to the fundamental aspects involved, but also for potential applications to classical optical information processing [13][14][15][16][17][18][19][20]. Nonseparable structures have also proved their utility in the quantum optical domain [22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Pacs Numbersmentioning

confidence: 99%

Tripartite nonseparability in classical optics

et al. 2016

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It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each of their degrees of freedom. Here we report the experimental creation of such a non-separable, tripartite GHZ-like state of path, polarization and transverse modes of a classical laser beam. We use a Mach-Zehnder interferometer with an additional mirror and other optical elements to perform measurements that violate Mermin's inequality. This demonstration of a classical optical analogue of tripartite entanglement paves the path to novel optical applications inspired by multipartite quantum information protocols. PACS numbers:A composite quantum system is said to be entangled when it is not fully described by the state of its components [1]. Besides indicating a departure from classical physics, entangled states represent an important resource for a number of quantum information protocols [2]. In classical optics, the mode structure associated with different degrees of freedom of the wave field can also be described by complex vector spaces. As examples, an arbitrary polarization can be written as a complex superposition of circularly polarized beams, and the spatial configuration of a paraxial beam can be decomposed in terms of Laguerre-Gaussian beams. These degrees of freedom can be represented on two independent Poincaré spheres [3], in complete analogy with the Bloch sphere used to represent qubit states [2]. Intriguingly, also in classical optics there are field configurations which cannot be described as a tensor product of definite modes of each individual degree of freedom of the system [4]. These non-separable structures display a classical analogue of quantum entanglement [5][6][7][8]. One example are vector vortex beams, which are non-separable superpositions of transverse modes and polarization states of a laser beam [9][10][11]. This analogy was used to demonstrate the topological phase acquired by entangled states evolving under local unitary operations [12]. Recently, it has attracted a growing interest due both to the fundamental aspects involved, but also for potential applications to classical optical information processing [13][14][15][16][17][18][19][20]. Nonseparable structures have also proved their utility in the quantum optical domain [22][23][24][25][26][27][28][29][30][31][32][33]. Analogously to its quantum counterpart, classical entanglement has been characterized via the violation of Bell-like inequalities [34][35][36].Composite quantum systems may have more than two parts. For tripartite systems, Mermin [37] simplified an earlier argument by Greenberger, Horne and Zeilinger * Corresponding author.[38], to show that any local hidden-variable theory for tripartite systems must satisfy (1) where Z, Y, Z represent the Pauli operators. This inequality is violated by the so-called GHZ-Mermin state:for which ZZZ = +1 and ZXX = XZX = XXZ = −1, resulting in M = 4, the maximum algebraic violation of Mermin's inequality (1). In [39], Spreeuw proposed a scheme in which t...

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“…The nonlinearity enables wave-wave interaction, necessary to achieve wave mixing, allowing the formation of waves for which the frequency and wave number are the sums of the frequencies and wave numbers of parent linear waves. For example, the mixing of OAM modes in nonlinear interaction by simultaneously exploiting different photonic degrees of freedom has been investigated in optical waves supporting OAM 17 , 18 . However, the classical forms of entanglement between degrees of freedom of a single system differ from entanglement between degrees of freedom of different subsystems 19 .…”

Section: Introductionmentioning

confidence: 99%

Experimental classical entanglement in a 16 acoustic qubit-analogue

Hasan

Runge

Deymier

2021

Sci Rep

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The possibility of achieving and controlling scalable classically entangled, i.e., inseparable, multipartite states, would fundamentally challenge the advantages of quantum systems in harnessing the power of complexity in information science. Here, we investigate experimentally the extent of classical entanglement in a $$16$$ 16 acoustic qubit-analogue platform. The acoustic qubit-analogue, a.k.a., logical phi-bit, results from the spectral partitioning of the nonlinear acoustic field of externally driven coupled waveguides. Each logical phi-bit is a two-level subsystem characterized by two independently measurable phases. The phi-bits are co-located within the same physical space enabling distance independent interactions. We chose a vector state representation of the $$16$$ 16 -phi-bit system which lies in a $${2}^{16}$$ 2 16 -dimensional Hilbert space. The calculation of the entropy of entanglement demonstrates the possibility of achieving inseparability of the vector state and of navigating the corresponding Hilbert space. This work suggests a new direction in harnessing the complexity of classical inseparability in information science.

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Arbitrary orbital angular momentum addition in second harmonic generation

Cited by 51 publications

References 48 publications

Orbital angular momentum mixing in type II second harmonic generation

Orbital angular momentum mixing in type II second harmonic generation

Tripartite nonseparability in classical optics

Experimental classical entanglement in a 16 acoustic qubit-analogue

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