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Arbitrary photonic wave plate operations on chip: realizing Hadamard, Pauli-X, and rotation gates for polarisation qubits.

Heilmann R, Gräfe M, Nolte S, Szameit A - Sci Rep (2014)

Bottom Line: By adjusting this length of the defect along the waveguide, the retardation between ordinary and extraordinary field components is precisely tunable including half-wave plate and quarter-wave plate operations.Our approach demonstrates the full range control of orientation and strength of the induced birefringence and thus allows arbitrary wave plate operations without affecting the degree of polarisation or introducing additional losses to the waveguides.The implemented gates are tested with classical and quantum light.

View Article: PubMed Central - PubMed

Affiliation: Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany.

ABSTRACT
Chip-based photonic quantum computing is an emerging technology that promises much speedup over conventional computers at small integration volumes. Particular interest is thereby given to polarisation-encoded photonic qubits, and many protocols have been developed for this encoding. However, arbitrary wave plate operation on chip are not available so far, preventing from the implementation of integrated universal quantum computing algorithms. In our work we close this gap and present Hadamard, Pauli-X, and rotation gates of high fidelity for photonic polarisation qubits on chip by employing a reorientation of the optical axis of birefringent waveguides. The optical axis of the birefringent waveguide is rotated due to the impact of an artificial stress field created by an additional modification close to the waveguide. By adjusting this length of the defect along the waveguide, the retardation between ordinary and extraordinary field components is precisely tunable including half-wave plate and quarter-wave plate operations. Our approach demonstrates the full range control of orientation and strength of the induced birefringence and thus allows arbitrary wave plate operations without affecting the degree of polarisation or introducing additional losses to the waveguides. The implemented gates are tested with classical and quantum light.

No MeSH data available.


Related in: MedlinePlus

Measured wave plate operations.(a) Experimental data and best fit model of the reorientation of the optical axis as a function of the azimuthal position of the defect. Larger error bars result from near λ operation of the integrated wave plate. (b) Intensity ratio P⊥/Ptotal between the power of the perpendicularly polarised light (H or V polarisation) and the total power as a function of the interaction length between defect and waveguide (assumed to be proportional to Δφ). The angle of the optical axis is fixed to α = 45° (black dots) or α = 22.5° (red triangles) and P⊥/Ptotal should follow (sin(2α) sin(Δφ/2))2.
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f2: Measured wave plate operations.(a) Experimental data and best fit model of the reorientation of the optical axis as a function of the azimuthal position of the defect. Larger error bars result from near λ operation of the integrated wave plate. (b) Intensity ratio P⊥/Ptotal between the power of the perpendicularly polarised light (H or V polarisation) and the total power as a function of the interaction length between defect and waveguide (assumed to be proportional to Δφ). The angle of the optical axis is fixed to α = 45° (black dots) or α = 22.5° (red triangles) and P⊥/Ptotal should follow (sin(2α) sin(Δφ/2))2.

Mentions: We extract a birefringence in the waveguide that is Δn = 0.65 … 1.32 × 10−5, depending of the azimuthal angle of the defect caused by the resulting overlap of the stress fields. The orientation of the optical axis as a monotonous function of the azimuthal angle θ of the defect is plotted in Fig. 2(a). For increasing θ also the tilt of the waveguide's optical axis α increases (in a nonlinear fashion) and reaches a maximum of αmax = 90° for θ = 90°. In order to understand our experimental data, we developed a simple heuristic model. As the birefringence in the waveguide is increased by approximately one order of magnitude in the presence of a defect, we consider only the defect's stress fields, represented by their centroids on either sides of the defect with coordinates (ri, θi) with respect to the waveguide. Assuming that the impact si of such a stress field i on the optical axis decreases exponentially with growing distances by the decay rate ρ, we obtain for our data the fit function with and dhor,vert as horizontal or vertical deposition, respectively, of the stress fields' centroids compared to the centre of the defect. The best fit shows ρ = 20(3), μm dhor = 7.95(10) μm, and dvert = −4.2(6) μm, suggesting that the centroids tend to lie below the envisaged level, which is caused by an elongated shape of the defect leading to an offset of θ0 = 11.9° for zero-crossing. For smaller angles the experimental data deviate from the predicted line leading to a tilt of the waveguide's optical axis by α = −6° at θ = 0°. This is due to the sequenced writing of the waveguide followed by the defect that has to be written in or through a yet present glass modification, which affects most notably the stress field on the left side of the defect. Hence, both stress fields will lie in different depths and the assumed symmetry, dvert,1 = dvert,2, is broken.


Arbitrary photonic wave plate operations on chip: realizing Hadamard, Pauli-X, and rotation gates for polarisation qubits.

Heilmann R, Gräfe M, Nolte S, Szameit A - Sci Rep (2014)

Measured wave plate operations.(a) Experimental data and best fit model of the reorientation of the optical axis as a function of the azimuthal position of the defect. Larger error bars result from near λ operation of the integrated wave plate. (b) Intensity ratio P⊥/Ptotal between the power of the perpendicularly polarised light (H or V polarisation) and the total power as a function of the interaction length between defect and waveguide (assumed to be proportional to Δφ). The angle of the optical axis is fixed to α = 45° (black dots) or α = 22.5° (red triangles) and P⊥/Ptotal should follow (sin(2α) sin(Δφ/2))2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3927208&req=5

f2: Measured wave plate operations.(a) Experimental data and best fit model of the reorientation of the optical axis as a function of the azimuthal position of the defect. Larger error bars result from near λ operation of the integrated wave plate. (b) Intensity ratio P⊥/Ptotal between the power of the perpendicularly polarised light (H or V polarisation) and the total power as a function of the interaction length between defect and waveguide (assumed to be proportional to Δφ). The angle of the optical axis is fixed to α = 45° (black dots) or α = 22.5° (red triangles) and P⊥/Ptotal should follow (sin(2α) sin(Δφ/2))2.
Mentions: We extract a birefringence in the waveguide that is Δn = 0.65 … 1.32 × 10−5, depending of the azimuthal angle of the defect caused by the resulting overlap of the stress fields. The orientation of the optical axis as a monotonous function of the azimuthal angle θ of the defect is plotted in Fig. 2(a). For increasing θ also the tilt of the waveguide's optical axis α increases (in a nonlinear fashion) and reaches a maximum of αmax = 90° for θ = 90°. In order to understand our experimental data, we developed a simple heuristic model. As the birefringence in the waveguide is increased by approximately one order of magnitude in the presence of a defect, we consider only the defect's stress fields, represented by their centroids on either sides of the defect with coordinates (ri, θi) with respect to the waveguide. Assuming that the impact si of such a stress field i on the optical axis decreases exponentially with growing distances by the decay rate ρ, we obtain for our data the fit function with and dhor,vert as horizontal or vertical deposition, respectively, of the stress fields' centroids compared to the centre of the defect. The best fit shows ρ = 20(3), μm dhor = 7.95(10) μm, and dvert = −4.2(6) μm, suggesting that the centroids tend to lie below the envisaged level, which is caused by an elongated shape of the defect leading to an offset of θ0 = 11.9° for zero-crossing. For smaller angles the experimental data deviate from the predicted line leading to a tilt of the waveguide's optical axis by α = −6° at θ = 0°. This is due to the sequenced writing of the waveguide followed by the defect that has to be written in or through a yet present glass modification, which affects most notably the stress field on the left side of the defect. Hence, both stress fields will lie in different depths and the assumed symmetry, dvert,1 = dvert,2, is broken.

Bottom Line: By adjusting this length of the defect along the waveguide, the retardation between ordinary and extraordinary field components is precisely tunable including half-wave plate and quarter-wave plate operations.Our approach demonstrates the full range control of orientation and strength of the induced birefringence and thus allows arbitrary wave plate operations without affecting the degree of polarisation or introducing additional losses to the waveguides.The implemented gates are tested with classical and quantum light.

View Article: PubMed Central - PubMed

Affiliation: Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany.

ABSTRACT
Chip-based photonic quantum computing is an emerging technology that promises much speedup over conventional computers at small integration volumes. Particular interest is thereby given to polarisation-encoded photonic qubits, and many protocols have been developed for this encoding. However, arbitrary wave plate operation on chip are not available so far, preventing from the implementation of integrated universal quantum computing algorithms. In our work we close this gap and present Hadamard, Pauli-X, and rotation gates of high fidelity for photonic polarisation qubits on chip by employing a reorientation of the optical axis of birefringent waveguides. The optical axis of the birefringent waveguide is rotated due to the impact of an artificial stress field created by an additional modification close to the waveguide. By adjusting this length of the defect along the waveguide, the retardation between ordinary and extraordinary field components is precisely tunable including half-wave plate and quarter-wave plate operations. Our approach demonstrates the full range control of orientation and strength of the induced birefringence and thus allows arbitrary wave plate operations without affecting the degree of polarisation or introducing additional losses to the waveguides. The implemented gates are tested with classical and quantum light.

No MeSH data available.


Related in: MedlinePlus