Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect
The theory of the beam splitter (BS) in quantum optics is well developed and based on fairly simple mathematical and physical foundations. This theory has been developed for any type of BS and is based on the constancy of the reflection coefficients <i>R</i> (or the transmission coeffici...
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4794 |
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| author | Dmitry Makarov |
| author_facet | Dmitry Makarov |
| author_sort | Dmitry Makarov |
| collection | DOAJ |
| description | The theory of the beam splitter (BS) in quantum optics is well developed and based on fairly simple mathematical and physical foundations. This theory has been developed for any type of BS and is based on the constancy of the reflection coefficients <i>R</i> (or the transmission coefficient <i>T</i>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>+</mo><mi>T</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>) and the phase shift <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>. It has recently been shown that the constancy of these coefficients cannot always be satisfied for a waveguide BS, where <i>R</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> depend in a special way on photon frequencies. Based on this, this review systematizes the concept of BS in quantum optics into “Conventional” and frequency-dependent BS, and also presents the theory of such BS. It is shown that the quantum entanglement, photon statistics at the output ports, and the Hong–Ou–Mandel (HOM) effect for such BS can be very different. Taking into account the fact that the waveguide BS is currently acquiring an important role in quantum technologies due to the possibility of its miniaturization, this review will be useful not only for theoreticians, but also for experimenters. |
| first_indexed | 2024-03-09T16:07:45Z |
| format | Article |
| id | doaj.art-10e5ee75697c456f83dfe24f543947db |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:07:45Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-10e5ee75697c456f83dfe24f543947db2023-11-24T16:29:51ZengMDPI AGMathematics2227-73902022-12-011024479410.3390/math10244794Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM EffectDmitry Makarov0Laboratory for Diagnostics of Carbon Materials and Spin-Optical Phenomena in Wide-Bandgap Semiconductors, Northern (Arctic) Federal University, Nab. Severnoi Dviny 17, 163002 Arkhangelsk, RussiaThe theory of the beam splitter (BS) in quantum optics is well developed and based on fairly simple mathematical and physical foundations. This theory has been developed for any type of BS and is based on the constancy of the reflection coefficients <i>R</i> (or the transmission coefficient <i>T</i>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>+</mo><mi>T</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>) and the phase shift <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>. It has recently been shown that the constancy of these coefficients cannot always be satisfied for a waveguide BS, where <i>R</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> depend in a special way on photon frequencies. Based on this, this review systematizes the concept of BS in quantum optics into “Conventional” and frequency-dependent BS, and also presents the theory of such BS. It is shown that the quantum entanglement, photon statistics at the output ports, and the Hong–Ou–Mandel (HOM) effect for such BS can be very different. Taking into account the fact that the waveguide BS is currently acquiring an important role in quantum technologies due to the possibility of its miniaturization, this review will be useful not only for theoreticians, but also for experimenters.https://www.mdpi.com/2227-7390/10/24/4794beam splitterwaveguide beam splitterquantum entanglementphotonsreflection coefficientphase shift |
| spellingShingle | Dmitry Makarov Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect Mathematics beam splitter waveguide beam splitter quantum entanglement photons reflection coefficient phase shift |
| title | Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect |
| title_full | Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect |
| title_fullStr | Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect |
| title_full_unstemmed | Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect |
| title_short | Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect |
| title_sort | theory for the beam splitter in quantum optics quantum entanglement of photons and their statistics hom effect |
| topic | beam splitter waveguide beam splitter quantum entanglement photons reflection coefficient phase shift |
| url | https://www.mdpi.com/2227-7390/10/24/4794 |
| work_keys_str_mv | AT dmitrymakarov theoryforthebeamsplitterinquantumopticsquantumentanglementofphotonsandtheirstatisticshomeffect |