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Advances in Quantum Optics and Quantum Information
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Advances in Quantum Optics and Quantum Information

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 30187

Special Issue Editor

Prof. Dr. Dmitry Makarov

E-Mail Website
Guest Editor
Department of Fundamental and Applied Physics, Northern (Arctic) Federal University named after M.V. Lomonosov, Arkhangelsk 163002, Russia
Interests: quantum entanglement; waveguide beam splitters; two-photon interference; single photons; photon sources; ultrashort laser pulses (USP); USP scattering theory

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to publish original scientific articles devoted to theoretical advances in quantum optics and quantum information. Any theoretical results in these fields of physics involve various mathematical approaches and modeling using numerical calculations. Often in the literature on these areas of physics, mathematical details are omitted and not discussed in detail. In this issue, detailed discussion of such mathematical approaches and modeling details will be welcome. Publications on important physics results already known but using original mathematical ideas that have led to simpler and faster results may be considered in this issue. Topics of interest to this Special Issue include but are not limited to quantum communication and cryptography, quantum metrology and sensing, quantum modeling, quantum gates, quantum control, hybrid quantum circuits, quantum electrodynamics of resonators, optical cavities, mechanical systems, single photon sources and detectors, beam splitters, and waveguide lattices.

Prof. Dr. Dmitry Makarov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum communication
  • Quantum algorithms
  • Cryptography
  • Quantum metrology
  • Quantum sensing
  • Quantum modeling
  • Quantum computing
  • Quantum gates
  • Quantum control
  • Optical cavities
  • Quantum entanglement
  • Photon sources
  • Beam splitters
  • Waveguide lattices
  • Two-photon interference
  • Three-photon interference
  • Qubits
  • Boson sampling
  • Teleportation
  • Quantum computer

Published Papers (17 papers)

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Research

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18 pages, 1359 KiB  
Article
Transfer of Quantum States and Stationary Quantum Correlations in a Hybrid Optomechanical Network
by Hugo Molinares, Bing He and Vitalie Eremeev
Mathematics 2023, 11(13), 2790; https://0-doi-org.brum.beds.ac.uk/10.3390/math11132790 - 21 Jun 2023
Viewed by 1044
Abstract
We present a systematic study on the effects of dynamical transfer and steady-state synchronization of quantum states in a hybrid optomechanical network consisting of two cavities, which carry atoms inside and interact via a common moving mirror such as the mechanical oscillator. It [...] Read more.
We present a systematic study on the effects of dynamical transfer and steady-state synchronization of quantum states in a hybrid optomechanical network consisting of two cavities, which carry atoms inside and interact via a common moving mirror such as the mechanical oscillator. It is found that a high fidelity transfer of Schrödinger’s cat and squeezed states between two cavities modes is possible. On the other hand, we demonstrate the synchronization effect of the cavity modes in a steady squeezed state with its high fidelity realized by the mechanical oscillator that intermediates the generation, transfer and stabilization of the squeezing. In this framework, we also study the generation and evolution of bipartite and tripartite entanglement and find its connection to the effects of quantum state transfer and synchronization. Particularly, when the transfer occurs at the maximal fidelity, any entanglement is almost zero, so the different cavity modes are disentangled. However, these modes become entangled when the two bosonic modes are synchronized in a stationary squeezed state. The results provided by the current study may find applications in quantum information technologies, in addition to the setups for metrology, where squeezed states are essential. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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12 pages, 2201 KiB  
Article
Improving Mechanical Oscillator Cooling in a Double-Coupled Cavity Optomechanical System with an Optical Parametric Amplifier
by Peipei Pan, Aixi Chen and Li Deng
Mathematics 2023, 11(9), 2218; https://0-doi-org.brum.beds.ac.uk/10.3390/math11092218 - 08 May 2023
Viewed by 1100
Abstract
We investigate the cooling phenomenon of a mechanical oscillator in a double-coupled cavity optomechanical system. Our model includes two single-mode optical cavities. The left cavity is an optomechanical system with an optical parametric amplifier, and the right cavity is a standard optical cavity. [...] Read more.
We investigate the cooling phenomenon of a mechanical oscillator in a double-coupled cavity optomechanical system. Our model includes two single-mode optical cavities. The left cavity is an optomechanical system with an optical parametric amplifier, and the right cavity is a standard optical cavity. The two optical cavities couple with each other by exchanging photons. The optomechanical system is effectively driven by an input laser field. By solving the linear quantum Langevin equation of the system under a steady-state condition, we can obtain the position fluctuation spectrum and momentum fluctuation spectrum of the mechanical oscillator, and then, the expression of its effective temperature is obtained. Through numerical analysis, we find the change in the effective temperature of the mechanical oscillator under different physical parameters. The results show that the cooling of the mechanical oscillator can be significantly improved in the presence of optical parameter amplification and adjustment of optical cavity parameters. Our cooling solutions have potential applications for the preparation of nonclassical states of mechanical oscillators, high-precision measurements, and quantum information processing. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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10 pages, 386 KiB  
Article
Exact Solutions of the Bloch Equations to the Asymmetric Hyperbolic Cosine Pulse with Chirped Frequency
by Sofiane Grira, Nadia Boutabba and Hichem Eleuch
Mathematics 2023, 11(9), 2159; https://0-doi-org.brum.beds.ac.uk/10.3390/math11092159 - 04 May 2023
Viewed by 1354
Abstract
In this research study, we derive the exact solutions of the Bloch equations describing the dynamics of a two-level atom with dephasing. In the two-level atom, a strong laser pump couples a ground state to an upper excited state with a time-dependent Rabi-frequency. [...] Read more.
In this research study, we derive the exact solutions of the Bloch equations describing the dynamics of a two-level atom with dephasing. In the two-level atom, a strong laser pump couples a ground state to an upper excited state with a time-dependent Rabi-frequency. The exact solutions are given for the atomic population inversion and the real and imaginary parts of the coherence while the input pulse is an asymmetric hyperbolic cosine form. Additionally, the system is under a chirped detuning. The method of solving the Bloch equations analytically is a very tedious part of the research, and as far as we know, there are few exact solutions available in this field. Hence, our solutions might be of great interest to various research areas, including nuclear magnetic resonance, where analytical solutions to the Bloch equations play a major role in the study of the information on the state of the medium as determined by the NMR signals. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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8 pages, 338 KiB  
Article
Quantum Theory of Scattering of Nonclassical Fields by Free Electrons
by Dmitry Makarov
Mathematics 2023, 11(9), 2094; https://0-doi-org.brum.beds.ac.uk/10.3390/math11092094 - 28 Apr 2023
Viewed by 908
Abstract
At present, there is no non-perturbative theory of scattering of nonclassical electromagnetic waves by free electrons that describes the scattering process completely with the help of quantum physics. In this paper, such a theory is presented, which takes into account the statistics and [...] Read more.
At present, there is no non-perturbative theory of scattering of nonclassical electromagnetic waves by free electrons that describes the scattering process completely with the help of quantum physics. In this paper, such a theory is presented, which takes into account the statistics and the number of scattered photons. This theory is completely analytical for an arbitrary number of electrons in the system and, in a particular case, is equivalent to the previous theory of scattering as the number of incident photons tends to infinity. It is shown that this theory can differ greatly from the previously known theory of Thomson scattering in the non-perturbative case and at relatively small numbers of incident photons. In addition, this theory is applicable to the scattering of ultrashort pulses by free electrons. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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10 pages, 869 KiB  
Article
Generation and Controllability of High-Dimensional Rogue Waves in an Electromagnetically Induced Transparent Medium
by Zhongyin Li, Ji Lin and Huijun Li
Mathematics 2023, 11(8), 1829; https://0-doi-org.brum.beds.ac.uk/10.3390/math11081829 - 12 Apr 2023
Viewed by 880
Abstract
We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level Λ-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external [...] Read more.
We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level Λ-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external potential, which result from the stark (Zeeman) effect contributed by an electric (magnetic) field. By adjusting the amplitude and width of the initial pulse, we can generate the high-dimensional rogue waves and obtain the phase-transition curves of high-dimensional rogue waves. In the system, the far-detuned electric field, the random weak magnetic field, and the Gauss weak magnetic field are not conducive to the excitation of high-dimensional rogue waves. The results not only provide a theoretical basis for the experimental realization or prevention of the high-dimensional rogue waves, but also prove the possibility of generating and controlling the rogue waves in other high-dimensional non-integrable systems. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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17 pages, 698 KiB  
Article
Lattice-Based Lightweight Quantum Resistant Scheme in 5G-Enabled Vehicular Networks
by Zeyad Ghaleb Al-Mekhlafi, Mahmood A. Al-Shareeda, Selvakumar Manickam, Badiea Abdulkarem Mohammed and Amjad Qtaish
Mathematics 2023, 11(2), 399; https://0-doi-org.brum.beds.ac.uk/10.3390/math11020399 - 12 Jan 2023
Cited by 20 | Viewed by 1656
Abstract
Both security and privacy are central issues and need to be properly handled because communications are shared among vehicles in open channel environments of 5G-enabled vehicular networks. Several researchers have proposed authentication schemes to address these issues. Nevertheless, these schemes are not only [...] Read more.
Both security and privacy are central issues and need to be properly handled because communications are shared among vehicles in open channel environments of 5G-enabled vehicular networks. Several researchers have proposed authentication schemes to address these issues. Nevertheless, these schemes are not only vulnerable to quantum attacks but also use heavy operations to generate and verify signatures of messages. Additionally, these schemes need an expensive component RoadSide Unit (RSU)-aided scheme during the joining phase. To address these issues, we propose a lightweight quantum-resistant scheme according to the lattice method in 5G-enabled vehicular networks. Our proposal uses matrix multiplication instead of operations-based bilinear pair cryptography or operations-based elliptic curve cryptography to generate and verify signatures of messages shared among vehicles. Our proposal satisfies a significant reduction in performance, which makes it lightweight enough to handle quantum attacks. Our proposal is based on 5G technology without using any RSU-aided scheme. Security analysis showed that our proposal satisfies privacy and security properties as well as resists quantum attacks. Finally, our proposal also shows favorable performance compared to other related work. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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14 pages, 3141 KiB  
Article
Design of an Exchange Protocol for the Quantum Blockchain
by Alexandru-Gabriel Tudorache
Mathematics 2022, 10(21), 3986; https://0-doi-org.brum.beds.ac.uk/10.3390/math10213986 - 27 Oct 2022
Cited by 1 | Viewed by 1617
Abstract
This paper explores the idea of a quantum exchange protocol between two entities, validated by (at least) a third one. Two entities, part of a greater system, decide they want to trade quantum goods: their exchange is configurable, and allows them to select [...] Read more.
This paper explores the idea of a quantum exchange protocol between two entities, validated by (at least) a third one. Two entities, part of a greater system, decide they want to trade quantum goods: their exchange is configurable, and allows them to select the type of good, from a selected preset, and the desired quantity, up to a maximum value (one of the quantum goods can be interpreted as quantum money/a form of quantum currency). Certain qubits should also be used as a way of storing the details of the transfer, after it has been validated (acting in a similar way to a quantum ledger). The quantum circuits of the proposed design are implemented using the Python programming language with the help of Qiskit, IBM’s open-source quantum framework. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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17 pages, 399 KiB  
Article
Quantum Communication with Polarization-Encoded Qubits under Majorization Monotone Dynamics
by Artur Czerwinski
Mathematics 2022, 10(21), 3932; https://0-doi-org.brum.beds.ac.uk/10.3390/math10213932 - 23 Oct 2022
Cited by 3 | Viewed by 1868
Abstract
Quantum communication can be realized by transmitting photons that carry quantum information. Due to decoherence, the information encoded in the quantum state of a single photon can be distorted, which leads to communication errors. In particular, we consider the impact of majorization monotone [...] Read more.
Quantum communication can be realized by transmitting photons that carry quantum information. Due to decoherence, the information encoded in the quantum state of a single photon can be distorted, which leads to communication errors. In particular, we consider the impact of majorization monotone dynamical maps on the efficiency of quantum communication. The mathematical formalism of majorization is revised with its implications for quantum systems. The discrimination probability for two arbitrary orthogonal states is used as a figure of merit to track the quality of quantum communication in the time domain. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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9 pages, 596 KiB  
Article
Continuous Variable Quantum Secret Sharing with Security Enhancement in Practical Quantum Communications
by Yun Mao, Yiwu Zhu, Yijun Wang and Ying Guo
Mathematics 2022, 10(20), 3768; https://0-doi-org.brum.beds.ac.uk/10.3390/math10203768 - 13 Oct 2022
Viewed by 1021
Abstract
Quantum communications can be conveniently implemented by two participants, but quantum secret key sharing (QSS) through multi-participant communication seems difficult in practice. In this paper, we propose a multi-participant QSS scheme with the local local oscillator (LLO) in continuous variable (CV) quantum communications. [...] Read more.
Quantum communications can be conveniently implemented by two participants, but quantum secret key sharing (QSS) through multi-participant communication seems difficult in practice. In this paper, we propose a multi-participant QSS scheme with the local local oscillator (LLO) in continuous variable (CV) quantum communications. It allows an honest participant called a dealer to share a secret key with the others, making it possible to establish a secret key if and only if all participants gather together. The LLO scheme, which eliminates the need for the local oscillator (LO) to be propagated in insecure channels, can be used to avoid the potential LO attack in the traditional CVQSS scheme. Numerical simulation shows that the performance of the LLO-based CVQSS can be improved in terms of the maximal transmission distance even if it is performed with the partially trusted noise. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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11 pages, 2102 KiB  
Article
Towards Quantum Noise Squeezing for 2-Micron Light with Tellurite and Chalcogenide Fibers with Large Kerr Nonlinearity
by Arseny A. Sorokin, Gerd Leuchs, Joel F. Corney, Nikolay A. Kalinin, Elena A. Anashkina and Alexey V. Andrianov
Mathematics 2022, 10(19), 3477; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193477 - 23 Sep 2022
Cited by 4 | Viewed by 1358
Abstract
Squeezed light—nonclassical multiphoton states with fluctuations in one of the quadrature field components below the vacuum level—has found applications in quantum light spectroscopy, quantum telecommunications, quantum computing, precision quantum metrology, detecting gravitational waves, and biological measurements. At present, quantum noise squeezing with optical [...] Read more.
Squeezed light—nonclassical multiphoton states with fluctuations in one of the quadrature field components below the vacuum level—has found applications in quantum light spectroscopy, quantum telecommunications, quantum computing, precision quantum metrology, detecting gravitational waves, and biological measurements. At present, quantum noise squeezing with optical fiber systems operating in the range near 1.5 μm has been mastered relatively well, but there are no fiber sources of nonclassical squeezed light beyond this range. Silica fibers are not suitable for strong noise suppression for 2 µm continuous-wave (CW) light since their losses dramatically deteriorate the squeezed state of required lengths longer than 100 m. We propose the generation multiphoton states of 2-micron 10-W class CW light with squeezed quantum fluctuations stronger than −15 dB in chalcogenide and tellurite soft glass fibers with large Kerr nonlinearities. Using a realistic theoretical model, we numerically study squeezing for 2-micron light in step-index soft glass fibers by taking into account Kerr nonlinearity, distributed losses, and inelastic light scattering processes. Quantum noise squeezing stronger than −20 dB is numerically attained for a customized As2Se3 fibers with realistic parameters for the optimal fiber lengths shorter than 1 m. For commercial As2S3 and customized tellurite glass fibers, the expected squeezing in the −20–−15 dB range can be reached for fiber lengths of the order of 1 m. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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12 pages, 2972 KiB  
Article
Parity Deformed Tavis-Cummings Model: Entanglement, Parameter Estimation and Statistical Properties
by Mariam Algarni, Kamal Berrada, Sayed Abdel-Khalek and Hichem Eleuch
Mathematics 2022, 10(17), 3051; https://0-doi-org.brum.beds.ac.uk/10.3390/math10173051 - 24 Aug 2022
Cited by 10 | Viewed by 1115
Abstract
In this paper, we introduce the parity extension of the harmonic oscillator systems to develop the generalized Tavis-Cummings model (T-CM) based on a specific deformation of the Heisenberg algebra. We present a quantum scheme of a two-qubit system (TQS) interacting with a quantized [...] Read more.
In this paper, we introduce the parity extension of the harmonic oscillator systems to develop the generalized Tavis-Cummings model (T-CM) based on a specific deformation of the Heisenberg algebra. We present a quantum scheme of a two-qubit system (TQS) interacting with a quantized field that is initially prepared in parity deformed coherent states (PDCSs). The dynamical features of the considered system are explored in the presence of parity deformed parameter (PDP) and time-dependent coupling (t-dc). In particular, we examine the amount of the entanglement formed in the qubit–field and qubit–qubit states. We find that the maximal amount of the entanglement may be occurred periodically during the time evolution. Finally, we investigate the influence of PDP on the Fisher information and the photon statistics of the deformed field with respect to the main parameters of the system. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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12 pages, 18061 KiB  
Article
Exact Solutions of the Bloch Equations of a Two-Level Atom Driven by the Generalized Double Exponential Quotient Pulses with Dephasing
by Sofiane Grira, Nadia Boutabba and Hichem Eleuch
Mathematics 2022, 10(12), 2105; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122105 - 17 Jun 2022
Cited by 4 | Viewed by 2630
Abstract
We theoretically investigate a two-level atom driven by a time-dependent external field with a generalized double exponential temporal shape, in the presence of dephasing. Therefore, we provide exact analytical solutions for the population inversion, the real and the imaginary parts of the coherence [...] Read more.
We theoretically investigate a two-level atom driven by a time-dependent external field with a generalized double exponential temporal shape, in the presence of dephasing. Therefore, we provide exact analytical solutions for the population inversion, the real and the imaginary parts of the coherence for a family of chirped and time-dependent laser waveforms. We demonstrate that the remaining atomic population inversion can be controlled by the manipulation of the pulse’s shape structure. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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8 pages, 1330 KiB  
Article
Generation of Higher-Order Hermite–Gaussian Modes via Cascaded Phase-Only Spatial Light Modulators
by Manjun Yan and Long Ma
Mathematics 2022, 10(10), 1631; https://0-doi-org.brum.beds.ac.uk/10.3390/math10101631 - 11 May 2022
Cited by 7 | Viewed by 1733
Abstract
The spatial distribution of higher-order Hermite–Gaussian (HG) modes is more complicated than the fundamental mode, and the characteristics of different modes and their orthogonal characteristics have essential applications in the fields of measurement, imaging, and large-capacity communications. The main issue in future applications [...] Read more.
The spatial distribution of higher-order Hermite–Gaussian (HG) modes is more complicated than the fundamental mode, and the characteristics of different modes and their orthogonal characteristics have essential applications in the fields of measurement, imaging, and large-capacity communications. The main issue in future applications is how to efficiently generate higher-order HG modes. The spatial light modulator has high spatial resolution and excellent maneuverability, so it is a simple and effective way to generate higher-order HG modes. Here, the efficient generation of higher-order HG modes via cascaded spatial light modulators was experimentally investigated. For the HG90 mode, the conversion efficiency is 61%. The method with high conversion efficiency has promising application potentials in biophotonics, laser physics, and quantum information. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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19 pages, 1291 KiB  
Article
Efficient and Secure Measure-Resend Authenticated Semi-Quantum Key Distribution Protocol against Reflecting Attack
by Hung-Wen Wang, Chia-Wei Tsai, Jason Lin, Yu-Yun Huang and Chun-Wei Yang
Mathematics 2022, 10(8), 1241; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081241 - 10 Apr 2022
Cited by 8 | Viewed by 1677
Abstract
In 2021, Chang et al. proposed an authenticated semi-quantum key-distribution (ASQKD) protocol using single photons and an authenticated channel. However, an eavesdropper can launch a reflective attack to forge the receiver’s identity without being detected. In addition, Chang et al.’s ASQKD protocol assumes [...] Read more.
In 2021, Chang et al. proposed an authenticated semi-quantum key-distribution (ASQKD) protocol using single photons and an authenticated channel. However, an eavesdropper can launch a reflective attack to forge the receiver’s identity without being detected. In addition, Chang et al.’s ASQKD protocol assumes an authenticated classical channel between the sender and the receiver. It is considered illogical to have an authenticated channel in the ASQKD protocol. If these security issues are not addressed, the ASQKD protocol will fail to deliver the secret key. Therefore, this study proposes an efficient and secure ASQKD protocol to circumvent these problems using only single photons. Security analysis proves that the proposed ASQKD protocol can effectively avoid reflecting attacks, collective attacks, and other typical attacks. Compared with the existing ASQKD protocols, this study has the following advantages: based on a single photon, it demands less advanced quantum devices, the communication efficiency is higher than most protocols, it reduces the length of the required pre-shared keys, endures reflecting attacks, collective attacks, and there is no need for the classical channel. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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9 pages, 2007 KiB  
Article
Peculiar Features of Quantum Oscillator Excitation by Pulses with Different Envelopes
by Valery Astapenko
Mathematics 2022, 10(8), 1227; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081227 - 08 Apr 2022
Cited by 2 | Viewed by 1053
Abstract
We investigate the excitation of a quantum harmonic oscillator by pulses with different envelopes in terms of the excitation probability during the action of a pulse. The majority of attention is given to the dependence of the probability on the pulse duration and [...] Read more.
We investigate the excitation of a quantum harmonic oscillator by pulses with different envelopes in terms of the excitation probability during the action of a pulse. The majority of attention is given to the dependence of the probability on the pulse duration and the pulse carrier frequency for three envelopes: exponential, double exponential, and rectangular. The choice of these envelopes makes it possible to cover various features of the excitation of a quantum oscillator by an external pulse. In particular, the presence of weak and strong excitation modes is established, for each of which the dependences of the process probability on pulse parameters are studied. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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9 pages, 666 KiB  
Article
Coupled Harmonic Oscillator in a System of Free Particles
by Dmitry Makarov
Mathematics 2022, 10(3), 294; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030294 - 18 Jan 2022
Cited by 1 | Viewed by 1907
Abstract
The coupled quantum harmonic oscillator is one of the most researched and important model systems in quantum optics and quantum informatics. This system is often investigated for quantum entanglement in the environment. As a result, such studies are complex and can only be [...] Read more.
The coupled quantum harmonic oscillator is one of the most researched and important model systems in quantum optics and quantum informatics. This system is often investigated for quantum entanglement in the environment. As a result, such studies are complex and can only be carried out using numerical methods that do not reveal the general pattern of such systems. In this work, the external environment is considered to be two independent particles interacting with coupled harmonic oscillators. It is shown that such a system has an exact analytical solution to the dynamic Schrödinger equation. The analysis of this solution is carried out, and the main parameters of this system are revealed. The solutions obtained can be used to study more complex systems and their quantum entanglement. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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Review

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25 pages, 5494 KiB  
Review
Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect
by Dmitry Makarov
Mathematics 2022, 10(24), 4794; https://0-doi-org.brum.beds.ac.uk/10.3390/math10244794 - 16 Dec 2022
Cited by 4 | Viewed by 5598
Abstract
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 R [...] Read more.
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 R (or the transmission coefficient T, where R+T=1) and the phase shift ϕ. It has recently been shown that the constancy of these coefficients cannot always be satisfied for a waveguide BS, where R and ϕ 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. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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