Coherent and incoherent superposition of transition matrix elements of the squeezing operator
We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969 Zh. Eksp. Teor. Fiz. 56 1375–90)...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2022-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ac6b4d |
| _version_ | 1827871033590284288 |
|---|---|
| author | Sándor Varró |
| author_facet | Sándor Varró |
| author_sort | Sándor Varró |
| collection | DOAJ |
| description | We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969 Zh. Eksp. Teor. Fiz. 56 1375–90) long ago, in their thorough analysis of the parametric excitation of harmonic oscillators. They expressed the matrix elements in terms of transcendental functions, the associated Legendre functions. In the present paper we will show that these matrix elements can also be derived in a different form, expressed by the classical Gegenbauer polynomials. This new expression makes it possible to determine coherent and incoherent superpositions of these matrix elements in closed analytic forms. As an application, we describe multiphoton transitions in the system ‘charged particle + electromagnetic radiation’, induced by a (strong) coherent field or by a black-body radiation component (with a Planck–Bose photon number distribution). The exact results are compared with the semi-classical ones. We will show that in case of interaction with a thermal field, the semi-classical result (with a Gaussian stochastic field amplitude) yields an acceptable approximation only in the Rayleigh–Jeans limit, however, in the Wien limit it completely fails. |
| first_indexed | 2024-03-12T16:04:15Z |
| format | Article |
| id | doaj.art-10d90c7b09814b8ebf38bd7797bfa669 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:04:15Z |
| publishDate | 2022-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-10d90c7b09814b8ebf38bd7797bfa6692023-08-09T14:24:19ZengIOP PublishingNew Journal of Physics1367-26302022-01-0124505303510.1088/1367-2630/ac6b4dCoherent and incoherent superposition of transition matrix elements of the squeezing operatorSándor Varró0Wigner Research Centre for Physics , Eötvös Loránd Research Network, Budapest, Hungary; ELI-ALPS Attosecond Light Pulse Source, ELI-HU Non-Profit Ltd. , Szeged, HungaryWe discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969 Zh. Eksp. Teor. Fiz. 56 1375–90) long ago, in their thorough analysis of the parametric excitation of harmonic oscillators. They expressed the matrix elements in terms of transcendental functions, the associated Legendre functions. In the present paper we will show that these matrix elements can also be derived in a different form, expressed by the classical Gegenbauer polynomials. This new expression makes it possible to determine coherent and incoherent superpositions of these matrix elements in closed analytic forms. As an application, we describe multiphoton transitions in the system ‘charged particle + electromagnetic radiation’, induced by a (strong) coherent field or by a black-body radiation component (with a Planck–Bose photon number distribution). The exact results are compared with the semi-classical ones. We will show that in case of interaction with a thermal field, the semi-classical result (with a Gaussian stochastic field amplitude) yields an acceptable approximation only in the Rayleigh–Jeans limit, however, in the Wien limit it completely fails.https://doi.org/10.1088/1367-2630/ac6b4dparametric processessqueezingphoton number distributionmultiphoton processesstrong-field physicsquantum optics |
| spellingShingle | Sándor Varró Coherent and incoherent superposition of transition matrix elements of the squeezing operator New Journal of Physics parametric processes squeezing photon number distribution multiphoton processes strong-field physics quantum optics |
| title | Coherent and incoherent superposition of transition matrix elements of the squeezing operator |
| title_full | Coherent and incoherent superposition of transition matrix elements of the squeezing operator |
| title_fullStr | Coherent and incoherent superposition of transition matrix elements of the squeezing operator |
| title_full_unstemmed | Coherent and incoherent superposition of transition matrix elements of the squeezing operator |
| title_short | Coherent and incoherent superposition of transition matrix elements of the squeezing operator |
| title_sort | coherent and incoherent superposition of transition matrix elements of the squeezing operator |
| topic | parametric processes squeezing photon number distribution multiphoton processes strong-field physics quantum optics |
| url | https://doi.org/10.1088/1367-2630/ac6b4d |
| work_keys_str_mv | AT sandorvarro coherentandincoherentsuperpositionoftransitionmatrixelementsofthesqueezingoperator |