Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach
Equivalent approaches to determine eigenfrequencies of the Liouvillians of open quantum systems are discussed using the solution of the Heisenberg-Langevin equations and the corresponding equations for operator moments. A simple damped two-level atom is analyzed to demonstrate the equivalence of bot...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2022-12-01
|
| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2022-12-22-883/pdf/ |
| _version_ | 1797978955385405440 |
|---|---|
| author | Jan Perina Jr Adam Miranowicz Grzegorz Chimczak Anna Kowalewska-Kudlaszyk |
| author_facet | Jan Perina Jr Adam Miranowicz Grzegorz Chimczak Anna Kowalewska-Kudlaszyk |
| author_sort | Jan Perina Jr |
| collection | DOAJ |
| description | Equivalent approaches to determine eigenfrequencies of the Liouvillians of open quantum systems are discussed using the solution of the Heisenberg-Langevin equations and the corresponding equations for operator moments. A simple damped two-level atom is analyzed to demonstrate the equivalence of both approaches. The suggested method is used to reveal the structure as well as eigenfrequencies of the dynamics matrices of the corresponding equations of motion and their degeneracies for interacting bosonic modes described by general quadratic Hamiltonians. Quantum Liouvillian exceptional and diabolical points and their degeneracies are explicitly discussed for the case of two modes. Quantum hybrid diabolical exceptional points (inherited, genuine, and induced) and hidden exceptional points, which are not recognized directly in amplitude spectra, are observed. The presented approach via the Heisenberg-Langevin equations paves the general way to a detailed analysis of quantum exceptional and diabolical points in infinitely dimensional open quantum systems. |
| first_indexed | 2024-04-11T05:31:15Z |
| format | Article |
| id | doaj.art-396df4f3fa4e4103bf1ecaa089537476 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-11T05:31:15Z |
| publishDate | 2022-12-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-396df4f3fa4e4103bf1ecaa0895374762022-12-22T17:04:17ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2022-12-01688310.22331/q-2022-12-22-88310.22331/q-2022-12-22-883Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approachJan Perina JrAdam MiranowiczGrzegorz ChimczakAnna Kowalewska-KudlaszykEquivalent approaches to determine eigenfrequencies of the Liouvillians of open quantum systems are discussed using the solution of the Heisenberg-Langevin equations and the corresponding equations for operator moments. A simple damped two-level atom is analyzed to demonstrate the equivalence of both approaches. The suggested method is used to reveal the structure as well as eigenfrequencies of the dynamics matrices of the corresponding equations of motion and their degeneracies for interacting bosonic modes described by general quadratic Hamiltonians. Quantum Liouvillian exceptional and diabolical points and their degeneracies are explicitly discussed for the case of two modes. Quantum hybrid diabolical exceptional points (inherited, genuine, and induced) and hidden exceptional points, which are not recognized directly in amplitude spectra, are observed. The presented approach via the Heisenberg-Langevin equations paves the general way to a detailed analysis of quantum exceptional and diabolical points in infinitely dimensional open quantum systems.https://quantum-journal.org/papers/q-2022-12-22-883/pdf/ |
| spellingShingle | Jan Perina Jr Adam Miranowicz Grzegorz Chimczak Anna Kowalewska-Kudlaszyk Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach Quantum |
| title | Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach |
| title_full | Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach |
| title_fullStr | Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach |
| title_full_unstemmed | Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach |
| title_short | Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach |
| title_sort | quantum liouvillian exceptional and diabolical points for bosonic fields with quadratic hamiltonians the heisenberg langevin equation approach |
| url | https://quantum-journal.org/papers/q-2022-12-22-883/pdf/ |
| work_keys_str_mv | AT janperinajr quantumliouvillianexceptionalanddiabolicalpointsforbosonicfieldswithquadratichamiltonianstheheisenberglangevinequationapproach AT adammiranowicz quantumliouvillianexceptionalanddiabolicalpointsforbosonicfieldswithquadratichamiltonianstheheisenberglangevinequationapproach AT grzegorzchimczak quantumliouvillianexceptionalanddiabolicalpointsforbosonicfieldswithquadratichamiltonianstheheisenberglangevinequationapproach AT annakowalewskakudlaszyk quantumliouvillianexceptionalanddiabolicalpointsforbosonicfieldswithquadratichamiltonianstheheisenberglangevinequationapproach |