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Coelho SS, Queiroz L, Alves DT. Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis-Riesenfeld Dynamical Invariant Method. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1851. [PMID: 36554256 PMCID: PMC9778280 DOI: 10.3390/e24121851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 12/14/2022] [Accepted: 12/16/2022] [Indexed: 06/17/2023]
Abstract
Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency ω0, which undergoes a sudden jump to a frequency ω1 and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis−Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when ω1<ω0. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state.
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Affiliation(s)
- Stanley S. Coelho
- Faculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, Brazil
| | - Lucas Queiroz
- Faculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, Brazil
| | - Danilo T. Alves
- Faculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, Brazil
- Centro de Física, Universidade do Minho, 4710-057 Braga, Portugal
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Citeli de Freitas M, Dantas Meireles V, Dodonov VV. Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E980. [PMID: 33286749 PMCID: PMC7597293 DOI: 10.3390/e22090980] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Revised: 08/23/2020] [Accepted: 08/31/2020] [Indexed: 11/16/2022]
Abstract
We consider the problem of minimization of products of mean values of the high powers of operators x and p. From this point of view, we study several two-term superpositions of the Fock states, as well as three popular families of infinite superpositions: squeezed states, even/odd coherent states, and orthogonal even coherent states (or compass states). The new element is the analysis of products of the corresponding (co)variances and the related generalized (Robertson-Schrödinger) intelligent states (RSIS). In particular, we show that both Fock and pure Gaussian homogeneous states are RSIS for the fourth powers (but not for the sixth ones). We show that lower bounds of the high-order uncertainty products can be significantly below the vacuum values. In this connection, the concept of significant and weak high-order squeezing is introduced.
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Affiliation(s)
- Miguel Citeli de Freitas
- Institute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, DF, Brazil; (M.C.d.F.); (V.D.M.)
| | - Vitor Dantas Meireles
- Institute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, DF, Brazil; (M.C.d.F.); (V.D.M.)
- Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos 13560-970, SP, Brazil
| | - Viktor V. Dodonov
- Institute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, DF, Brazil; (M.C.d.F.); (V.D.M.)
- International Center for Physics, University of Brasilia, Brasilia 70919-970, DF, Brazil
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Algarni M, Al-Ghamdi H, Abdel-Khalek S. Entanglement and atomic Fisher information of a two qubits and optical field in squeezed thermal state. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-179532] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- M. Algarni
- Mathematical Sciences Department, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
| | - H. Al-Ghamdi
- Physics Department, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
| | - S. Abdel-Khalek
- Mathematics Department, Faculty of Sciences, Taif University, Taif, Saudi Arabia
- Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt
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Maslennikov G, Ding S, Hablützel R, Gan J, Roulet A, Nimmrichter S, Dai J, Scarani V, Matsukevich D. Quantum absorption refrigerator with trapped ions. Nat Commun 2019; 10:202. [PMID: 30643131 PMCID: PMC6331551 DOI: 10.1038/s41467-018-08090-0] [Citation(s) in RCA: 50] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2017] [Accepted: 12/07/2018] [Indexed: 11/09/2022] Open
Abstract
In recent years substantial efforts have been expended in extending thermodynamics to single quantum systems. Quantum effects have emerged as a resource that can improve the performance of heat machines. However in the fully quantum regime their implementation still remains a challenge. Here, we report an experimental realization of a quantum absorption refrigerator in a system of three trapped ions, with three of its normal modes of motion coupled by a trilinear Hamiltonian such that heat transfer between two modes refrigerates the third. We investigate the dynamics and steady-state properties of the refrigerator and compare its cooling capability when only thermal states are involved to the case when squeezing is employed as a quantum resource. We also study the performance of such a refrigerator in the single shot regime made possible by coherence and demonstrate cooling below both the steady-state energy and a benchmark set by classical thermodynamics.
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Affiliation(s)
- Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Shiqian Ding
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore.,JILA, National Institute of Standards and Technology and University of Colorado, and Department of Physics, University of Colorado, Boulder, CO, 80309, USA
| | - Roland Hablützel
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Jaren Gan
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Alexandre Roulet
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Stefan Nimmrichter
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Jibo Dai
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Valerio Scarani
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore.,Department of Physics, National University of Singapore, 2 Science Dr 3, Singapore, 117551, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore. .,Department of Physics, National University of Singapore, 2 Science Dr 3, Singapore, 117551, Singapore.
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Abd Al-Kader GM, Obada ASF. Analytic Representations Based on SU(1,1) Lie Algebra Coherent States for Squeezed Displaced Fock States. APPLIED CATEGORICAL STRUCTURES 2008; 16:3-11. [DOI: 10.1007/s10485-006-9032-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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D’Auria V, Porzio A, Solimeno S, Olivares S, Paris MGA. Characterization of bipartite states using a single homodyne detector. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/1464-4266/7/12/044] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Dodonov VV. `Nonclassical' states in quantum optics: a `squeezed' review of the first 75 years. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/1464-4266/4/1/201] [Citation(s) in RCA: 639] [Impact Index Per Article: 29.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Marian P, Marian TA, Scutaru H. Inseparability of mixed two-mode Gaussian states generated with aSU(1,1) interferometer. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/35/322] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Vourdas A, Bishop RF. Thermal coherent states in the Bargmann representation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:3331-3339. [PMID: 9911281 DOI: 10.1103/physreva.50.3331] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Selvadoray M, Kumar MS, Simon R. Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 49:4957-4967. [PMID: 9910816 DOI: 10.1103/physreva.49.4957] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Marian P, Marian TA. Squeezed states with thermal noise. II. Damping and photon counting. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:4487-4495. [PMID: 9909457 DOI: 10.1103/physreva.47.4487] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Marian P, Marian TA. Squeezed states with thermal noise. I. Photon-number statistics. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:4474-4486. [PMID: 9909456 DOI: 10.1103/physreva.47.4474] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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