The Quantum analysis of Nondegenerate Three-Level Laser with Spontaneous Emission and Noiseless Vacuum Reservoir
Keywords:operator dynamics, quadrature squeezing, second-order correlations, photon entanglement
The analysis of quantum properties of the cavity light produced by a coherently driven nondegenerate three-level laser possessing an open cavity and coupled to a two-mode vacuum reservoir is presented. The normal ordering of noise operators associated with the vacuum reservoir is considered. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, the squeezing properties, entanglement amplification, and the normalized second-order correlation function of the cavity radiation are described. The three-level laser generates squeezed light under certain conditions, with maximum intracavity squeezing being 50% below the vacuum-state level. Moreover, it is found that the presence of spontaneous emission increases the quadrature squeezing and entanglement and decreses the mean photon number of the two-mode cavity radiation.
J.M. Liu, B.S. Shi, X.F. Fan, J. Li, G.C. Guo. Wigner function description of continuous variable entanglement swapping. J. Opt. B: Quant. Semiclass. Opt. 3, 189 (2001). https://doi.org/10.1088/1464-4266/3/4/301
S.L. Braunstein, H.J. Kimble. Dense coding for continuous variables. Phys. Rev. A 61, 42302 (2000). https://doi.org/10.1103/PhysRevA.61.042302
S. Lloyd and S.L. Braunstein. Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784 (1999). https://doi.org/10.1103/PhysRevLett.82.1784
S.L. Braunstein. Quantum error correction for communication with linear optics. Nature 394, 47 (1998). https://doi.org/10.1038/27850
T.C. Ralph. Continuous variable quantum cryptography. Phys. Rev. A 61, 010302 (2000). https://doi.org/10.1103/PhysRevA.62.062306
A. Einstein, B. Podolsky, R. Rosen. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935). https://doi.org/10.1103/PhysRev.47.777
M.O. Scully, K. Wodkiewicz, M.S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn. Two-photon correlated-spontaneous-emission laser: Quantum noise quenching and squeezing. Phys. Rev. Lett. 60, 1832 (1988). https://doi.org/10.1103/PhysRevLett.60.1832
E. Alebachew. Enhanced squeezing and entanglement in a non-degenerate three-level cascade laser with injected squeezed light. Opt. Commun. 280, 133 (2007). https://doi.org/10.1016/j.optcom.2007.08.017
T. Abebe. Enhancement of squeezing and entanglement in a non-degenerate three-level cascade laser with coherently driven cavity. Ukr. J. Phys. 63, No. 8, 733 (2018). https://doi.org/10.15407/ujpe63.8.733
N. Lu, F.X. Zhao, J. Bergou. Nonlinear theory of a two-photon correlated-spontaneous-emission laser: A coherently pumped two-level-two-photon laser. Phys. Rev. A 39, 5189 (1989). https://doi.org/10.1103/PhysRevA.39.5189
N. Lu, S.Y. Zhu. Quantum theory of two-photon correlated-spontaneous-emission lasers: Exact atom-field interaction Hamiltonian approach. Phys. Rev. A 40, 5735 (1989). https://doi.org/10.1103/PhysRevA.40.5735
C.A. Blockley, D.F. Walls. Intensity fluctuations in a frequency down-conversion process with three-level atoms Phys. Rev. A 43, 5049 (1991). https://doi.org/10.1103/PhysRevA.43.5049
N.A. Ansari, J. Gea-Banacloche, M.S. Zubairy. Phase-sensitive amplification in a three-level atomic system. Phys. Rev. A 41, 5179 (1990). https://doi.org/10.1103/PhysRevA.41.5179
N.A. Ansari. Effect of atomic coherence on the second-and higher-order squeezing in a two-photon three-level cascade atomic system. Phys. Rev. A 48, 4686 (1993). https://doi.org/10.1103/PhysRevA.48.4686
J. Anwar, M.S. Zubairy. Quantum-statistical properties of noise in a phase-sensitive linear amplifier. Phys. Rev. A 49, 481 (1994). https://doi.org/10.1103/PhysRevA.49.481
N.A. Ansari. Theory of a two-mode phase-sensitive amplifier. Phys. Rev. A 46, 1560 (1992). https://doi.org/10.1103/PhysRevA.46.1560
H. Xiong, M.O. Scully, M.S. Zubairy. Correlated spontaneous emission laser as an entanglement amplifier. Phys. Rev. Lett. 94, 023601 (2005). https://doi.org/10.1103/PhysRevLett.94.023601
C.M. Caves, B.L. Schumaker. New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states. Phys. Rev. A 31, 3068 (1985). https://doi.org/10.1103/PhysRevA.31.3068
C.J. Villas-Boas, M.H.Y. Moussa. One-step generation of high-quality squeezed and EPR states in cavity QED. Eur. Phys. J. D 32, 147 (2005). https://doi.org/10.1140/epjd/e2004-00178-y
S. Tesfa. Entanglement amplification in a nondegenerate three-level cascade laser. Phys. Rev. A 74, 043816 (2006). https://doi.org/10.1103/PhysRevA.74.043816
E. Alebachew, K. Fesseha. Coherently driven three-level laser with parametric amplifier. Opt. Commun. 265, 314 (2006). https://doi.org/10.1016/j.optcom.2006.03.017
F. Kassahun. Three-level laser dynamics with the atoms pumped by electron bombardment. https://arXiv:1105.1438v3 quant-ph (2012).
F. Kassahun. Stimulated emission by two-level atoms pumped to the upper level. Opt. Commun. 284, 1357 (2011). https://doi.org/10.1016/j.optcom.2010.11.026
F. Kassahun. Refined Quantum Analysis of Light (CreateSpace Independent Publ. Platform, 2014).
L.M. Duan, G. Giedke, J.I. Cirac, P. Zoller. Inseparability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2722 (2000). https://doi.org/10.1103/PhysRevLett.84.2722
M.O. Scully, M.S. Zubairy. Quantum Optics (Cambridge Univ. Press, 1997).
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.