Abstract
We introduce Hermite-polynomial-field excited coherent state (HPFECS) and then investigate analytically its evolution in an amplitude damping channel. We find that it evolves into a Laguerre-polynomial-weighted-chaotic photon field in this process, which turns out to be a new nonclassical state. The Q-function of this novel state is also given.
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This work is supported by the Natural Science Foundation of the Anhui Higher Education Institutions of China (Grant No. KJ2016A672).
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Appendix A: Derivation of (12)
Appendix A: Derivation of (12)
Using the operator of the Hermite polynomials method, we have
then we construct
From (57), we see
Combining (56) and (58) we lead to
Since the both sides of (59) are in antinormal ordering. we restore to
1.1 Appendix B: Derivation of (14)
1.2 Appendix C: Derivation of (35)
Using basis functions in complete space, we have
Introducing a special function for two-mode hermite polynomials, then we can get
The (35) is derived by simple subsitution.
1.3 Appendix D: Derivation of (37)
In the spirit of the operator of Hermite polynomial method, we consider
Then we make the sum
Combining (64) and (65) we lead to
Since the both sides of (66) are in antinormal ordering, we restore to
1.4 Appendix E: Derivation of (46)
Using the operator of the Hermite polynomials method, we have
where the symbol ⋮ ⋮ denotes the anti-normally ordered product of operators a and a‡.
Converting normal ordering to antinormal ordering, we lead to
Letting \(a^{\dag }\rightarrow x^{\prime },a\rightarrow y^{\prime }, \) we obtain
Using the formula
we have
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Zhang, Cc., Du, Jm. & Ren, G. Amplitude Damping of Hermite-Polynomial-Field Excited Coherent State. Int J Theor Phys 58, 261–274 (2019). https://doi.org/10.1007/s10773-018-3928-7
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DOI: https://doi.org/10.1007/s10773-018-3928-7