dorsal/arxiv
View SchemaReply on `comment on our paper `Single two-level ion in an anharmonic-oscillator trap: Time evolution of the Q function and population inversion ''
| Authors | S. Shelly Sharma, N. K. Sharma, Larry Zamick |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9903068 |
| URL | https://arxiv.org/abs/quant-ph/9903068 |
| DOI | 10.1103/PhysRevA.59.3138 |
| Journal | Phys.Rev.A59:3138-3140,1999 |
Abstract
We show here that the model Hamiltonian used in our paper for ion vibrating in a q-analog harmonic oscillator trap and interacting with a classical single-mode light field is indeed obtained by replacing the usual bosonic creation and annihilation operators of the harmonic trap model by their q-deformed counterparts. The approximations made in our paper amount to using for the ion-laser interaction in a q-analog harmonic oscillator trap, the operator $F_{q}=exp{-(|\epsilon|^2}/2)}exp{i\epsilon A^{\dagger}}exp{i\epsilon A}$, which is analogous to the corresponding operator for ion in a harmonic oscillator trap that is $F=exp{-(|\epsilon|^2 /2)}exp{i\epsilon a^{\dagger }}exp{i\epsilon a}$. In our article we do not claim to have diagonalized the operator, $F_q = exp{i \epsilon (A^{\dagger}+A)}$, for which the basis states |g,m> and |e,m> are not analytic vectors.
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"abstract": "We show here that the model Hamiltonian used in our paper for ion vibrating\nin a q-analog harmonic oscillator trap and interacting with a classical\nsingle-mode light field is indeed obtained by replacing the usual bosonic\ncreation and annihilation operators of the harmonic trap model by their\nq-deformed counterparts. The approximations made in our paper amount to using\nfor the ion-laser interaction in a q-analog harmonic oscillator trap, the\noperator $F_{q}=exp{-(|\\epsilon|^2}/2)}exp{i\\epsilon A^{\\dagger}}exp{i\\epsilon\nA}$, which is analogous to the corresponding operator for ion in a harmonic\noscillator trap that is $F=exp{-(|\\epsilon|^2 /2)}exp{i\\epsilon a^{\\dagger\n}}exp{i\\epsilon a}$. In our article we do not claim to have diagonalized the\noperator, $F_q = exp{i \\epsilon (A^{\\dagger}+A)}$, for which the basis states\n|g,m\u003e and |e,m\u003e are not analytic vectors.",
"arxiv_id": "quant-ph/9903068",
"authors": [
"S. Shelly Sharma",
"N. K. Sharma",
"Larry Zamick"
],
"categories": [
"quant-ph",
"nucl-th"
],
"doi": "10.1103/PhysRevA.59.3138",
"journal_ref": "Phys.Rev.A59:3138-3140,1999",
"title": "Reply on `comment on our paper `Single two-level ion in an anharmonic-oscillator trap: Time evolution of the Q function and population inversion \u0027\u0027",
"url": "https://arxiv.org/abs/quant-ph/9903068"
},
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