dorsal/arxiv
View SchemaSchr\"{o}dinger cat state of trapped ions in harmonic and anharmonic oscillator traps
| Authors | S. Shelly Sharma, N. K. Sharma |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011090 |
| URL | https://arxiv.org/abs/quant-ph/0011090 |
| DOI | 10.1088/0953-4075/35/7/303 |
| Journal | J.Phys. B35 (2002) 1643 |
Abstract
We examine the time evolution of a two level ion interacting with a light field in harmonic oscillator trap and in a trap with anharmonicities. The anharmonicities of the trap are quantified in terms of the deformation parameter $\tau $ characterizing the q-analog of the harmonic oscillator trap. Initially the ion is prepared in a Schr\"{o}dinger cat state. The entanglement of the center of mass motional states and the internal degrees of freedom of the ion results in characteristic collapse and revival pattern. We calculate numerically the population inversion I(t), quasi-probabilities $Q(t),$ and partial mutual quantum entropy S(P), for the system as a function of time. Interestingly, small deformations of the trap enhance the contrast between population inversion collapse and revival peaks as compared to the zero deformation case. For \beta =3 and $4,(% \beta $ determines the average number of trap quanta linked to center of mass motion) the best collapse and revival sequence is obtained for \tau =0.0047 and \tau =0.004 respectively. For large values of \tau decoherence sets in accompanied by loss of amplitude of population inversion and for \tau \sim 0.1 the collapse and revival phenomenon disappear. Each collapse or revival of population inversion is characterized by a peak in S(P) versus t plot. During the transition from collapse to revival and vice-versa we have minimum mutual entropy value that is S(P)=0. Successive revival peaks show a lowering of the local maximum point indicating a dissipative irreversible change in the ionic state. Improved definition of collapse and revival pattern as the anharminicity of the trapping potential increases is also reflected in the Quasi- probability versus t plots.
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"abstract": "We examine the time evolution of a two level ion interacting with a light\nfield in harmonic oscillator trap and in a trap with anharmonicities. The\nanharmonicities of the trap are quantified in terms of the deformation\nparameter $\\tau $ characterizing the q-analog of the harmonic oscillator trap.\nInitially the ion is prepared in a Schr\\\"{o}dinger cat state. The entanglement\nof the center of mass motional states and the internal degrees of freedom of\nthe ion results in characteristic collapse and revival pattern. We calculate\nnumerically the population inversion I(t), quasi-probabilities $Q(t),$ and\npartial mutual quantum entropy S(P), for the system as a function of time.\nInterestingly, small deformations of the trap enhance the contrast between\npopulation inversion collapse and revival peaks as compared to the zero\ndeformation case. For \\beta =3 and $4,(% \\beta $ determines the average number\nof trap quanta linked to center of mass motion) the best collapse and revival\nsequence is obtained for \\tau =0.0047 and \\tau =0.004 respectively. For large\nvalues of \\tau decoherence sets in accompanied by loss of amplitude of\npopulation inversion and for \\tau \\sim 0.1 the collapse and revival phenomenon\ndisappear. Each collapse or revival of population inversion is characterized by\na peak in S(P) versus t plot. During the transition from collapse to revival\nand vice-versa we have minimum mutual entropy value that is S(P)=0. Successive\nrevival peaks show a lowering of the local maximum point indicating a\ndissipative irreversible change in the ionic state. Improved definition of\ncollapse and revival pattern as the anharminicity of the trapping potential\nincreases is also reflected in the Quasi- probability versus t plots.",
"arxiv_id": "quant-ph/0011090",
"authors": [
"S. Shelly Sharma",
"N. K. Sharma"
],
"categories": [
"quant-ph",
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],
"doi": "10.1088/0953-4075/35/7/303",
"journal_ref": "J.Phys. B35 (2002) 1643",
"title": "Schr\\\"{o}dinger cat state of trapped ions in harmonic and anharmonic oscillator traps",
"url": "https://arxiv.org/abs/quant-ph/0011090"
},
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