dorsal/arxiv
View SchemaQuantum chaos and fractals with atoms in cavities
| Authors | M. Uleysky, L. Kon'kov, S. Prants |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212008 |
| URL | https://arxiv.org/abs/quant-ph/0212008 |
| DOI | 10.1016/S1007-5704(03)00043-1 |
| Journal | M. Uleysky, L. Kon'kov, S. Prants. Quantum chaos and fractals with atoms in cavities. Communications in Nonlinear Science and Numerical Simulation. V.8 N3/4 (2003) 329-347. |
Abstract
We study the coupled translational, electronic, and field dynamics of the combined system "a two-level atom + a single-mode quantized field + a standing-wave ideal cavity". We derive Hamilton -- Schr\"odinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At large values of detuning $|\delta|\gg 1$, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler -- Rabi resonance, deep Rabi oscillations that may occur at any large value of $|\delta|$ to be equal to $|\alpha p_0|$, is found numerically and described analytically (with $\alpha$ to be the normalized recoil frequency and $p_0$ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. In the chaotic regime values of the population inversion $z_{out}$, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion $z_{in}$ that the probability of detecting any value of $z_{out}$ in the admissible interval becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.
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"abstract": "We study the coupled translational, electronic, and field dynamics of the\ncombined system \"a two-level atom + a single-mode quantized field + a\nstanding-wave ideal cavity\". We derive Hamilton -- Schr\\\"odinger equations for\nprobability amplitudes and averaged position and momentum of a point-like atom\ninteracting with the quantized field in a standing-wave cavity. They\nconstitute, in general, an infinite-dimensional set of equations with an\ninfinite number of integrals of motion which may be reduced to a dynamical\nsystem with four degrees of freedom if the quantized field is supposed to be\ninitially prepared in a Fock state. This system is found to produce semiquantum\nchaos with positive values of the maximal Lyapunov exponent. At large values of\ndetuning $|\\delta|\\gg 1$, the Rabi atomic oscillations are usually shallow, and\nthe dynamics is found to be almost regular. The Doppler -- Rabi resonance, deep\nRabi oscillations that may occur at any large value of $|\\delta|$ to be equal\nto $|\\alpha p_0|$, is found numerically and described analytically (with\n$\\alpha$ to be the normalized recoil frequency and $p_0$ the initial atomic\nmomentum). Two gedanken experiments are proposed to detect manifestations of\nsemiquantum chaos in real experiments. In the chaotic regime values of the\npopulation inversion $z_{out}$, measured with atoms after transversing a\ncavity, are so sensitive to small changes in the initial inversion $z_{in}$\nthat the probability of detecting any value of $z_{out}$ in the admissible\ninterval becomes almost unity in a short time. Chaotic wandering of a two-level\natom in a quantized Fock field is shown to be fractal. Fractal-like structures,\ntypical for chaotic scattering, are numerically found in the dependence of the\ntime of exit of atoms from the cavity on their initial momenta.",
"arxiv_id": "quant-ph/0212008",
"authors": [
"M. Uleysky",
"L. Kon\u0027kov",
"S. Prants"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1016/S1007-5704(03)00043-1",
"journal_ref": "M. Uleysky, L. Kon\u0027kov, S. Prants. Quantum chaos and fractals with\n atoms in cavities. Communications in Nonlinear Science and Numerical\n Simulation. V.8 N3/4 (2003) 329-347.",
"title": "Quantum chaos and fractals with atoms in cavities",
"url": "https://arxiv.org/abs/quant-ph/0212008"
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