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Bakke K, Salvador C. A doubly anharmonic oscillator in an induced electric dipole system. Proc Math Phys Eng Sci 2018; 474:20170881. [DOI: 10.1098/rspa.2017.0881] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Accepted: 08/03/2018] [Indexed: 11/12/2022] Open
Abstract
The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schrödinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values.
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Oliveira AB, Bakke K. Some aspects of an induced electric dipole moment in rotating and non-rotating frames. R Soc Open Sci 2017; 4:170541. [PMID: 28680691 PMCID: PMC5493933 DOI: 10.1098/rsos.170541] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2017] [Accepted: 05/26/2017] [Indexed: 05/20/2023]
Abstract
Quantum effects on a neutral particle (atom or molecule) with an induced electric dipole moment are investigated when it is subject to the Kratzer potential and a scalar potential proportional to the radial distance. In addition, this neutral is placed in a region with electric and magnetic fields. This system is analysed in both non-rotating and rotating reference frames. Then, it is shown that bound state solutions to the Schrödinger equation can be achieved and, in the search for polynomial solutions to the radial wave function, a restriction on the values of the cyclotron frequency is analysed in both reference frames.
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Oliveira AB, Bakke K. Effects on a Landau-type system for a neutral particle with no permanent electric dipole moment subject to the Kratzer potential in a rotating frame. Proc Math Phys Eng Sci 2016; 472:20150858. [PMID: 27436966 PMCID: PMC4950191 DOI: 10.1098/rspa.2015.0858] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2015] [Accepted: 05/10/2016] [Indexed: 11/12/2022] Open
Abstract
The behaviour of a neutral particle (atom, molecule) with an induced electric dipole moment in a region with a uniform effective magnetic field under the influence of the Kratzer potential (Kratzer 1920 Z. Phys.3, 289-307. (doi:10.1007/BF01327754)), and rotating effects is analysed. It is shown that the degeneracy of the Landau-type levels is broken and the angular frequency of the system acquires a new contribution that stems from the rotation effects. Moreover, in the search for bound state solutions, it is shown that the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum, the angular velocity of the rotating frame and by the parameters associated with the Kratzer potential.
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Affiliation(s)
| | - Knut Bakke
- Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa, Paraíba, Brazil
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Schweiner F, Main J, Cartarius H, Wunner G. Classical dynamics and localization of resonances in the high-energy region of the hydrogen atom in crossed fields. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:012915. [PMID: 25679690 DOI: 10.1103/physreve.91.012915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2014] [Indexed: 06/04/2023]
Abstract
When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom, a saddle point (called the Stark saddle point) appears. For energies slightly above the saddle point energy, one can find classical orbits that are located in the vicinity of this point. We follow those so-called quasi-Penning orbits to high energies and field strengths, observing structural changes and uncovering their bifurcation behavior. By plotting the stability behavior of those orbits against energy and field strength, the appearance of a stability apex is reported. A cusp bifurcation, located in the vicinity of the apex, will be investigated in detail. In this cusp bifurcation, another orbit of similar shape is found. This orbit becomes completely stable in the observed region of positive energy, i.e., in a region of parameter space, where the Kepler-like orbits located around the nucleus are already unstable. By quantum mechanically exact calculations, we prove the existence of signatures in quantum spectra belonging to those orbits. Husimi distributions are used to compare quantum-Poincaré sections with the extension of the classical torus structure around the orbits. Since periodic orbit theory predicts that each classical periodic orbit contributes an oscillating term to photoabsorption spectra, we finally give an estimation for future experiments, which could verify the existence of the stable orbits.
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Affiliation(s)
- Frank Schweiner
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jörg Main
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Holger Cartarius
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Günter Wunner
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
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Abstract
The optical response of the fluorescent molecule IR144 in solution is probed by pairs of collinear pulses with intensity just above the linear dependence using two different pulse shaping methods. The first approach mimics a Michelson interferometer, while the second approach, known as multiple independent comb shaping (MICS), eliminates spectral interference. The comparison of interfering and non-interfering pulses reveals that linear interference between the pulses leads to the loss of experimental information at early delay times. In both cases, the delay between the pulses is controlled with attosecond resolution and the sample fluorescence and stimulated emission are monitored simultaneously. An out-of-phase behavior is observed for fluorescence and stimulated emission, with the fluorescence signal having a minimum at zero time delay. Experimental findings are modeled using a two-level system with relaxation that closely matches the phase difference between fluorescence and stimulated emission and the relative intensities of the measured effects.
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Affiliation(s)
- Arkaprabha Konar
- †Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Jay D Shah
- †Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Vadim V Lozovoy
- †Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Marcos Dantus
- †Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
- ‡Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
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Lougovski P, Solano E, Zhang ZM, Walther H, Mack H, Schleich WP. Fresnel representation of the Wigner function: an operational approach. Phys Rev Lett 2003; 91:010401. [PMID: 12906520 DOI: 10.1103/physrevlett.91.010401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2002] [Revised: 04/16/2003] [Indexed: 05/24/2023]
Abstract
We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in ion traps [Phys. Rev. Lett. 76, 1796 (1996)]] and in cavity QED [Nature (London) 403, 743 (2000)]]. The values of the Wigner functions of the underlying states at the origin of phase space are W(|0>)(0)=+1.75 for the vibrational ground state and W(|1>)(0)=-1.4 for the one-photon number state. We generalize this method to wave packets in arbitrary potentials.
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Affiliation(s)
- P Lougovski
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
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Kalinski M, Eberly JH. New States of Hydrogen in a Circularly Polarized Electromagnetic Field. Phys Rev Lett 1996; 77:2420-2423. [PMID: 10061949 DOI: 10.1103/physrevlett.77.2420] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Uzer T, Farrelly D. Threshold ionization dynamics of the hydrogen atom in crossed electric and magnetic fields. Phys Rev A 1995; 52:R2501-R2504. [PMID: 9912634 DOI: 10.1103/physreva.52.r2501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wang Q, Starace AF. Coherent control of H- photodetachment in parallel static electric and magnetic fields. Phys Rev A 1995; 51:1260-1276. [PMID: 9911708 DOI: 10.1103/physreva.51.1260] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Fielding HH, Wals J. Rydberg-electron wave-packet dynamics in parallel electric and magnetic fields and evidence for stabilization. Phys Rev A 1995; 51:611-619. [PMID: 9911621 DOI: 10.1103/physreva.51.611] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wals J, Fielding HH, Christian JF, Snoek LC. Observation of Rydberg wave packet dynamics in a Coulombic and magnetic field. Phys Rev Lett 1994; 72:3783-3786. [PMID: 10056296 DOI: 10.1103/physrevlett.72.3783] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Broers B, Christian JF. Experimental investigation of rubidium atoms above the field-ionization limit using a time-resolved wave-packet approach. Phys Rev A 1994; 49:2498-2507. [PMID: 9910525 DOI: 10.1103/physreva.49.2498] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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