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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] [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. ROYAL SOCIETY OPEN SCIENCE 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] [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] [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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Kaplan AE. Gradient marker: a universal wave pattern in an inhomogeneous continuum. PHYSICAL REVIEW LETTERS 2012; 109:153901. [PMID: 23102308 DOI: 10.1103/physrevlett.109.153901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2012] [Indexed: 06/01/2023]
Abstract
Wave transport in a media with a slow spatial gradient of its characteristics is found to exhibit a universal wave pattern ("gradient marker") in a vicinity of the maxima or minima of the gradient. The pattern is common for optics, quantum mechanics, and any other propagation governed by the same wave equation. Derived analytically, it has an elegantly simple yet nontrivial profile found in perfect agreement with numerical simulations for specific examples. We also find resonant states in continuum in the case of quantum wells, and formulated criteria for their existence.
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Affiliation(s)
- A E Kaplan
- Electrical and Computer Engineering Department, The Johns Hopkins University, Baltimore, Maryland 21218, USA.
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Abstract
This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.
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Affiliation(s)
- Kenji Ohmori
- Institute for Molecular Science, National Institutes of Natural Sciences; The Graduate University for Advanced Studies (SOKENDAI); and CREST, Japan Science and Technology Agency, Myodaiji, Okazaki 444-8585, Japan
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Ohmori K. Development of ultrahigh-precision coherent control and its applications. PROCEEDINGS OF THE JAPAN ACADEMY. SERIES B, PHYSICAL AND BIOLOGICAL SCIENCES 2008; 84:167-75. [PMID: 18941296 PMCID: PMC3665367 DOI: 10.2183/pjab.84.167] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/19/2008] [Accepted: 03/31/2008] [Indexed: 05/26/2023]
Abstract
Coherent control is based on optical manipulation of the amplitudes and phases of wave functions. It is expected to be a key technique to develop novel quantum technologies such as bond-selective chemistry and quantum computing, and to better understand the quantum worldview founded on wave-particle duality. We have developed high-precision coherent control by imprinting optical amplitudes and phases of ultrashort laser pulses on the quantum amplitudes and phases of molecular wave functions. The history and perspective of coherent control and our recent achievements are described.
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Affiliation(s)
- Kenji Ohmori
- Institute for Molecular Science, National Institutes of Natural Sciences, Aichi, Japan.
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Tekavec PF, Dyke TR, Marcus AH. Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation. J Chem Phys 2006; 125:194303. [PMID: 17129099 DOI: 10.1063/1.2386159] [Citation(s) in RCA: 82] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
Studies of wave packet dynamics often involve phase-selective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phase-selective measurements that combines acousto-optic phase modulation with ultrashort laser excitation to produce an intensity-modulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90 degrees. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signal-to-noise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system--atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.
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Affiliation(s)
- Patrick F Tekavec
- Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
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Ohmori K, Katsuki H, Chiba H, Honda M, Hagihara Y, Fujiwara K, Sato Y, Ueda K. Real-time observation of phase-controlled molecular wave-packet interference. PHYSICAL REVIEW LETTERS 2006; 96:093002. [PMID: 16606260 DOI: 10.1103/physrevlett.96.093002] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2005] [Indexed: 05/08/2023]
Abstract
The quantum interference of two molecular wave packets has been precisely controlled in the B electronic state of the I2 molecule by using a pair of fs laser pulses whose relative phase is locked within the attosecond time scale and its real-time evolution has been observed by another fs laser pulse. It is clearly observed that the temporal evolution changes drastically as a function of the relative phase between the locked pulses, allowing us to read both amplitude and phase information stored in the wave functions of the molecular ensemble.
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Affiliation(s)
- Kenji Ohmori
- Institute for Molecular Science, National Institutes of Natural Sciences, Myodaiji, Okazaki 444-8585, Japan.
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Martínez-Galicia R, Romero-Rochín V. Molecular wave packet interferometry and quantum entanglement. J Chem Phys 2005; 122:094101. [PMID: 15836106 DOI: 10.1063/1.1852456] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study wave packet interferometry (WPI) considering the laser pulse fields both classical and quantum mechanically. WPI occurs in a molecule after subjecting it to the interaction with a sequence of phase-locked ultrashort laser pulses. Typically, the measured quantity is the fluorescence of the molecule from an excited electronic state. This signal has imprinted the interference of the vibrational wave packets prepared by the different laser pulses of the sequence. The consideration of the pulses as quantum entities in the analysis allows us to study the entanglement of the laser pulse states with the molecular states. With a simple model for the molecular system, plus several justified approximations, we solve for the fully quantum mechanical molecule-electromagnetic field state. We then study the reduced density matrices of the molecule and the laser pulses separately. We calculate measurable corrections to the case where the fields are treated classically.
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Affiliation(s)
- Ricardo Martínez-Galicia
- Instituto de Física, Universidad Nacional Autonoma de México, Apartado Postal 20-364, 01000 México, Distrito Federal, Mexico
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Ohmori K, Sato Y, Nikitin EE, Rice SA. High-precision molecular wave-packet interferometry with HgAr dimers. PHYSICAL REVIEW LETTERS 2003; 91:243003. [PMID: 14683114 DOI: 10.1103/physrevlett.91.243003] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2003] [Indexed: 05/24/2023]
Abstract
Molecular wave-packet (WP) interferometry has been demonstrated in the A electronic state of the HgAr van der Waals complex with two time-delayed UV fs pulses at 254 nm. The interferograms of three vibrational levels in the WP's display almost 100% fringe contrast as a function of the interpulse delay tau, which is tuned with sub-10 as stability and resolution. It is clearly observed that the three interferograms show their dephasing and rephasing within a single vibrational period, allowing us to prepare arbitrary relative populations of the three levels by adjusting a single parameter tau.
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Affiliation(s)
- Kenji Ohmori
- Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan.
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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. PHYSICAL REVIEW LETTERS 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] [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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Hertz E, Faucher O, Lavorel B, Chaux R. Controlling molecular alignment rephasing through interference of Raman-induced rotational coherence. J Chem Phys 2000. [DOI: 10.1063/1.1309526] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Blanchet V, Bouchène MA, Girard B. Temporal coherent control in the photoionization of Cs2: Theory and experiment. J Chem Phys 1998. [DOI: 10.1063/1.475896] [Citation(s) in RCA: 95] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Leichtle C, Averbukh IS, Schleich WP. Multilevel quantum beats: An analytical approach. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:5299-5312. [PMID: 9914098 DOI: 10.1103/physreva.54.5299] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Leichtle C, Averbukh IS, Schleich WP. Generic Structure of Multilevel Quantum Beats. PHYSICAL REVIEW LETTERS 1996; 77:3999-4002. [PMID: 10062362 DOI: 10.1103/physrevlett.77.3999] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Averbukh IS, Vrakking MJ, Villeneuve DM, Stolow A. Wave Packet Isotope Separation. PHYSICAL REVIEW LETTERS 1996; 77:3518-3521. [PMID: 10062240 DOI: 10.1103/physrevlett.77.3518] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Knospe O, Schmidt R. Revivals of wave packets: General theory and application to Rydberg clusters. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:1154-1160. [PMID: 9913584 DOI: 10.1103/physreva.54.1154] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Dupret K, Delande D. Nonlinear wave-packet dynamics for a generic one-dimensional time-independent system and its application to the hydrogen atom in a weak magnetic field. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 53:1257-1272. [PMID: 9913014 DOI: 10.1103/physreva.53.1257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Buchleitner A, Delande D. Nondispersive Electronic Wave Packets in Multiphoton Processes. PHYSICAL REVIEW LETTERS 1995; 75:1487-1490. [PMID: 10060310 DOI: 10.1103/physrevlett.75.1487] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Hanson LG, Lambropoulos P. Nondispersing wave packets in two-electron atoms: Atomic mode locking by loss modulation. PHYSICAL REVIEW LETTERS 1995; 74:5009-5012. [PMID: 10058660 DOI: 10.1103/physrevlett.74.5009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Jarzynski C. Geometric phase effects for wave-packet revivals. PHYSICAL REVIEW LETTERS 1995; 74:1264-1267. [PMID: 10058976 DOI: 10.1103/physrevlett.74.1264] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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