Details
| Original language | English |
|---|---|
| Pages (from-to) | 4-50 |
| Number of pages | 47 |
| Journal | Journal of low temperature physics |
| Volume | 210 |
| Issue number | 1-2 |
| Publication status | Published - Jan 2023 |
Abstract
Fifty years ago Kostin (J Chem Phys 57(9):3589–3591, 1972. https://doi.org/10.1063/1.1678812) proposed a description of damping in quantum mechanics based on a nonlinear Schrödinger equation with the potential being governed by the phase of the wave function. We show for the example of a moving Gaussian wave packet, that the deceleration predicted by this equation is the result of the same non-dissipative, homogeneous but time-dependent force, that also stops a classical particle. Moreover, we demonstrate that the Kostin equation is a special case of the linear Schrödinger equation with three potentials: (i) a linear potential corresponding to this stopping force, (ii) an appropriately time-dependent parabolic potential governed by a specific time dependence of the width of the Gaussian wave packet and (iii) a specific time-dependent off-set. The freedom of the width opens up the possibility of engineering the final state by the time dependence of the quadratic potential. In this way the Kostin equation is a precursor of the modern field of coherent control. Motivated by these insights, we analyze in position and in phase space the deceleration of a Gaussian wave packet due to potentials in the linear Schrödinger equation similar to those in the Kostin equation.
Keywords
- Coherent control, Cooling, Gaussian wave packet, Kostin equation, Nonlinear Schrödinger equation, Quantum dynamics, Wigner phase space
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Materials Science(all)
- General Materials Science
- Physics and Astronomy(all)
- Condensed Matter Physics
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In: Journal of low temperature physics, Vol. 210, No. 1-2, 01.2023, p. 4-50.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Kostin Equation, the Deceleration of a Quantum Particle and Coherent Control
AU - Losert, Harald
AU - Ullinger, Freyja
AU - Zimmermann, Matthias
AU - Efremov, Maxim A.
AU - Rasel, Ernst M.
AU - Schleich, Wolfgang P.
N1 - Funding Information: We thank R. Folman, M. Freyberger, A. Friedrich, N. Gaaloul, E. Giese, F. Narducci, G.G. Rozenman and L. Wörner for many stimulating discussions on this topic, and M.C. Downer and P. Hommelhoff for their help with the references. W.P.S. is grateful to Texas A&M University for a Faculty Fellowship at the Hagler Institute for Advanced Study at the Texas A&M University as well as to the Texas A&M AgriLife Research.
PY - 2023/1
Y1 - 2023/1
N2 - Fifty years ago Kostin (J Chem Phys 57(9):3589–3591, 1972. https://doi.org/10.1063/1.1678812) proposed a description of damping in quantum mechanics based on a nonlinear Schrödinger equation with the potential being governed by the phase of the wave function. We show for the example of a moving Gaussian wave packet, that the deceleration predicted by this equation is the result of the same non-dissipative, homogeneous but time-dependent force, that also stops a classical particle. Moreover, we demonstrate that the Kostin equation is a special case of the linear Schrödinger equation with three potentials: (i) a linear potential corresponding to this stopping force, (ii) an appropriately time-dependent parabolic potential governed by a specific time dependence of the width of the Gaussian wave packet and (iii) a specific time-dependent off-set. The freedom of the width opens up the possibility of engineering the final state by the time dependence of the quadratic potential. In this way the Kostin equation is a precursor of the modern field of coherent control. Motivated by these insights, we analyze in position and in phase space the deceleration of a Gaussian wave packet due to potentials in the linear Schrödinger equation similar to those in the Kostin equation.
AB - Fifty years ago Kostin (J Chem Phys 57(9):3589–3591, 1972. https://doi.org/10.1063/1.1678812) proposed a description of damping in quantum mechanics based on a nonlinear Schrödinger equation with the potential being governed by the phase of the wave function. We show for the example of a moving Gaussian wave packet, that the deceleration predicted by this equation is the result of the same non-dissipative, homogeneous but time-dependent force, that also stops a classical particle. Moreover, we demonstrate that the Kostin equation is a special case of the linear Schrödinger equation with three potentials: (i) a linear potential corresponding to this stopping force, (ii) an appropriately time-dependent parabolic potential governed by a specific time dependence of the width of the Gaussian wave packet and (iii) a specific time-dependent off-set. The freedom of the width opens up the possibility of engineering the final state by the time dependence of the quadratic potential. In this way the Kostin equation is a precursor of the modern field of coherent control. Motivated by these insights, we analyze in position and in phase space the deceleration of a Gaussian wave packet due to potentials in the linear Schrödinger equation similar to those in the Kostin equation.
KW - Coherent control
KW - Cooling
KW - Gaussian wave packet
KW - Kostin equation
KW - Nonlinear Schrödinger equation
KW - Quantum dynamics
KW - Wigner phase space
UR - http://www.scopus.com/inward/record.url?scp=85138297716&partnerID=8YFLogxK
U2 - 10.1007/s10909-022-02857-y
DO - 10.1007/s10909-022-02857-y
M3 - Article
AN - SCOPUS:85138297716
VL - 210
SP - 4
EP - 50
JO - Journal of low temperature physics
JF - Journal of low temperature physics
SN - 0022-2291
IS - 1-2
ER -