Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

Shape effects in some two-state models with non-analytic pulse envelopes

Nikolay V. Vitanov

Published May 28, 1995• 3 citations
Publisher

Abstract

Previous work has suggested that non-analyticity of the time-dependent coupling between two states can lead to spurious non-physical contributions to transition probability. We demonstrate that this does not occur for the exponential pulses in the Demkov (1963) and Nikitin (1970) models, nor for the case of a rectangular pulse. Analysis in terms of adiabaticity suggests that the specific properties of the transition probabilities in these models at large detuning are due to pulse shape effects.

DOI
10.1088/0953-4075/28/10/010

Related papers

Strong-couplingSmatrices for the generalized exponential models of nonadiabatic transitions

Predrag Krstić, R.K. Janev

Strong-coupling S matrices for the anti-Demkov, Nikitin, and Demkov models of nonadiabatic transitions are derived. On this basis, analytic expressions for the channel probabilities, which include the effects of the turning point, are also derived. The two states are assumed quasistationary and coupled by a complex interaction.

Physical Review A•Jun 1, 1988•10 citations

Nonadiabatic transitions in a two-level quantum system: Pulse-shape dependence of the transition probability for a two-level atom driven by a pulsed radiation field

P. R. Berman, Lixin Yan, Keng-Hwee Chiam +1 more

The problem of a two-level atom interacting with a radiation pulse is studied in the limit that the atom-field detuning times the pulse duration is much greater than unity. Owing to the large atom-field detuning, transitions result from nonadiabatic coupling of the states by the field. The transition probability for the atom to be excited following the pulse is studied as a function of field strength for five different pulse shapes: hyperbolic secant, Lorentzian, hyperbolic secant squared, Lorentzian squared, and Gaussian. It is shown that the behavior of the transition probability differs qualitatively for these pulses. An explanation of this qualitative difference is given in terms of the Massey parameter. Numerical solutions are compared with asymptotic solutions and several anomalies are noted. In the limit of large field strength, a universal expression for the transition probability is found. An interesting feature of the solutions is that, in the limit of very large field strengths, the transition probability for a Gaussian pulse can approach unity despite the fact that the pulse has an exponentially small Fourier amplitude at the atom-field detuning. This apparent violation of the energy-time uncertainty principle is explained in terms of the nonlinear atom-field interactions.

Physical Review A•Jan 1, 1998•28 citations

Uniform analytic description of dephasing effects in two-state transitions

X. Lacour, S. Guérin, Леонід Петрович Яценко +2 more

We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, along with several other models, such as a Gaussian model and a Landau-Zener model with a pulsed coupling.

Physical Review A•Mar 27, 2007•32 citations

On pulse-induced transition amplitudes in a two-state quantum system without level crossings

Karl-Erik Thylwe, H. J. Korsch

An exact dynamical parametrization of pulse-induced transition amplitudes in a Rosen–Zener- or Nikitin-type two-level system is constructed. The three dynamical parameters are closely related to the shape of the interaction pulse and are convenient to calculate. The Milne equation with a complex coefficient function is essential for these calculations. Its complex solution is non-oscillatory and makes the computation of transition probabilities efficient. The paper reviews the quantum calculations for the rectangular pulse, which has well-defined duration and strength. By comparing transition matrix elements from a rectangular pulse with those of a general symmetric pulse, we introduce effective strength and effective duration for a general pulse. It is also possible to define an equivalent rectangular pulse, with respect to the transition probabilities, for each general pulse.

Journal of Physics A Mathematical and General•Aug 13, 2002•2 citations

Pulsed excitation of a transition to a decaying level

Nikolay V. Vitanov, Stig Stenholm

The paper presents an analytic study of a two-state system which interacts with an external pulsed field. The excited state is supposed to decay out of the system with a decay rate \ensuremath{\Gamma}. We present two exact analytic solutions, viz., the finite Landau-Zener model and the Demkov-Kunike model. We also derive an approximate formula for arbitrary pulse shapes and detunings in the limit of a large decay rate. It gives the exact result for the original Landau-Zener model and the correct asymptotics for large \ensuremath{\Gamma} in the general case. We conclude that the independence of the final ground-state population on the decay rate, recently established for the original Landau-Zener model [V. M. Akulin and W. P. Schleich, Phys. Rev. A 46, 4110 (1992)], is only valid for the latter and not for any other model. The results show that the population loss ultimately decreases at large decay rates which can be viewed as a quantum analog of the overdamped oscillator.

Physical Review A•Apr 1, 1997•51 citations

Pulse-shape effects in qubit dynamics demonstrated on an IBM quantum computer

Ivo S. Mihov, Nikolay V. Vitanov

We present a study of the coherent interaction of a qubit with a pulse-shaped external field of a constant carrier frequency. We explore, theoretically and experimentally, the transition line profile (the dependence of the transition probability on the detuning) for five different pulse shapes: Rectangular, Gaussian, hyperbolic-secant, squared hyperbolic-secant, and exponential. The theoretical description for all cases but ${\mathrm{sech}}^{2}$ is based on the analytical solutions to the Schr\"odinger equation or accurate approximations available in the literature. For the ${\mathrm{sech}}^{2}$ pulse we derive an analytical expression for the transition probability using the Rosen-Zener conjecture, which proves very accurate. In addition, the same conjecture turns out to provide very accurate approximations for the Gaussian and exponential pulses. The experimental results are obtained with one of IBMQ's quantum processors. An excellent agreement between theory and experiment is observed, demonstrating some pulse-shape-dependent fine features of the transition probability profile. The mean absolute error (a measure of the accuracy of the fit) features an improvement by a factor of 4 to 7 for the analytic models compared to the commonly used Lorentzian fits. Moreover, the uncertainty of the qubit's resonance frequency is reduced by a factor of 4 for the analytic models compared to the Lorentzian fits. These results demonstrate both the accuracy of the analytic modeling of quantum dynamics and the excellent coherent properties of IBMQ's qubit.

arXiv:2301.10004•Physical Review A•Oct 10, 2023•7 citations
Previous work has suggested that non-analyticity of the time-dependent coupling between two states can lead to spurious non-physical contributions to transition probability. We demonstrate that this does not occur for the exponential pulses in the Demkov (1963) and Nikitin (1970) models, nor for the case of a rectangular pulse. Analysis in terms of adiabaticity suggests that the specific properties of the transition probabilities in these models at large detuning are due to pulse shape effects.
The problem of a two-level atom interacting with a radiation pulse is studied in the limit that the atom-field detuning times the pulse duration is much greater than unity. Owing to the large atom-field detuning, transitions result from nonadiabatic coupling of the states by the field. The transition probability for the atom to be excited following the pulse is studied as a function of field strength for five different pulse shapes: hyperbolic secant, Lorentzian, hyperbolic secant squared, Lorentzian squared, and Gaussian. It is shown that the behavior of the transition probability differs qualitatively for these pulses. An explanation of this qualitative difference is given in terms of the Massey parameter. Numerical solutions are compared with asymptotic solutions and several anomalies are noted. In the limit of large field strength, a universal expression for the transition probability is found. An interesting feature of the solutions is that, in the limit of very large field strengths, the transition probability for a Gaussian pulse can approach unity despite the fact that the pulse has an exponentially small Fourier amplitude at the atom-field detuning. This apparent violation of the energy-time uncertainty principle is explained in terms of the nonlinear atom-field interactions.
We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, along with several other models, such as a Gaussian model and a Landau-Zener model with a pulsed coupling.
An exact dynamical parametrization of pulse-induced transition amplitudes in a Rosen–Zener- or Nikitin-type two-level system is constructed. The three dynamical parameters are closely related to the shape of the interaction pulse and are convenient to calculate. The Milne equation with a complex coefficient function is essential for these calculations. Its complex solution is non-oscillatory and makes the computation of transition probabilities efficient. The paper reviews the quantum calculations for the rectangular pulse, which has well-defined duration and strength. By comparing transition matrix elements from a rectangular pulse with those of a general symmetric pulse, we introduce effective strength and effective duration for a general pulse. It is also possible to define an equivalent rectangular pulse, with respect to the transition probabilities, for each general pulse.
The paper presents an analytic study of a two-state system which interacts with an external pulsed field. The excited state is supposed to decay out of the system with a decay rate \ensuremath{\Gamma}. We present two exact analytic solutions, viz., the finite Landau-Zener model and the Demkov-Kunike model. We also derive an approximate formula for arbitrary pulse shapes and detunings in the limit of a large decay rate. It gives the exact result for the original Landau-Zener model and the correct asymptotics for large \ensuremath{\Gamma} in the general case. We conclude that the independence of the final ground-state population on the decay rate, recently established for the original Landau-Zener model [V. M. Akulin and W. P. Schleich, Phys. Rev. A 46, 4110 (1992)], is only valid for the latter and not for any other model. The results show that the population loss ultimately decreases at large decay rates which can be viewed as a quantum analog of the overdamped oscillator.
We present a study of the coherent interaction of a qubit with a pulse-shaped external field of a constant carrier frequency. We explore, theoretically and experimentally, the transition line profile (the dependence of the transition probability on the detuning) for five different pulse shapes: Rectangular, Gaussian, hyperbolic-secant, squared hyperbolic-secant, and exponential. The theoretical description for all cases but sech2{\mathrm{sech}}^{2}sech2 is based on the analytical solutions to the Schr\"odinger equation or accurate approximations available in the literature. For the sech2{\mathrm{sech}}^{2}sech2 pulse we derive an analytical expression for the transition probability using the Rosen-Zener conjecture, which proves very accurate. In addition, the same conjecture turns out to provide very accurate approximations for the Gaussian and exponential pulses. The experimental results are obtained with one of IBMQ's quantum processors. An excellent agreement between theory and experiment is observed, demonstrating some pulse-shape-dependent fine features of the transition probability profile. The mean absolute error (a measure of the accuracy of the fit) features an improvement by a factor of 4 to 7 for the analytic models compared to the commonly used Lorentzian fits. Moreover, the uncertainty of the qubit's resonance frequency is reduced by a factor of 4 for the analytic models compared to the Lorentzian fits. These results demonstrate both the accuracy of the analytic modeling of quantum dynamics and the excellent coherent properties of IBMQ's qubit.