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Evolution of momentum-dependent observables under stochastic phase noise in Rabi oscillations

Samuel Böhringer, Fabian Kienle, Richard Lopp

We derive the equations of motion of arbitrary momentum-dependent observables for a fully first-quantized, driven two-level atom in a linear potential under the presence of a stochastic laser phase. In particular, we show that such momentum-dependent observables evolve under stochastic differential equations (SDEs) in the form of geometrical Brownian motion and find that these SDEs reduce to ordinary differential equations (ODEs) for the expectation values under white laser phase noise. As an example, we solve these ODEs numerically and determine the effect of laser phase noise on Rabi oscillations including quantized center-of-mass degrees of freedom of the atom. Moreover, the SDE formalism we derive holds for any phase noise source and can also be applied to extended noise models such as color noise.We derive the equations of motion of arbitrary momentum-dependent observables for a fully first-quantized, driven two-level atom in a linear potential under the presence of a stochastic laser phase. In particular, we show that such momentum-dependent observables evolve under stochastic differential equations (SDEs) in the form of geometrical Brownian motion and find that these SDEs reduce to ordinary differential equations (ODEs) for the expectation values under white laser phase noise. As an example, we solve these ODEs numerically and determine the effect of laser phase noise on Rabi oscillations including quantized center-of-mass degrees of freedom of the atom. Moreover, the SDE formalism we derive holds for any phase noise source and can also be applied to extended noise models such as color noise.

Physical Review ResearchApr 14, 20253 citations

The stochastic solution of the many-body Schroedinger equation for fermions

David M. Ceperley

Lecture notes in physicsJan 1, 198111 citations

Boson and Fermion Brownian Motion

Alexander E. Kobryn, Tsuyoshi Hayashi, Toshihico Arimitsu

Dynamics of quantum systems which are perturbed by linear coupling to the reservoir stochastically can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). To work it out one needs definition of quantum Brownian motion. Since till very recent times only its boson version has been known, in present paper we demonstrate definition which makes possible consideration also for fermion Brownian motion.

arXiv:math-ph/0502045Journal of the Physical Society of JapanJan 1, 20035 citations

Quantum stochastic differential equations for boson and fermion systems—method of non-equilibrium thermo field dynamics

A.E. Kobryn, T. Hayashi, T. Arimitsu

arXiv:math-ph/0304023Annals of PhysicsSep 16, 200310 citations

Well‐posedness of quantum stochastic differential equations driven by fermion Brownian motion in noncommutative Lp‐space

Guangdong Jing, Penghui Wang, Shan Wang

This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space for . First, we investigate the existence and uniqueness of ‐solutions of quantum stochastic differential equations in an infinite time horizon by using the noncommutative Burkholder–Gundy inequality given by Pisier and Xu and the noncommutative generalized Minkowski inequality. Then, we investigate the stability, self‐adjointness, and Markov properties of ‐solutions and analyze the error of numerical schemes of quantum stochastic differential equations. The results of this paper can be utilized for investigating the optimal control of quantum stochastic systems with infinite dimensions.This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space for . First, we investigate the existence and uniqueness of ‐solutions of quantum stochastic differential equations in an infinite time horizon by using the noncommutative Burkholder–Gundy inequality given by Pisier and Xu and the noncommutative generalized Minkowski inequality. Then, we investigate the stability, self‐adjointness, and Markov properties of ‐solutions and analyze the error of numerical schemes of quantum stochastic differential equations. The results of this paper can be utilized for investigating the optimal control of quantum stochastic systems with infinite dimensions.

Mathematical Methods in the Applied SciencesMar 24, 20243 citations

Fermion Ito's formula and stochastic evolutions

David Applebaum, R. L. Hudson

Communications in Mathematical PhysicsDec 1, 1984114 citations

Fermion diffusions

Abstract

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Fermion diffusions

Abstract

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