© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1911.01369 · Physical Review Letters

Quantum Fluctuations of the Center of Mass and Relative Parameters of Nonlinear Schrödinger Breathers

Oleksandr V. Marchukov, Boris A. Malomed, Vanja Dunjko, Joanna Ruhl, Maxim Olshanii, Randall G. Hulet, Vladimir Yurovsky

Published Jul 28, 2020• 29 citations

Abstract

We study quantum fluctuations of macroscopic parameters of a nonlinear Schrödinger breather-a nonlinear superposition of two solitons, which can be created by the application of a fourfold quench of the scattering length to the fundamental soliton in a self-attractive quasi-one-dimensional Bose gas. The fluctuations are analyzed in the framework of the Bogoliubov approach in the limit of a large number of atoms N, using two models of the vacuum state: white noise and correlated noise. The latter model, closer to the ab initio setting by construction, leads to a reasonable agreement, within 20% accuracy, with fluctuations of the relative velocity of constituent solitons obtained from the exact Bethe-ansatz results [Phys. Rev. Lett. 119, 220401 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.220401] in the opposite low-N limit (for N≤23). We thus confirm, for macroscopic N, the breather dissociation time to be within the limits of current cold-atom experiments. Fluctuations of soliton masses, phases, and positions are also evaluated and may have experimental implications.

DOI: 10.1103/physrevlett.125.050405

Related papers

Canonical approach to quantum fluctuations

Joanna Ruhl, Vanja Dunjko, Maxim Olshanii

We present a canonical formalism for computing quantum fluctuations of certain discrete degrees of freedom in systems governed by integrable partial differential equations with known Hamiltonian structure, provided these models are classical-field approximations of underlying many-body quantum systems. We then apply the formalism to both the 2-soliton and 3-soliton breather solutions of the nonlinear Schrödinger equation, assuming the breathers are created from an initial elementary soliton by quenching the coupling constant. In particular, we compute the immediate post-quench quantum fluctuations in the positions, velocities, norms, and phases of the constituent solitons. For each case, we consider both the white-noise and correlated-noise models for the fluctuation vacuum state. Unlike previous treatments of the problem, our method allows for analytic solutions. Additionally, in the correlated-noise case, we consider the particle-number-conserving (also called $U(1)$-symmetry-conserving) Bogoliubov modes, i.e., modes with the proper correction to preserve the total particle number. We find that in most (but not all) cases, these corrections do not change the final result.

arXiv:2506.21709•Physical Review A•Apr 10, 2026•0 citations

Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitaevskii Breather

Sumita Datta, Vanja Dunjko, Maxim Olshanii

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored, indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculation, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

Physics•Jan 10, 2022•4 citations

Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitevskii Breather

Sumita Datta, Vanja Dunjko, Maxim Olshanii

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored,indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculations, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

arXiv:2201.03765•Jan 11, 2022•0 citations

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

Vladimir Yurovsky, Boris A. Malomed, Randall G. Hulet +1 more

We use the ab initio Bethe ansatz dynamics to predict the dissociation of one-dimensional cold-atom breathers that are created by a quench from a fundamental soliton. We find that the dissociation is a robust quantum many-body effect, while in the mean-field (MF) limit the dissociation is forbidden by the integrability of the underlying nonlinear Schrödinger equation. The analysis demonstrates the possibility to observe quantum many-body effects without leaving the MF range of experimental parameters. We find that the dissociation time is of the order of a few seconds for a typical atomic-soliton setting.

arXiv:1706.07114•Physical Review Letters•Nov 28, 2017•29 citations

Overcoming Decoherence to Observe Quantum Fluctuations in Matter-Wave Breathers

Ricardo Espinoza Masbernat

The description of quantum many-body phenomena that go beyond a mean-field approximation is often difficult or, more typically, impossible to achieve. Experiments in this regime are also challenging due to technological constraints. An exception may be the dissociation of matter-wave breathers, which in 1D are exactly integrable solutions of the mean-field Gross-Pitaevskii equation, by quantum fluctuations. Breathers are coherent superpositions of fundamental solitons. To study these effects on the decoherence of 7Li matter-wave breathers, we first characterize the decoherence due to mean-field phenomena in quasi-1D. We find that mean-field decoherence of breathers is caused primarily by density-dependent atom loss. We also find that the mechanisms of atom loss present in our experiment, i.e. inelastic collisions with background gas and three-body recombination, have different effects on breather coherence. After identifying the sources of mean-field decoherence, we seek to suppress them so that dissociation by quantum fluctuations may be observable. For this purpose, we present a theoretical proposal and its experimental implementation aimed at enhancing the measure of breather dissociation, i.e. the relative distance between constituent solitons, via expansion in an anti-trapping harmonic potential.

•Dec 4, 2023•0 citations

Measurement of a one-dimensional matter-wave quantum breather

Piotr Staroń, Andrzej Syrwid, Krzysztof Sacha

Employing the Bethe ansatz approach and numerical simulations of measurements of particles' positions we investigate a post-quench many-body dynamics of attractively interacting bosons on a ring, which in the mean-field approach corresponds to the so-called breather solution. Despite the fact that the initial many-body ground state is translationally invariant, the measurements reveal breather dynamics if quantum fluctuations of the center of mass of the system are extracted. Moreover, the analysis of the many-body evolution shows signatures of dissociation of the solitons that form the breather.

arXiv:2007.08365•Physical Review A•Dec 7, 2020•3 citations

We study quantum fluctuations of macroscopic parameters of a nonlinear Schrödinger breather-a nonlinear superposition of two solitons, which can be created by the application of a fourfold quench of the scattering length to the fundamental soliton in a self-attractive quasi-one-dimensional Bose gas. The fluctuations are analyzed in the framework of the Bogoliubov approach in the limit of a large number of atoms N, using two models of the vacuum state: white noise and correlated noise. The latter model, closer to the ab initio setting by construction, leads to a reasonable agreement, within 20% accuracy, with fluctuations of the relative velocity of constituent solitons obtained from the exact Bethe-ansatz results [Phys. Rev. Lett. 119, 220401 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.220401] in the opposite low-N limit (for N≤23). We thus confirm, for macroscopic N, the breather dissociation time to be within the limits of current cold-atom experiments. Fluctuations of soliton masses, phases, and positions are also evaluated and may have experimental implications.

We present a canonical formalism for computing quantum fluctuations of certain discrete degrees of freedom in systems governed by integrable partial differential equations with known Hamiltonian structure, provided these models are classical-field approximations of underlying many-body quantum systems. We then apply the formalism to both the 2-soliton and 3-soliton breather solutions of the nonlinear Schrödinger equation, assuming the breathers are created from an initial elementary soliton by quenching the coupling constant. In particular, we compute the immediate post-quench quantum fluctuations in the positions, velocities, norms, and phases of the constituent solitons. For each case, we consider both the white-noise and correlated-noise models for the fluctuation vacuum state. Unlike previous treatments of the problem, our method allows for analytic solutions. Additionally, in the correlated-noise case, we consider the particle-number-conserving (also called

U(1)

-symmetry-conserving) Bogoliubov modes, i.e., modes with the proper correction to preserve the total particle number. We find that in most (but not all) cases, these corrections do not change the final result.

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored, indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculation, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored,indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculations, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

We use the ab initio Bethe ansatz dynamics to predict the dissociation of one-dimensional cold-atom breathers that are created by a quench from a fundamental soliton. We find that the dissociation is a robust quantum many-body effect, while in the mean-field (MF) limit the dissociation is forbidden by the integrability of the underlying nonlinear Schrödinger equation. The analysis demonstrates the possibility to observe quantum many-body effects without leaving the MF range of experimental parameters. We find that the dissociation time is of the order of a few seconds for a typical atomic-soliton setting.

The description of quantum many-body phenomena that go beyond a mean-field approximation is often difficult or, more typically, impossible to achieve. Experiments in this regime are also challenging due to technological constraints. An exception may be the dissociation of matter-wave breathers, which in 1D are exactly integrable solutions of the mean-field Gross-Pitaevskii equation, by quantum fluctuations. Breathers are coherent superpositions of fundamental solitons. To study these effects on the decoherence of 7Li matter-wave breathers, we first characterize the decoherence due to mean-field phenomena in quasi-1D. We find that mean-field decoherence of breathers is caused primarily by density-dependent atom loss. We also find that the mechanisms of atom loss present in our experiment, i.e. inelastic collisions with background gas and three-body recombination, have different effects on breather coherence. After identifying the sources of mean-field decoherence, we seek to suppress them so that dissociation by quantum fluctuations may be observable. For this purpose, we present a theoretical proposal and its experimental implementation aimed at enhancing the measure of breather dissociation, i.e. the relative distance between constituent solitons, via expansion in an anti-trapping harmonic potential.

Employing the Bethe ansatz approach and numerical simulations of measurements of particles' positions we investigate a post-quench many-body dynamics of attractively interacting bosons on a ring, which in the mean-field approach corresponds to the so-called breather solution. Despite the fact that the initial many-body ground state is translationally invariant, the measurements reveal breather dynamics if quantum fluctuations of the center of mass of the system are extracted. Moreover, the analysis of the many-body evolution shows signatures of dissociation of the solitons that form the breather.