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arXiv:2303.07004 · Communications Physics

Incommensurable matter-wave jets in quasi-1D geometry

Tadej Mežnaršič, Rok Žitko, Katja Gosar, Jure Pirman, Katja Arh, Matevž Jug, Erik Zupanič, P. Jeglič

Published Feb 7, 2025• 0 citations
arXivHTMLPDF

Abstract

Abstract Bose-Einstein condensates subjected to modulation of the interaction between atoms exhibit the emergence of density waves and matter-wave jets with a velocity proportional to the square root of the modulation frequency. Matter-wave jets have been studied in two- and one-dimensional systems showing that for sufficiently strong modulation additional higher harmonic matter-wave jets emerge. Here we report the experimental observation of incommensurable “golden” $$\frac{1+\sqrt{5}}{2}$$ 1 + 5 2 matter-wave jets in a Bose-Einstein condensate exposed to a single frequency interaction modulation. We study the formation of higher-order jets in quasi-one-dimensional geometry with numerical one dimensional (1D) Gross-Pitaevskii equation simulation. We explore the process of jet formation experimentally and theoretically for a wide range of modulation amplitudes and frequencies and establish a phase diagram delineating different regimes of jet formation. The observation of incommensurate jets provides a new route to an aperiodic density modulation of the condensate without employing an external potential.

DOI
10.1038/s42005-025-01937-1

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Abstract Bose-Einstein condensates subjected to modulation of the interaction between atoms exhibit the emergence of density waves and matter-wave jets with a velocity proportional to the square root of the modulation frequency. Matter-wave jets have been studied in two- and one-dimensional systems showing that for sufficiently strong modulation additional higher harmonic matter-wave jets emerge. Here we report the experimental observation of incommensurable “golden” 1+52\frac{1+\sqrt{5}}{2}21+5​​ 1 + 5 2 matter-wave jets in a Bose-Einstein condensate exposed to a single frequency interaction modulation. We study the formation of higher-order jets in quasi-one-dimensional geometry with numerical one dimensional (1D) Gross-Pitaevskii equation simulation. We explore the process of jet formation experimentally and theoretically for a wide range of modulation amplitudes and frequencies and establish a phase diagram delineating different regimes of jet formation. The observation of incommensurate jets provides a new route to an aperiodic density modulation of the condensate without employing an external potential.
We demonstrate the emission of correlated atom jets from a matter-wave soliton in a quasi-one-dimensional optical trap. We characterize the dependence of jet properties on the frequency, amplitude, and length of the modulation, and qualitatively reproduce the trends in the mean-field picture with a one-dimensional time-dependent Gross-Pitaevskii equation simulation. High-order jets are observed for sufficiently long pulses. A double-pulse modulation sequence produces consecutive jets, and a multipulse sequence may lead to irregular three-dimensional jets at a finite angle to the direction of the channel. In the limit of vanishing high-order jets beyond-mean-field number correlations of jet pairs are demonstrated, implying possible number squeezing.
Abstract In this work, we investigate the modulational instability of plane wave solutions within a modified Gross–Pitaevskii equation framework. The equation features cubic and quartic nonlinearity. It models the behaviour of quasi-one-dimensional Bose–Einstein condensates in symmetric Bose-Bose mixtures of ultra-dilute cold atoms. The cases of equal amplitudes in both species, as well as of unequal amplitudes are studied. Our study demonstrates the pivotal role of the competition between mean-field attractions and quantum fluctuation-induced repulsions. This competition significantly affects the emergence and evolution of modulational instability. By employing linear stability analysis, we identify the essential conditions that lead to modulational instability. We find that the stability of plane wave solutions significantly depends on the interaction among system parameters. Further development of the instability leads to the fragmentation of the BEC into a chain of quantum droplets. We calculated the number of quantum droplets generated during the nonlinear stage of the instability. Our analytical results are corroborated by numerical simulations of the modified quasi-1D Gross–Pitaevskii equation. These simulations vividly depict the formation, interaction, and coalescence of droplets during the nonlinear phase of modulational instability. The investigation shows that the linear stability analysis of the modified Gross–Pitaevskii equation, considering quantum fluctuations, precisely predicts the initial stage of modulational instability phenomena across different domains of parameter space. In contrast, the later nonlinear stage, studied through numerical simulations, reveals the formation and nonintegrable dynamics of quantum droplets.
Emission of matter wave jets has been recently observed in a Bose-Einstein condensate confined by a cylindrical box potential, induced by a periodically modulated inter-particle interaction (Nature {\bf 551}, 356 (2017)). In this letter we apply the number-conserving time-dependent Bogoliubov theory to study the highly non-equilibrium quantum dynamics in this system. Without any fitting parameter, our theoretical calculations on the dynamics of the jet emission and the angular density correlation are in excellent quantitative agreement with the experimental measurements. In particular, our theory interprets the angular density correlation of the jets as the Hanbury-Brown-Twiss effect between the excited quasi-particles with different angular momenta, and this explains the puzzling observation of the asymmetric density correlations between the jets with the same and opposite momenta. We also analytically show that the number of atoms in the jet emission increases quadratically at early times and is followed by an exponential growth at later times.
We investigate the localized nonlinear matter waves of the quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity in the harmonic potential. It is shown that all of the Bose-Einstein condensates, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies, which are mathematically exact orthogonal solutions of the Gross-Pitaevskii equation. Their properties are determined by the principal quantum number nnn and secondary quantum number lll: the parity of the matter wave functions and the corresponding energy levels depend only on nnn, and the numbers of density packets for each quantum state depend on both nnn and lll, which describe the topological properties of the atom packets. We also give an experimental protocol to observe these phenomena in future experiments.
We experimentally study the excitation modes of bright matter-wave solitons in a quasi-one-dimensional geometry. The solitons are created by quenching the interactions of a Bose-Einstein condensate of cesium atoms from repulsive to attractive in combination with a rapid reduction of the longitudinal confinement. A deliberate mismatch of quench parameters allows for the excitation of breathing modes of the emerging soliton and for the determination of its breathing frequency as a function of atom number and confinement. In addition, we observe signatures of higher-order solitons and the splitting of the wave packet after the quench. Our experimental results are compared to analytical predictions and to numerical simulations of the one-dimensional Gross-Pitaevskii equation.
In a basic physical model where two-dimensional (2D) matter-wave solitons may be stable, namely, the Gross-Pitaevskii equation with the self-attractive nonlinearity and quasi-one-dimensional (1D) optical-lattice (OL) potential, we test robustness of the solitons against periodic time modulation of the OL strength. Stability diagrams for the 2D solitons are presented in the plane of the modulation depth and frequency. Basic features of the diagrams are explained with the help of the variational approximation for the stationary counterpart of the model. In the Bose-Einstein condensate of 7Li^{7}\text{L}\text{i}7Li atoms, the stable 2D solitons may contain the number of atoms in the range of 104−−105{10}^{4}--{10}^{5}104−−105, relevant values of the OL strength and modulation frequency being, respectively, $\ensuremath{\lesssim}5$ recoil energies and $\ensuremath{\lesssim}10\text{ }\text{kHZ}$. Head-on collisions between stable 2D solitons moving in the unconfined direction are studied in detail too, for velocities up to $\ensuremath{\sim}5\text{ }\text{cm}∕\text{s}$. A border between quasi-elastic collisions and merger of the solitons into a single localized state is identified. In some cases, the soliton produced by the merger is stable against collapse, which was not observed before in the static OL potential either.