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Anisotropic collisions of dipolar Bose–Einstein condensates in the universal regime

Nathaniel Burdick, Sykes, Andrew G, Yijun Tang, Benjamin Lev

Published Nov 1, 2016• 12 citations
OpenAlex

Abstract

We report the measurement of collisions between two Bose-Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulations to provide a detailed comparison between theoretical two-body cross sections and the experimental observations.

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Anisotropic collisions of dipolar Bose–Einstein condensates in the universal regime

Nathaniel Burdick, Andrew G Sykes, Yijun Tang +1 more

We report the measurement of collisions between two Bose–Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulations to provide a detailed comparison between theoretical two-body cross sections and the experimental observations.

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Abstract Two bright solitons in a dipolar Bose–Einstein condensate (BEC) can form stable bound states, known as soliton molecules. In this paper we study the scattering of a two-soliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Collisions of soliton molecules with single solitons are investigated, the latter playing the role of a localized defect. Due to the long-range character of dipolar forces solitons interact with each other even though their waveforms do not appreciably overlap. This is an essentially different feature of dipolar solitons compared to their counterparts in BECs with contact atomic interactions. The result of scattering significantly depends on the potential’s strength and velocity of collision. For weak potentials and/or low velocity the molecule preserves its coherence, meantime the internal modes are excited. Scattering by strong potentials at moderately high velocity ends up with dissociation of the molecule. The theoretical model is based on the variational approximation for the nonlocal Gross–Pitaevskii equation (GPE). Predictions of the mathematical model are compared with numerical simulations of the nonlocal GPE, and good qualitative agreement between them is demonstrated.

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We study collisional rethermalization in ultracold dipolar thermal gases, made intricate by their anisotropic differential cross sections. Theoretical methods are provided to derive the number of collisions per rethermalization [Monroe et al., Phys. Rev. Lett. 70, 414 (1993)], which, for dipolar gases, is highly dependent on the dipole alignment axis. These methods are formulated to be easily applied in experimental contexts, even reducing to analytic expressions if the route to thermal equilibrium is governed by short-time dynamics. In the analytic case, collisional rethermalization is fully characterized by the dipole magnitude and orientation, scattering length, and thermalization geometry. These models compare favorably to Monte Carlo simulations and are shown to model well a recent experimental result on the rethermalization of polar molecular samples.

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The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^d x = n a 0 d , with n n the density, d d the dimensionality of the space ( d=1,2,3 d = 1 , 2 , 3 ) and a_0 a 0 the s s -wave scattering length. The universal regime typically extends up to x\approx 0.001 x ≈ 0.001 , while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes a_0 a 0 depend on the polarization angle \alpha α , so different combinations of n and \alpha α can lead to the same value of the gas parameter x. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large gas parameter values. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of x x that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.

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We propose a method for simulating a single realization of a collision of two Bose-Einstein condensates. Recently [Phys. Rev. Lett. 94, 200401 (2005)], we introduced a quantum model of incoherent elastic scattering in a collision of two counterpropagating atomic Gaussian wave packets. Here we show that this model is capable of generating data that can be interpreted as results of a single collisional event. We find a range of parameters, including relative velocity, population, and the size of colliding condensates, where the structure of the halo of scattered atoms in a single realization strongly differs from that averaged over many realizations.

Physical Review Letters•Oct 25, 2006•24 citations
We report the measurement of collisions between two Bose-Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulations to provide a detailed comparison between theoretical two-body cross sections and the experimental observations.
We report the measurement of collisions between two Bose–Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulations to provide a detailed comparison between theoretical two-body cross sections and the experimental observations.
Abstract Two bright solitons in a dipolar Bose–Einstein condensate (BEC) can form stable bound states, known as soliton molecules. In this paper we study the scattering of a two-soliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Collisions of soliton molecules with single solitons are investigated, the latter playing the role of a localized defect. Due to the long-range character of dipolar forces solitons interact with each other even though their waveforms do not appreciably overlap. This is an essentially different feature of dipolar solitons compared to their counterparts in BECs with contact atomic interactions. The result of scattering significantly depends on the potential’s strength and velocity of collision. For weak potentials and/or low velocity the molecule preserves its coherence, meantime the internal modes are excited. Scattering by strong potentials at moderately high velocity ends up with dissociation of the molecule. The theoretical model is based on the variational approximation for the nonlocal Gross–Pitaevskii equation (GPE). Predictions of the mathematical model are compared with numerical simulations of the nonlocal GPE, and good qualitative agreement between them is demonstrated.
We study collisional rethermalization in ultracold dipolar thermal gases, made intricate by their anisotropic differential cross sections. Theoretical methods are provided to derive the number of collisions per rethermalization [Monroe et al., Phys. Rev. Lett. 70, 414 (1993)], which, for dipolar gases, is highly dependent on the dipole alignment axis. These methods are formulated to be easily applied in experimental contexts, even reducing to analytic expressions if the route to thermal equilibrium is governed by short-time dynamics. In the analytic case, collisional rethermalization is fully characterized by the dipole magnitude and orientation, scattering length, and thermalization geometry. These models compare favorably to Monte Carlo simulations and are shown to model well a recent experimental result on the rethermalization of polar molecular samples.
The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^d x = n a 0 d , with n n the density, d d the dimensionality of the space ( d=1,2,3 d = 1 , 2 , 3 ) and a_0 a 0 the s s -wave scattering length. The universal regime typically extends up to x\approx 0.001 x ≈ 0.001 , while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes a_0 a 0 depend on the polarization angle \alpha α , so different combinations of n and \alpha α can lead to the same value of the gas parameter x. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large gas parameter values. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of x x that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.
We investigate the coherent collision of anisotropic quasi-two-dimensional bright solitons in dipolar Bose-Einstein condensates. Our analysis is based on the extended Gross-Pitaevskii equation, and we use the split-operator method for the grid calculations and the time-dependent variational principle with an Ansatz of coupled Gaussian functions to calculate the time evolution of the ground state. We compare the results of both approaches for collisions where initially the solitons are in the repelling side-by-side configuration and move towards each other with a specific momentum. We change the relative phases of the condensates, and introduce a total angular momentum by shifting the solitons in opposite directions along the polarization axis. Our calculations show that collisions result in breathing-mode-like excitations of the solitons.
We propose a method for simulating a single realization of a collision of two Bose-Einstein condensates. Recently [Phys. Rev. Lett. 94, 200401 (2005)], we introduced a quantum model of incoherent elastic scattering in a collision of two counterpropagating atomic Gaussian wave packets. Here we show that this model is capable of generating data that can be interpreted as results of a single collisional event. We find a range of parameters, including relative velocity, population, and the size of colliding condensates, where the structure of the halo of scattered atoms in a single realization strongly differs from that averaged over many realizations.