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arXiv:1202.1689 · Physical Review A

Creating two-dimensional bright solitons in dipolar Bose-Einstein condensates

Patrick Köberle, Damir Zajec, Günter Wunner, Boris A. Malomed

Published Feb 24, 2012• 48 citations
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Abstract

We propose a realistic experimental setup for creating quasi-two-dimensional (2D) bright solitons in dipolar Bose-Einstein condensates (BECs), the existence of which was proposed by Tikhonenkov et al. [Phys. Rev. Lett. 100, 090406 (2008)]. A challenging feature of the expected solitons is their strong inherent anisotropy due to the necessary in-plane orientation of the local moments in the dipolar gas. This may be the first chance of making multidimensional matter-wave solitons, as well as solitons featuring the anistropy due to their intrinsic dynamics. Our analysis is based on the extended Gross-Pitaevskii equation, which includes three-body losses and noise in the scattering length, induced by fluctuations of currents inducing the necessary magnetic fields, which are factors crucial to the adequate description of experimental conditions. By means of systematic three-dimensional (3D) simulations, we find a ramping scenario for the change of the scattering length and trap frequencies which results in the creation of robust solitons, that readily withstand the concomitant excitation of the condensate.

DOI
10.1103/physreva.85.023630

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We propose a realistic experimental setup for creating quasi-two-dimensional (2D) bright solitons in dipolar Bose-Einstein condensates (BECs), the existence of which was proposed by Tikhonenkov et al. [Phys. Rev. Lett. 100, 090406 (2008)]. A challenging feature of the expected solitons is their strong inherent anisotropy due to the necessary in-plane orientation of the local moments in the dipolar gas. This may be the first chance of making multidimensional matter-wave solitons, as well as solitons featuring the anistropy due to their intrinsic dynamics. Our analysis is based on the extended Gross-Pitaevskii equation, which includes three-body losses and noise in the scattering length, induced by fluctuations of currents inducing the necessary magnetic fields, which are factors crucial to the adequate description of experimental conditions. By means of systematic three-dimensional (3D) simulations, we find a ramping scenario for the change of the scattering length and trap frequencies which results in the creation of robust solitons, that readily withstand the concomitant excitation of the condensate.
We analyze the physics of bright solitons in 2D dipolar Bose-Einstein condensates. These solitons, which are not possible in short-range interacting gases, constitute the first realistic proposal of fully mobile stable 2D solitons in ultracold gases. In particular, we discuss the necessary conditions for the existence of stable 2D bright solitary waves by means of a 3D analysis of the lowest-lying excitations. We show that the anisotropy of the dipolar potential is crucial, since sufficiently large dipolar interactions can destabilize the 2D soliton. Additionally, we study the scattering of solitary waves, which, contrary to the contact-interacting case, is inelastic and could lead to fusion of the waves. Finally, the experimental possibilities for observability are discussed.
Abstract We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose–Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to a 1D OL trap can have both repulsive and attractive contact interactions. Dark-in-bright solitons are the excited states of bright solitons. The solitons, when subjected to a small perturbation, exhibit sustained breathing oscillation. Dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium velocities the collision between two solitons is found to be quasi-elastic. Results are demonstrated by a numerical simulation of the three-dimensional mean-field Gross–Pitaevskii equation in three spatial dimensions employing realistic interaction parameters for a dipolar 164 Dy BEC.
The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate plane. The tilting angle constitutes an additional tuning parameter, which helps us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without changing its interaction parameters or trap geometry. The phonon instability in a homogeneous two-dimensional condensate of tilted dipoles always features a transient stripe pattern, which eventually breaks into a metastable soliton gas. Finally, we demonstrate how a dipolar BEC in a shallow trap can eventually be turned into a self-trapped matter wave by an adiabatic approach involving the tuning of the tilting angle.
Starting with a Gaussian variational ansatz, we predict anisotropic bright solitons in quasi-2D Bose-Einstein condensates consisting of atoms with dipole moments polarized perpendicular to the confinement direction. Unlike isotropic solitons predicted for the moments aligned with the confinement axis [Phys. Rev. Lett. 95, 200404 (2005)10.1103/PhysRevLett.95.200404], no sign reversal of the dipole-dipole interaction is necessary to support the solitons. Direct 3D simulations confirm their stability.
We demonstrate robust, stable, mobile excited states of quasi-two-dimensional (quasi-2D) dipolar Bose–Einstein condensate (BEC) solitons for repulsive contact interaction with a harmonic trap along the x direction perpendicular to the polarization direction z . Such a soliton can freely move in the y – z plane. A rich variety of such excitations is considered: one quanta of excitation for movement along (i) y axis or (ii) z axis or (iii) both. A proposal for creating these excited solitonic states in a laboratory by phase imprinting is also discussed. We also consider excited states of quasi-2D dipolar BEC soliton where the sign of the dipolar interaction is reversed by a rotating orienting field. In this sign-changed case the soliton moves freely in the x – y plane under the action of a harmonic trap in the z direction. At medium velocity the head-on collision of two such solitons is found to be quasi elastic with practically no deformation. The findings are illustrated using numerical simulation in three and two spatial dimensions employing realistic interaction parameters for a dipolar 164 Dy BEC.
We demonstrate robust, stable, mobile excited states of quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate (BEC) solitons for repulsive contact interaction with a harmonic trap along the x direction perpendicular to the polarization direction z. Such a soliton can freely move in the y − z plane. A rich variety of such excitations is considered: one quanta of excitation for movement along (i) y axis or (ii) z axis or (iii) both. A proposal for creating these excited solitonic states in a laboratory by phase imprinting is also discussed. We also consider excited states of quasi-2D dipolar BEC soliton where the sign of the dipolar interaction is reversed by a rotating orienting field. In this sign-changed case the soliton moves freely in the x − y plane under the action of a harmonic trap in the z direction. At medium velocity the head-on collision of two such solitons is found to be quasi elastic with practically no deformation. The findings are illustrated using numerical simulation in three and two spatial dimensions employing realistic interaction parameters for a dipolar 164Dy BEC.