We model the behavior of $N$ classical impurity fields immersed in a larger Bose-Einstein condensate by $N+1$ coupled nonlinear Schr\"odinger equations in one, two, and three space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for self-localization of the impurity fields. We derive analytically the attractive tail of the impurity-impurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore numerically the resulting phase diagram, which contains four phases: (I) all fields are miscible; (II) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; (III) the localized impurity fields stay miscible with the condensate, but not with each other; and (IV) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e., they possess a nonclassical rotational inertia, which---combined with lattice order---is a characteristic of supersolidity.We model the behavior of $N$ classical impurity fields immersed in a larger Bose-Einstein condensate by $N+1$ coupled nonlinear Schr\"odinger equations in one, two, and three space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for self-localization of the impurity fields. We derive analytically the attractive tail of the impurity-impurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore numerically the resulting phase diagram, which contains four phases: (I) all fields are miscible; (II) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; (III) the localized impurity fields stay miscible with the condensate, but not with each other; and (IV) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e., they possess a nonclassical rotational inertia, which---combined with lattice order---is a characteristic of supersolidity.

arXiv:0904.1569Physical Review AJul 16, 20096 citations

Suppression and enhancement of impurity scattering in a bose-einstein condensate

Chikkatur, Gorlitz, Dan Stamper-Kurn +3 more

Quantum Electronics and Laser Science ConferenceJan 1, 20002 citations

Bose–Einstein condensation in the presence of an impurity

Paola Giacconi, Fabio Maltoni B, Roberto Soldati

arXiv:cond-mat/0007395Physics Letters AJan 1, 20012 citations

Impurity Crystal in a Bose-Einstein Condensate

David C K Roberts, Sergio Rica

We investigate the behavior of impurity fields immersed in a larger condensate field in various dimensions. We discuss the localization of a single impurity field within a condensate and note the effects of surface energy. We derive the functional form of the attractive condensate-mediated interaction between two impurities. Generalizing the analysis to N impurity fields, we show that within various parameter regimes a crystal of impurity fields can form spontaneously in the condensate. Finally, the system of condensate and crystallized impurity structure is shown to have nonclassical rotational inertia, which is characteristic of superfluidity; i.e., the system can be seen to exhibit supersolid behavior.We investigate the behavior of impurity fields immersed in a larger condensate field in various dimensions. We discuss the localization of a single impurity field within a condensate and note the effects of surface energy. We derive the functional form of the attractive condensate-mediated interaction between two impurities. Generalizing the analysis to N impurity fields, we show that within various parameter regimes a crystal of impurity fields can form spontaneously in the condensate. Finally, the system of condensate and crystallized impurity structure is shown to have nonclassical rotational inertia, which is characteristic of superfluidity; i.e., the system can be seen to exhibit supersolid behavior.

arXiv:0812.0079Physical Review LettersJan 15, 200918 citations

Medium-induced interaction between impurities in a Bose-Einstein condensate

Moritz Drescher, Manfred Salmhofer B, Tilman Enss

We consider two heavy particles immersed in a Bose-Einstein condensate in three dimensions and compute their mutual interaction induced by excitations of the medium. For an ideal Bose gas, the induced interaction is Newtonian up to a shift in distance, which depends on the coupling strength between impurities and Bosons. For a real BEC, we find that, on short distances, the induced potential is dominated by three-body physics of a single Boson bound to the impurities, leading to an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. In particular, we find that both regimes are realized for all impurity-boson couplings and determine the corresponding crossover scales. The transition from the real to the ideal condensate at low gas parameters is investigated.We consider two heavy particles immersed in a Bose-Einstein condensate in three dimensions and compute their mutual interaction induced by excitations of the medium. For an ideal Bose gas, the induced interaction is Newtonian up to a shift in distance, which depends on the coupling strength between impurities and Bosons. For a real BEC, we find that, on short distances, the induced potential is dominated by three-body physics of a single Boson bound to the impurities, leading to an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. In particular, we find that both regimes are realized for all impurity-boson couplings and determine the corresponding crossover scales. The transition from the real to the ideal condensate at low gas parameters is investigated.

arXiv:2303.01916Physical Review AJun 6, 202313 citations

We model the behavior of

N

classical impurity fields immersed in a larger Bose-Einstein condensate by

N+1

coupled nonlinear Schr\"odinger equations in one, two, and three space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for self-localization of the impurity fields. We derive analytically the attractive tail of the impurity-impurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore numerically the resulting phase diagram, which contains four phases: (I) all fields are miscible; (II) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; (III) the localized impurity fields stay miscible with the condensate, but not with each other; and (IV) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e., they possess a nonclassical rotational inertia, which---combined with lattice order---is a characteristic of supersolidity.