Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) have introduced a model of two counter-propagating atomic Gaussian wavepackets incorporating dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first order approximation we derive analytical expressions for the density matrix and anomalous density which provides excellent insight into correlation properties of scattered atoms.Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) have introduced a model of two counter-propagating atomic Gaussian wavepackets incorporating dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first order approximation we derive analytical expressions for the density matrix and anomalous density which provides excellent insight into correlation properties of scattered atoms.

arXiv:cond-mat/0512082Dec 5, 20050 citations

Elastic Scattering Loss of Atoms from Colliding Bose-Einstein Condensate Wave Packets

Y. B. Band, Marek Trippenbach, J. P. Burke +1 more

Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.

arXiv:cond-mat/0005021Physical Review LettersJun 12, 200073 citations

Simulation of a Single Collision of Two Bose-Einstein Condensates

Jan Chwedeńczuk, Paweł Zin, Kazimierz Rza̧żewski +1 more

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.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 LettersOct 25, 200624 citations

Quantum Multimode Model of Elastic Scattering from Bose-Einstein Condensates

Paweł Zin, Jan Chwedeńczuk, Andrzej Veitia +2 more

Mean field approximation treats only coherent aspects of the evolution of a Bose-Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study a semianalytic model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of incoherent scattering processes. Within the model we can treat processes of the elastic collision of atoms into the initially empty modes, and observe how, with growing occupation, the bosonic enhancement is slowly kicking in. A condition for the bosonic enhancement effect is found in terms of relevant parameters. Scattered atoms form a squeezed state. Not only are we able to calculate the dynamics of mode occupation, but also the full statistics of scattered atoms.Mean field approximation treats only coherent aspects of the evolution of a Bose-Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study a semianalytic model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of incoherent scattering processes. Within the model we can treat processes of the elastic collision of atoms into the initially empty modes, and observe how, with growing occupation, the bosonic enhancement is slowly kicking in. A condition for the bosonic enhancement effect is found in terms of relevant parameters. Scattered atoms form a squeezed state. Not only are we able to calculate the dynamics of mode occupation, but also the full statistics of scattered atoms.

arXiv:cond-mat/0412622Physical Review LettersMay 23, 200537 citations

Suppression of elastic scattering loss for slowly colliding Bose-Einstein condensates

Y. B. Band, John H. Burke, Andrea Simoni +1 more

Superfluid suppression of the elastic scattering loss in atomic Bose condensed systems can be significant when the ratio of the relative velocity of the wave packets to the critical velocity is $\ensuremath{\sim}1.$ We show how to incorporate the effect of such losses and their suppression into the time-dependent dynamics of two colliding condensate wave packets. We illustrate the magnitude of the effect through three-dimensional simulations of the collision dynamics of an $|F=2,{M}_{F}=2〉$ with an $|F=2,{M}_{F}=1〉{}^{87}\mathrm{Rb}$ condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the ${M}_{F}=1$ wave packet for suitable experimental conditions.Superfluid suppression of the elastic scattering loss in atomic Bose condensed systems can be significant when the ratio of the relative velocity of the wave packets to the critical velocity is $\ensuremath{\sim}1.$ We show how to incorporate the effect of such losses and their suppression into the time-dependent dynamics of two colliding condensate wave packets. We illustrate the magnitude of the effect through three-dimensional simulations of the collision dynamics of an $|F=2,{M}_{F}=2〉$ with an $|F=2,{M}_{F}=1〉{}^{87}\mathrm{Rb}$ condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the ${M}_{F}=1$ wave packet for suitable experimental conditions.

Physical Review AJul 1, 200111 citations

Single quantum realization of a collision of two Bose--Einstein condensates

Jan Chwedeńczuk, Paweł Zin, Kazimierz Rza̧żewski +1 more

We propose a method for simulating a single realization of a collision of two Bose--Einstein condensates. Recently in Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) we introduced a quantum model of an incoherent elastic scattering in a collision of two counter-propagating atomic Gaussian wavepackets. Here show that this model is capable of generating the data that can be interpreted as results of a single collision event. We find a range of parameters, including relative velocity, population and the size of colliding condensates, where the structure of hallo of scattered atoms in a single realization strongly differs from that averaged over many realizations.We propose a method for simulating a single realization of a collision of two Bose--Einstein condensates. Recently in Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) we introduced a quantum model of an incoherent elastic scattering in a collision of two counter-propagating atomic Gaussian wavepackets. Here show that this model is capable of generating the data that can be interpreted as results of a single collision event. We find a range of parameters, including relative velocity, population and the size of colliding condensates, where the structure of hallo of scattered atoms in a single realization strongly differs from that averaged over many realizations.

arXiv:cond-mat/0606327Jun 13, 20060 citations

|F=2,{M}_{F}=2〉

with an

|F=2,{M}_{F}=1〉{}^{87}\mathrm{Rb}

condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the

{M}_{F}=1

wave packet for suitable experimental conditions.