Since its first observation in 1995,1 Bose-Einstein condensation (BEC) experiments in dilute gases have been performed with only a few different kinds of magnetic traps. In addition, the effect of the confining potential on, e.g., the condensation process,2 has not been investigated experimentally. We have performed a BEC experiment with 87Rb atoms in a Ioffe-Pritchard magnetic potential,3 which opens up the possibility to study, e.g., Bose–Einstein condensates released in only one dimension.
Since its first observation in 1995,1 Bose-Einstein condensation (BEC) experiments in dilute gases have been performed with only a few different kinds of magnetic traps. In addition, the effect of the confining potential on, e.g., the condensation process,2 has not been investigated experimentally. We have performed a BEC experiment with 87Rb atoms in a Ioffe-Pritchard magnetic potential,3 which opens up the possibility to study, e.g., Bose–Einstein condensates released in only one dimension.
Since its first observation in 1995, Bose-Einstein condensation (BEC) experiments in dilute gases have been performed with only a few different kinds of magnetic traps. We have performed a BEC experiment with /sup 87/Rb atoms in a Ioffe-Pritchard magnetic potential, which opens up the possibility to study, e.g., Bose-Einstein condensates released in only one dimension. Our trap consists of a clip-like coil, which generates a pure two-dimensional (2D) quadrupole field for radial confinement. The axial confinement is provided by two plane pinch coils inside the clip-coil. These two coils create a bottle field. Two additional Helmholtz coils on the same symmetry axis are used to compensate the homogeneous part of the bottle field. By continuously varying the currents through the coils, the trapping potential can be changed from a 3D spherical harmonic to a 2D linear potential. The change can be done adiabatically or nonadiabatically by switching off the axial confinement slowly, or instantaneously respectively. This opens up the possibility to study 1D nonlinear atom optics. In combination with, e.g., far detuned light sheets, a Fabry-Perot type interferometer for a condensate might be realizable. Our experiments are performed in a vacuum system with two magneto-optical traps, which serves as the source of cold atoms for the magnetic trap. 10/sup 9/ atoms are captured in less than one minute. RF-induced evaporative cooling is used to increase the phase space density of the trapped atomic cloud. The BEC phase transition occurs at a temperature of 550 nK with 10/sup 6/ particles in the trap. Pure condensates with more than 10/sup 5/ atoms were produced.
Summary form only given.Since its first observation in 1995, Bose-Einstein condensation (BEC) experiments in dilute gases have been performed with only a few different kinds of magnetic traps. We have performed a BEC experiment with /sup 87/Rb atoms in a Ioffe-Pritchard magnetic potential, which opens up the possibility to study, e.g., Bose-Einstein condensates released in only one dimension. Our trap consists of a clip-like coil, which generates a pure two-dimensional (2D) quadrupole field for radial confinement. The axial confinement is provided by two plane pinch coils inside the clip-coil. These two coils create a bottle field. Two additional Helmholtz coils on the same symmetry axis are used to compensate the homogeneous part of the bottle field. By continuously varying the currents through the coils, the trapping potential can be changed from a 3D spherical harmonic to a 2D linear potential. The change can be done adiabatically or nonadiabatically by switching off the axial confinement slowly, or instantaneously respectively. This opens up the possibility to study 1D nonlinear atom optics. In combination with, e.g., far detuned light sheets, a Fabry-Perot type interferometer for a condensate might be realizable. Our experiments are performed in a vacuum system with two magneto-optical traps, which serves as the source of cold atoms for the magnetic trap. 10/sup 9/ atoms are captured in less than one minute. RF-induced evaporative cooling is used to increase the phase space density of the trapped atomic cloud. The BEC phase transition occurs at a temperature of 550 nK with 10/sup 6/ particles in the trap. Pure condensates with more than 10/sup 5/ atoms were produced.
We present the first experimental realization of Bose–Einstein condensation in a purely magnetic double-well potential. This has been achieved by combining a static Ioffe–Pritchard trap with a time orbiting potential. The double trap can be rapidly switched to a single-harmonic trap of identical oscillation frequencies, thus accelerating the two condensates towards each other. Furthermore, we show that time-averaged potentials can be used as a means to control the radial confinement of the atoms. Manipulation of the radial confinement allows vortices and radial quadrupole oscillations to be excited.
For sufficiently low temperatures, a Bose gas experiences a transition into a Bose-Einstein condensate, characterized by a macroscopic occupation of the ground state of the system. The development of efficient cooling and trapping techniques for neutral atoms led in 1995, to the first observation of BEC in dilute alkali gases in 87Rb [1]. This remarkable achievement has been followed by BEC experiments in various other elements. The BEC has become during the last years, one of the most active and fruitful research areas of modern atomic physics, constituting an interdisciplinary field, which links atomic physics with various other research areas, like quantum optics, condensed-matter physics, and very especially nonlinear physics.
Abstract. New developments of optical trapping techniques make it possible to confine atoms independently of their spin orientation in experiments and thus result in spinor condensates. As a continuation of our previous work [M. Li, X. Luo, J. Wei, and M. Zhen, SIAM J. Math. Anal., 56 (2024), pp. 4375–4414], we investigate physical states as well as qualitative properties describing the aggregation and extinction of atoms, of spin-1 Bose–Einstein condensate in an Ioffe–Pritchard magnetic field, through two conserved quantities, the number of atoms and the total magnetization. Unlike the related free case which is well studied in [Y. Z. Kong, Q. X. Wang, and D. Zhao, Calc. Var. Partial Differential Equations, 60 (2021), 152] and our previous work, the presence of the Ioffe–Pritchard magnetic field, which competes dramatically with the harmonic trapping, requires new ideas to capture the physical states and analyze their qualitative properties. Based on the ferromagnetic or antiferromagnetic characterization of spin-1 Bose–Einstein condensate, our results support some experimental observations in [T. Ho and S. Yip, Phys. Rev. Lett., 84 (2000), pp. 4031–4034; C. Law, H. Pu, and N. Bigelow, Phys. Rev. Lett., 81 (1998), pp. 5257–5261] and some numerical analysis on ground states reported in [W. Bao, I. Chern, and Y. Zhang, J. Comput. Phys., 253 (2013), pp. 189–208; W. Bao and F. Lim, SIAM J. Sci. Comput., 30 (2008), pp. 1925–1948; W. Bao and H. Wang, SIAM J. Numer. Anal., 45 (2007), pp. 2177–2200].
In 1925, Einstein predicted the condensation of bosons into the ground state of the system for low (but finite) temperatures. Several phenomena, including superfluidity and superconductivity have been associated with Bose-Einstein condensation, but these systems interact strongly with their environment and pure Bose-Einstein condensation could not be established. It took 70 years, in which time the laser was discovered, and laser cooling techniques to manipulate atoms in a dilute atomic gas, before Bose-Einstein condensation in dilute atomic gases could be demonstrated in 1995. In the first condensation experiments, BECs were created in a magnetic trap. Since in a magnetic trap not all mF states of the atom can be trapped simultaneously, thereby limiting the number of experiments that can be done, other ways of trapping and generating BECs were sought and found. In 2001, the first all-optical BEC was made, where the dipole force was used to trap atoms in the crossing of two far red detuned laser beams. In an optical dipole trap not only atoms in different internal states can be trapped, but also different atomic species simultaneously. In this thesis, the formation of an all-optical Bose-Einstein condensate with rubidium atoms is presented. Conventional all-optical BECs are usually created in high power CO2 laser dipole traps, or have complicated laser cooling schemes and complex dipole trap setups. In our simple and straightforward setup, we load rubidium atoms from a magneto-optical trap into a crossed optical dipole trap created by a single frequency Yb:YAG laser with a wavelength at 1030 nm. The small wavelength allows for a small diffraction limit, and permits us to use standard optical materials, thus making the experimental setup cost effective. Other attempts to achieve Bose-Einstein condensation in a multi-mode (frequency) fiber laser at 1064 nm failed, because the atom loss was quite high. It is assumed that the multi-mode character of the fiber laser induces Raman transitions in rubidium atoms, thereby heating them. We can trap about ∼ 5E7 atoms in a single beam dipole trap out of ∼ 5E9 atoms trapped in theMOT, and ∼ 350,000 atoms can be trapped in a crossed beam dipole trap due to the smaller trap volume. 70% of the atoms in the dipole trap is optically pumped into one mF state. Quantum degeneracy is reached by evaporatively cooling the atoms in the crossed dipole trap by ramping down the laser power with three linear ramps. We can independently change the power of each beam by an AOM. This allows us to use one beam as an atom waveguide for future experiments. After evaporation, we typically have about 10,000 atoms at a temperature below the critical temperature. We have proved Bose-Einstein condensation by using the anisotropic expansion of a quantum degenerate gas trapped in an anisotropic potential. The aspect ratio of our atom cloud changed during a time of flight from 0.7 to 1.2 in 10 ms, thus proving that we have reached quantum degeneracy. We have about 5,000 condensed atoms in our optical dipole trap at a temperature less than 100 nK. The remaining atoms are thermal. Bose-Einstein condensation is obtained within 8 s, and we can repeat the experiment every 30 s. It should be mentioned that the Bose-Einstein experiment was moved from the ”Leibniz Universität Hannover” to the ”Technische Universität Darmstadt”, and had to be completely rebuilt. All-optical Bose-Einstein condensation was reached within one year after the move. Our Bose-Einstein condensation setup presents an ideal starting point for using our condensates in combination with miniaturized atom optical setups based on our novel microfabricated optical elements. With our microlenses, we can create a number of possible dipole trap configurations, such as the dipole trap array or the cylindrical microlens array. Using microlenses in miniaturized atom optical setups opens a completely new field of coherent atom optics. Also because the tight confinement of the microtraps allows us to load a 3D BEC, a 1D BEC, or a Tonks-Girardeau gas in the micropotentials depending on the density.