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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Spinor BEC in Triangular Optical Lattices

C. Becker, Parvis Soltan-Panahi, Jochen Kronjäger, Simon Stellmer, Kai Bongs, K. Sengstock

Published Jun 1, 2007• 2 citations
Publisher

Abstract

In this paper the authors present the first experiments loading a Bose-Einstein condensate into a triangular optical lattice. The lattice is formed by three interfering laser beams intersecting at a relative angle of 120deg in one plane in addition to one retroreflected beam perpendicular to this plane. Depending on the strength of this last beam, the lattice potential can be tuned from a triangular lattice of Id tubes to a Id stack of 2d triangular lattice sheets. As an interesting aspect, the triangular lattice can be transformed into a "magnetic" hexagonal one with sublattices for the different spin orientations, just by rotating the laser polarization.

DOI
10.1109/cleoe-iqec.2007.4386710

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In this paper the authors present the first experiments loading a Bose-Einstein condensate into a triangular optical lattice. The lattice is formed by three interfering laser beams intersecting at a relative angle of 120deg in one plane in addition to one retroreflected beam perpendicular to this plane. Depending on the strength of this last beam, the lattice potential can be tuned from a triangular lattice of Id tubes to a Id stack of 2d triangular lattice sheets. As an interesting aspect, the triangular lattice can be transformed into a "magnetic" hexagonal one with sublattices for the different spin orientations, just by rotating the laser polarization.
Over recent years, exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand experimental environments with non-cubic lattice geometries. In this paper, we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step, the superfluid–Mott insulator (SF–MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this, we study the physics of spinor Bose–Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF–MI transition. Our results suggest that, below the SF–MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly, this opens up new perspectives for a lattice-driven tuning of a spin dynamics resonance occurring through the interplay of the quadratic Zeeman effect and spin-dependent interaction. Finally, we discuss further lattice configurations that can be realized with our setup.
Abstract We present a simple recipe for the rapid formation of spinor Bose–Einstein condensates of 87 Rb atoms in a three-beam crossed optical dipole trap (ODT). Two laser Gaussian beams were crossed at a small angle to form an effective single potential in the intersection region with an independent and widely tunable trap volume and aspect ratio, for both efficient atom loading and number density enhancement. A third Gaussian beam was then introduced to create a potential dimple at the trap center to further increase the atom number density and collision rate, which enabled rapid evaporation to a Bose condensation. In this configuration, 2 × 10 6 atoms were loaded into the three-beam crossed trap from a vapor cell magneto-optical trap, and condensates of 3 × 10 4 – 4.5 × 10 4 atoms were created after 3–5 s of rapid evaporation. The demonstration of efficient and robust BEC production in this ODT suggests the applicability of this trapping geometry to lasers with any far off-resonant wavelengths. To prepare the spinor condensates with a wide tunability of spin population, control of the magnetic fields was first employed during evaporation to polarize the spin states, and the tuning mechanism is discussed. Spinor condensates with an arbitrary spin population were then created via multiple microwave pulses driving the ground hyperfine transitions.
The physics of quantum degenerate cold gases in optical lattices has rapidly grown to an extremely dynamic field over the past few years. In the experimental realizations, however, mainly cubic symmetries (or their two- and one-dimensional projections) are considered. We have implemented an optical lattice with an underlying triangular symmetry in order to investigate strongly correlated ultra-cold atoms in a novel experimental geometry. Exhibiting an explicit polarization dependence (compare figure 1) the optical lattice realized here should allow for the creation and analysis of thus far unexplored magnetic phases. Experiments attending to the quantum phase transition from a superfluid to a Mott-insulating state in a three- as well as in a two-dimensional system with triangular symmetry have been performed. Similarities as well as differences to the findings obtained in cubic lattices will be discussed and can be attributed to the inherent differences in the crucial lattice parameters such as tunneling energy J and on-site interaction U.
In recent years, ultracold atomic gases have been used as tools to study strongly-correlated systems reminiscent of interesting systems from solid-state physics. At temperatures just above absolute zero, particles with integer quantum spin ("bosons") begin to congregate in the ground state of the trapping potential. As the temperature of the system falls below a critical temperature Tc (in this experiment near 200 nK) it undergoes a phase transition called Bose-Einstein condensation. A Bose-Einstein condensate is often described as a macroscopic quantum body, and due to its phase coherence (analogous to an "atom laser") can be used to simulate solid-state systems in a periodic potential called an optical lattice, which resembles that experienced by electrons in the periodic Coulomb potential of a solid-state crystal lattice. These optical lattices are formed by the interference pattern of multiple laser beams, and the associated spatially-dependent Stark shift, resulting in trapping potential for the BEC. The lattice analogs of simple atomic structures have been widely studied. In this thesis, we study the possibility of loading a BEC into multi-dimensional optical lattices. The crystallography of four-beam three-dimensional optical lattices is investigated, and an apparatus is constructed to produce two- to four-beam lattice geometries. We study the structure of the lattice through the technique of Kapitza-Dirac scattering.
Abstract We investigate a Bose–Einstein condensate of F = 187Rb atoms in a 2D spin-dependent optical lattice generated by intersecting laser beams with a superposition of polarizations. For 87Rb the effective interaction of an atom with the electromagnetic field contains scalar and vector (called a fictitious magnetic field, B fic) potentials. The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic rotational motion angular momentum and the hyperfine spin. The ground state of the QR is affected upon applying an external magnetic field, B ext, perpendicular to the plane of QR motion and a sudden change of its topology occurs as the ratio B ext/B fic exceeds a critical value. It is shown that the change of topology of the QR ground state is a result of combined action of Zeeman and Einstein–de Haas effects. The first transfers atoms to the largest hyperfine component to polarize the sample along the field as the external magnetic field is increased. The second sweeps spin to rotational angular momentum, modifying the kinetic energy of the atoms.
We investigate the properties of a Bose-Einstein condensate (BEC) of F=1F=1F=1 87^{87}87Rb atoms in a 2D spin-dependent optical lattice potential generated by intersecting laser beams with a superposition of polarizations. For 87^{87}87Rb, where the total electronic angular momentum is J=1/2J = 1/2J=1/2, the effective interaction of an atom with the electromagnetic field contains a scalar potential VVV and a vector potential (often called fictitious magnetic field). The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic motion rotational angular momentum around the lattice minima and the atomic hyperfine spin FFF. Properties of the QR are strongly affected when an external magnetic field perpendicular to the plane of QR motion is applied. A topological phase transition occurs as the ratio of the external transverse magnetic field to fictitious magnetic field exceeds critical value. At such a quantum phase transition the symmetry of the ground state changes and is expressed in the change of the spin texture.