Spinor condensates with a laser-induced quadratic Zeeman effect

Abstract

We show that an effective quadratic Zeeman effect can be generated in 52 Cr by proper laser configurations, and in particular by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create S = 1/2 systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems. PACS numbers:Spinor Bose-Einstein condensates (BEC) have recently attracted a growing interest. A spinor gas is formed by atoms in two or more internal states, which can be simultaneously confined by optical dipole traps [1]. Spinor BECs present a rich variety of possible ground states, including ferromagnetic and polar phases for spin-1 BECs [2,3], and an additional cyclic phase for the spin-2 case [4,5]. Elegant topological classifications of the possible spinor ground-states have been recently proposed [6,7]. The spinor dynamics has been also actively studied, in particular the coherent oscillations between the different spinor components [8]. In addition, a spinor gas has been recently quenched across a transition between phases of different symmetries, inducing topological defects [9,10].The recent creation of a Chromium BEC [11] opens new interesting possibilities for the spinor physics. The ground state of 52 Cr is 7 S 3 , constituting the first accessible example of a spin-3 BEC. The spin-3 BEC presents a novel rich ground-state phase diagram at low magnetic fields [12,13,14]. In particular, the existence of biaxial spin-nematic phases [12] opens fascinating links between the spin-3 BECs and the physics of liquid crystals. In addition, 52 Cr has a large magnetic moment µ = 6µ B , where µ B is the Bohr magneton, i.e. six times larger than that of alkali atoms. The corresponding large dipoledipole interaction (DDI) can lead to novel effects in the BEC physics [15]. In particular, dipolar effects were observed for the first time ever in quantum gases in the expansion of a Chromium BEC [16]. The DDI plays also a significant role in the spinor dynamics, since it violates spin conservation, allowing for the transfer of spin into center-of-mass angular momentum, i.e. the equivalent to the Einstein-de Haas effect (EdH) [13,17]. Interestingly, the EdH and other dipolar effects may be also observed in 87 Rb spinor BECs since, in spite of its low µ, the * Present address: TOPTICA Photonics AG, Lochhamer Schlag 19, D-82166 Gräfelfing, Germany.DDI may be significant when compared to the low energy scales associated with the spinor physics [18,19].In the presence of an external magnetic field, B, the different Zeeman sublevels (with quantum number m) of a spinor BEC acquire different shifts due to the linear Zeeman effect (LZE), ∆E LZE (m) = gµ B Bm, with g the Landé factor. The LZE plays no ...

Dynamics in spinor condensates tuned by a microwave dressing field

“…Spin-dynamics in F =1 antiferromagnetic and ferromagnetic spinor BECs have been studied in magnetic fields where q net > 0 with 23 Na and 87 Rb atoms, respectively [1]. A few methods have been explored for generating a negative quadratic Zeeman shift, such as via a microwave dressing field [1,11,[19][20][21] or through a linearly polarized off-resonant laser beam [22]. In this paper, we choose the first method.…”

Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate

“…By controlling the quadratic level shift [39,40], the BN phase could be realized by experimentally simple means. The ground-state phase diagram is shown in Fig.…”

“…Preparation of spin-2 BECs has been achieved using 87 Rb [27,[35][36][37], which, like 23 Na, is predicted to exhibit the nematic phases [20,38]. The BN phase can then be realized by controlling the quadratic level shift, e.g., by microwave dressing [39] or laser fields [40]. Both 87 Rb and 23 Na are commonly used in spinor-BEC experiments, making the BN phase the most likely candidate for realization of a ground-state manifold supporting nonAbelian defects.…”

Stability and internal structure of vortices in spin-1 Bose-Einstein condensates with conserved magnetization

“…This can be induced by combining a static magnetic field with a microwave dressing field, generating and ac Stark shift that corresponds to a highly tunable quadratic level shift [87]. The level shift may also be induced by lasers [88]. Here we take g 2 B 2 z = −0.2 ω.…”