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arXiv:cond-mat/9811161 · Physical Review Letters

Observation of Metastable States in Spinor Bose-Einstein Condensates

H.‐J. Miesner, Dan Stamper-Kurn, J. Stenger, S. Inouye, A. P. Chikkatur, Wolfgang Ketterle

Published Mar 15, 1999• 387 citations
arXivHTMLPDF

Abstract

Bose-Einstein condensates have been prepared in long-lived metastable excited states. Two complementary types of metastable states were observed. The first is due to the immiscibility of multiple components in the condensate, and the second to local suppression of spin-relaxation collisions. Relaxation via recondensation of noncondensed atoms, spin relaxation, and quantum tunneling was observed. These experiments were done with $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ spinor Bose-Einstein condensates of sodium confined in an optical dipole trap.

DOI
10.1103/physrevlett.82.2228

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Bose-Einstein condensates have been prepared in long-lived metastable excited states. Two complementary types of metastable states were observed. The first is due to the immiscibility of multiple components in the condensate, and the second to local suppression of spin-relaxation collisions. Relaxation via recondensation of noncondensed atoms, spin relaxation, and quantum tunneling was observed. These experiments were done with F=1F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1F=1 spinor Bose-Einstein condensates of sodium confined in an optical dipole trap.
Quantum tunneling was observed in the decay of metastable spin domains in gaseous Bose-Einstein condensates. A mean-field description of the tunneling was developed and compared with measurement. The tunneling rates are a sensitive probe of the boundary between spin domains, and indicate a spin structure which is prohibited in the bulk fluid. These experiments were performed with optically trapped F=1F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1F=1 spinor Bose-Einstein condensates of sodium.
Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.
The study of quantum degenerate gases has many applications in topics such as condensed matter dynamics, precision measurements and quantum phase transitions. We built an apparatus to create 87Rb Bose-Einstein condensates (BECs) and generated, via optical and magnetic interactions, novel quantum systems in which we studied the contained phase transitions. For our first experiment we quenched multi-spin component BECs from a miscible to dynamically unstable immiscible state. The transition rapidly drives any spin fluctuations with a coherent growth process driving the formation of numerous spin polarized domains. At much longer times these domains coarsen as the system approaches equilibrium. For our second experiment we explored the magnetic phases present in a spin-1 spin-orbit coupled BEC and the contained quantum phase transitions. We observed ferromagnetic and unpolarized phases which are stabilized by the spin-orbit coupling’s explicit locking between spin and motion. These two phases are separated by a critical curve containing both first-order and second-order transitions joined at a critical point. The narrow first-order transition gives rise to long-lived metastable states. For our third experiment we prepared independent BECs in a double-well potential, with an artificial magnetic field between the BECs. We transitioned to a single BEC by lowering the barrier while expanding the region of artificial field to cover the resulting single BEC. We compared the vortex distribution nucleated via conventional dynamics to those produced by our procedure, showing our dynamical process populates vortices much more rapidly and in larger number than conventional nucleation.
The recently realized multicomponent Bose-Einstein condensates provide opportunities to explore the rich physics brought about by the spin degrees of freedom. For instance, we can study spin waves and phase separation, macroscopic quantum tunneling, Rabi oscillations, the coupling between spin gradients and superfluid flow, squeezed spin states, vortices and other topological excitations. Theoretically, there have been already some studies of the ground-state properties of these systems and their line-like vortex excitations. In analogy with nuclear physics or the quantum Hall effect, we explore here the possibility of observing point-like topological excitations or skyrmions. These are nontrivial spin textures that in principle can exist in a spinor Bose-Einstein condensate. In particular, we investigate the stability of skyrmions in a fictitious spin-1/2 condensate of Rb87 atoms. We find that skyrmions can exist in this case only as a metastable state, but with a lifetime of the order of, or even longer than, the typical lifetime of the condensate itself. In addition to determining the size and the lifetime of the skyrmion, we also present its spin texture and finally briefly consider its dynamical properties.
Two groups, in Orsay and in Paris, have recently obtained experimental evidence for Bose-Einstein condensation on He4 atoms in the metastable state 23S1. The condensates which have been obtained are the first ones where atoms are condensed, not in their electronic ground state, but in an excited state, in this case a metastable state about 20 eV above the ground state. In principle, Penning collisions should very rapidly destroy the cloud of cold metastable atoms and it seems hopeless to observe Bose-Einstein condensation in such a system. But, as suggested by Shlyapnikov et al, the conservation of the total spin during the collision reduces the Penning collision cross-sections by several orders of magnitude and this explains why large enough densities of metastable atoms can be obtained to observe the condensation. We briefly describe the first experimental results which have been obtained in Paris. Atoms are optically detected by optical imaging at 1083 nm (wavelength of the transition connecting the metastable state 23S1 to the triplet state 23P2). The evolution of the anisotropy of the images during a ballistic expansion gives clear evidence for the condensation. Orders of magnitude are also obtained for the scattering length describing the collision between 2 metastable atoms. The large value of this scattering length (of the order of 10 nm) allows one to reach the so called hydrodynamic regime where the mean free path between 2 collisions in the thermal cloud becomes smaller than the size of the cloud. Preliminary results showing the transition between the collisionless regime and the hydrodynamic regime are presented and compared to theoretical predictions.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.