Condensates of spin-1 sodium display rich spin dynamics due to the antiferromagnetic nature of the interactions in this system. We use Faraday rotation spectroscopy to make a continuous and minimally destructive measurement of the dynamics over multiple spin oscillations on a single evolving condensate. This method provides a sharp signature to locate a magnetically tuned separatrix in phase space which depends on the net magnetization. We also observe a phase transition from a two- to a three-component condensate at a low but finite temperature using a Stern-Gerlach imaging technique. This transition should be preserved as a zero-temperature quantum phase transition.
We observe coherent spin oscillations in an antiferromagnetic spin-1 Bose-Einstein condensate of sodium. The variation of the spin oscillations with magnetic field shows a clear signature of nonlinearity, in agreement with theory, which also predicts anharmonic oscillations near a critical magnetic field. Measurements of the magnetic phase diagram agree with predictions made in the approximation of a single spatial mode. The oscillation period yields the best measurement to date of the sodium spin-dependent interaction coefficient, determining that the difference between the sodium spin-dependent s-wave scattering lengths a(f=2) - a(f=0) is 2.47+/-0.27 Bohr radii.
We investigate the spin-interaction energy spectrum of spin turbulence in a driven spinor Bose-Einstein condensate. Continuous spin driving of a spin-1 condensate produces a nonequilibrium steady state with spatially fluctuating magnetization. We observe a power-law scaling consistent with the
−7/3 exponent predicted for spin-wave turbulence, which persists across our full range of drive strengths despite substantial changes in the spectral anisotropy. After switching off the drive, we track the free-decay evolution and find evidence consistent with a direct cascade of spin-interaction energy toward higher wavenumbers. These results establish an energy-spectral hallmark of spin turbulence and enable quantitative studies of cascade dynamics in spinor superfluids.
We experimentally study spin dynamics in a sodium antiferromagnetic spinor condensate as a result of spin-dependent interactions
c and microwave dressing field interactions characterized by the net quadratic Zeeman effect
qnet. In contrast to magnetic fields, microwave dressing fields enable us to access both negative and positive values of
qnet. We find an experimental signature to determine the sign of
qnet and observe harmonic spin population oscillations at every
qnet except near each separatrix in phase space where spin oscillation period diverges. No spin domains and spatial modes are observed in our system. Our data in the negative
qnet region exactly resembles what is predicted to occur in a ferromagnetic spinor condensate in the positive
qnet region. This observation agrees with an important prediction derived from the mean-field theory: spin dynamics in spin-1 condensates substantially depends on the sign of
qnet/c. This work uses only one atomic species to reveal mean-field spin dynamics, especially the remarkably different relationship between each separatrix and the magnetization, of spin-1 antiferromagnetic and ferromagnetic spinor condensates.
We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor F=1 Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicates the absence of metastability.
We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor
F=1 Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicate the absence of metastability.