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arXiv:1310.6785 · Physical Review A

Dynamics in spinor condensates tuned by a microwave dressing field

Lichao Zhao, Jie Jiang, Tao Tang, Micah Webb, Yingmei Liu

Published Feb 10, 2014• 82 citations
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Abstract

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 ${q}_{\mathrm{net}}$. In contrast to magnetic fields, microwave dressing fields enable us to access both negative and positive values of ${q}_{\mathrm{net}}$. We find an experimental signature to determine the sign of ${q}_{\mathrm{net}}$ and observe harmonic spin population oscillations at every ${q}_{\mathrm{net}}$ 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 ${q}_{\mathrm{net}}$ region exactly resembles what is predicted to occur in a ferromagnetic spinor condensate in the positive ${q}_{\mathrm{net}}$ 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 ${q}_{\mathrm{net}}/c$. 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.

DOI
10.1103/physreva.89.023608

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We experimentally study spin dynamics in a sodium antiferromagnetic spinor condensate as a result of spin-dependent interactions ccc and microwave dressing field interactions characterized by the net quadratic Zeeman effect qnet{q}_{\mathrm{net}}qnet​. In contrast to magnetic fields, microwave dressing fields enable us to access both negative and positive values of qnet{q}_{\mathrm{net}}qnet​. We find an experimental signature to determine the sign of qnet{q}_{\mathrm{net}}qnet​ and observe harmonic spin population oscillations at every qnet{q}_{\mathrm{net}}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{q}_{\mathrm{net}}qnet​ region exactly resembles what is predicted to occur in a ferromagnetic spinor condensate in the positive qnet{q}_{\mathrm{net}}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{q}_{\mathrm{net}}/cqnet​/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.
Spinor condensates immersed in a microwave dressing field, which access both negative and positive values of the net quadratic Zeeman effect, have been realized in a recent experiment. In this report, we study the ground state properties of a spinor condensate with a microwave dressing field which enables us to access both negative and positive values of quadratic Zeeman energy. The ground state exhibits three different phases by varying the magnetization and the net quadratic Zeeman energy for both cases of ferromagnetic and antiferromagnetic interactions. We investigate the atomic-number fluctuations of the ground state and show that the hyperfine state displays super-Poissonian and sub-Poissonian distributions in the different phases. We also discuss the dynamical properties and show that the separatrix has a remarkable relation to the magnetization.
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.
This thesis discusses non-equilibrium phenomena in antiferromagnetic spinor quantum gases. We investigate, both experimentally and theoretically, the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition. A microwave dressing field was used as a novel tool to access the polar to antiferrmagnetic quantum phase transition at the quadratic Zeeman shift, q=0. By performing instantaneous quenches across the phase transition,a dynamical instability was induced in the atomic cloud. This lead to pair formation and rapid amplification of spin +/-1 atoms through spin-mixing collisions. The spatial ordering kinetics in the vicinity of the phase transition was quantified by performing the local spin measurement. The coarsening dynamics was observed for the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud. Rich nonequilibrium behavior was observed in the form of growth and decay of both nematic and magnetic spin waves, following the quench. The spatiotemporal evolution was characterized through two particle correlations between atoms in each pair of spin states, which revealed dramatic differences between the dynamics of the spin correlations and those of the spin populations. \nFinally, we demonstrate the remarkable influence of linear Zeeman term on non-equilibrium dynamics of spinor Bose-Einstein condensates. We show that contrary to prior understanding magnetic field gradient actually suppresses the tendency of spin 0 state to separate into spin +/-1 state. This reconciles the Bogoliubov discrepancies and leads to a dramatic sharpening of the transition point, resulting in a resolution at the 1 Hz level. Our results point to the use of dynamics, rather than equilibrium quantities for high precision measurements of phase transitions in quantum gases.
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.
23Na^{23}\mathrm{Na}23Na spin-1 Bose-Einstein condensates are used to experimentally demonstrate that mean-field physics beyond the single-mode approximation can be relevant during the nonequilibrium dynamics. The experimentally observed spin oscillation dynamics and associated dynamical spatial structure formation confirm theoretical predictions that are derived by solving a set of coupled mean-field Gross-Pitaevskii equations [J. Jie et al., Phys. Rev. A 102, 023324 (2020)]. The experiments rely on microwave dressing of the f=1f=1f=1 hyperfine states, where fff denotes the total angular momentum of the 23Na^{23}\mathrm{Na}23Na atom. The fact that physics beyond the single-mode approximation at the mean-field level, i.e., spatial mean-field dynamics that distinguishes the spatial density profiles associated with different Zeeman levels, can, in certain parameter regimes, have a pronounced effect on the dynamics when the spin healing length is comparable to or larger than the size of the Bose-Einstein condensate has implications for using Bose-Einstein condensates as models for quantum phase transitions and spin squeezing studies as well as for nonlinear SU(1,1) interferometers.
We experimentally study two quantum phase transitions in a sodium spinor condensate immersed in a microwave dressing field. We also demonstrate that many previously unexplored regions in the phase diagram of spinor condensates can be investigated by adiabatically tuning the microwave field across one of the two quantum phase transitions. This method overcomes two major experimental challenges associated with some widely used methods, and is applicable to other atomic species. Agreements between our data and the mean-field theory for spinor Bose gases are also discussed.