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arXiv:1607.04574 · Physical Review A

Spin-dipole oscillation and polarizability of a binary Bose-Einstein condensate near the miscible-immiscible phase transition

Tom Bienaimé, Eleonora Fava, Giacomo Colzi, Carmelo Mordini, Simone Serafini, Chunlei Qu, S. Stringari, Giacomo Lamporesi, Gabriele Ferrari

Published Dec 30, 2016• 47 citations
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Abstract

We report on the measurement of the spin-dipole (SD) polarizability and of the frequency of the SD oscillation of a two-component Bose-Einstein condensate of sodium atoms occupying the $|3{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2},F=1,{m}_{F}=\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}$ hyperfine states. This binary spin mixture presents the important properties of being, at the same time, fully miscible and rid of the limit set by buoyancy. It is also characterized by a huge enhancement of the SD polarizability and by the consequent softening of the frequency of the SD oscillation, due to the vicinity to the transition to the immiscible phase. The experimental data are successfully compared with the predictions of theory.

DOI
10.1103/physreva.94.063652

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We report on the measurement of the spin-dipole (SD) polarizability and of the frequency of the SD oscillation of a two-component Bose-Einstein condensate of sodium atoms occupying the ∣32S1/2,F=1,mF=\ifmmode±\else\textpm\fi1\ensuremath⟩|3{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2},F=1,{m}_{F}=\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}∣32S1/2​,F=1,mF​=\ifmmode±\else\textpm\fi1\ensuremath⟩ hyperfine states. This binary spin mixture presents the important properties of being, at the same time, fully miscible and rid of the limit set by buoyancy. It is also characterized by a huge enhancement of the SD polarizability and by the consequent softening of the frequency of the SD oscillation, due to the vicinity to the transition to the immiscible phase. The experimental data are successfully compared with the predictions of theory.
The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled setting. In a homogeneous system, the transition between mixed and separated phases is fully characterized by a miscibility parameter based on the ratio of intra- to interspecies interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.
We investigate the effects of dipole-dipole (DD) interactions on immiscibility-miscibility transitions (IMT's) in two-component Bose-Einstein condensates (BEC's) trapped in the harmonic-oscillator (HO) potential, with the components linearly coupled by a resonant electromagnetic field (accordingly, the components represent two different spin states of the same atom). The problem is studied by means of direct numerical simulations. Different mutual orientations of the dipolar moments in the two components are considered. It is shown that, in the binary BEC formed by dipoles with the same orientation and equal magnitudes, the IMT cannot be induced by the DD interaction alone, being possible only in the presence of the linear coupling between the components, while the miscibility threshold is affected by the DD interactions. However, in the binary condensate with the two dipolar components polarized in opposite directions, the IMT can be induced without any linear coupling. Further, we demonstrate that those miscible and immiscible localized states, formed in the presence of the DD interactions, which are unstable evolve into robust breathers, which tend to keep the original miscibility or immiscibility, respectively. An exception is the case of a very strong DD attraction, when narrow stationary modes are destroyed by the instability. The binary BEC composed of copolarized dipoles with different magnitudes are briefly considered as well.
The spin dynamics of a harmonically trapped Bose-Einstein condensed binary mixture of sodium atoms is experimentally investigated at finite temperature. In the collisional regime the motion of the thermal component is shown to be damped because of spin drag, while the two condensates exhibit a counterflow oscillation without friction, thereby providing direct evidence for spin superfluidity. Results are also reported in the collisionless regime where the spin components of both the condensate and thermal part oscillate without damping, their relative motion being driven by a mean-field effect. We also measure the static polarizability of the condensed and thermal parts and we find a large increase of the condensate polarizability with respect to the T=0 value, in agreement with the predictions of theory.
We investigate the spectrum of spin conductivity for a miscible two-component Bose-Einstein condensate (BEC) that exhibits spin superfluidity. By using the Bogoliubov theory, the regular part being the spin conductivity at finite ac frequency and the spin Drude weight characterizing the $\ensuremath{\delta}$-function peak at zero frequency are analytically computed. We demonstrate that the spectrum exhibits a power-law behavior at low frequency, reflecting gapless density and spin modes specific to the binary BEC. At the phase transition points into immiscible and quantum-droplet states, the change in quasiparticle dispersion relations modifies the power law. In addition, the spin Drude weight becomes finite, indicating zero spin resistivity due to spin superfluidity. Our results also suggest that the Andreev-Bashkin drag density is accessible by measuring the spin conductivity spectrum.
Using a sum rule approach we investigate the dipole oscillation of a spin-orbit coupled Bose-Einstein condensate confined in a harmonic trap. The crucial role played by the spin polarizability of the gas is pointed out. We show that the lowest dipole frequency exhibits a characteristic jump at the transition between the stripe and spin-polarized phase. Near the second-order transition between the spin-polarized and the single minimum phase the lowest frequency is vanishingly small for large condensates, reflecting the divergent behavior of the spin polarizability. We compare our results with recent experimental measurements as well as with the predictions of effective mass approximation.
The effects of atom numbers on the miscibility-immiscibility transition of a harmonically trapped population imbalanced binary Bose-Einstein condensate are investigated. In two-dimensional parameter space expanded by the strength of interspecies interaction and the ratio of atom numbers between two components, we have mapped out the ground-state phase diagrams for the ideal model without intraspecies interactions, and for the $^{23}\mathrm{Na}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixture and the $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture with experimentally accessible intraspecies scattering lengths, respectively. It is found that all the phase diagrams include the miscible, symmetric immiscible, and asymmetric immiscible phases, and there exists a tricritical point where those three different phases merge. Furthermore, the phase boundaries among those three phases show a strong dependence on the atom numbers of two components. These results can be observed in current experiments.