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arXiv:1105.2857 · Physical Review A

Anomalous tunneling of collective excitations and effects of superflow in the polar phase of a spin-1 spinor Bose-Einstein condensate

Shohei Watabe, Yusuke S. Kato, Yoji Ohashi

Published Jul 25, 2011• 9 citations
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Abstract

We investigate tunneling properties of collective modes in the polar phase of a spin-1 spinor Bose-Einstein condensate (BEC). This spinor BEC state has two kinds of gapless modes (i.e., Bogoliubov and spin-wave). Within the framework of mean-field theory at $T=0$, we show that these Goldstone modes exhibit perfect transmission in the low-energy limit. Their anomalous tunneling behavior still holds in the presence of superflow, except in the critical current state. In the critical current state, while the tunneling of Bogoliubov mode is accompanied by finite reflection, the spin wave still exhibits perfect transmission, unless the strengths of spin-dependent and spin-independent interactions take the same value. We discuss the relation between perfect transmission of a spin wave and underlying superfluidity through a comparison of wave functions of the spin wave and the condensate.

DOI
10.1103/physreva.84.013616

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We investigate tunneling properties of collective modes in the polar phase of a spin-1 spinor Bose-Einstein condensate (BEC). This spinor BEC state has two kinds of gapless modes (i.e., Bogoliubov and spin-wave). Within the framework of mean-field theory at T=0T=0T=0, we show that these Goldstone modes exhibit perfect transmission in the low-energy limit. Their anomalous tunneling behavior still holds in the presence of superflow, except in the critical current state. In the critical current state, while the tunneling of Bogoliubov mode is accompanied by finite reflection, the spin wave still exhibits perfect transmission, unless the strengths of spin-dependent and spin-independent interactions take the same value. We discuss the relation between perfect transmission of a spin wave and underlying superfluidity through a comparison of wave functions of the spin wave and the condensate.
We investigate the tunneling properties of collective excitations in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate (BEC). In addition to the Bogoliubov mode, this superfluid phase has two spin excitations, namely, the gapless transverse spin wave and the quadrupolar mode with a finite excitation gap. In the mean-field theory at T=0T=0T=0, we examine how these collective modes tunnel through a barrier potential that couples to the local density of particles. In the presence of supercurrent with a finite momentum qqq, while the Bogoliubov mode shows the so-called anomalous tunneling behavior (which is characterized by perfect transmission) in the low-energy limit, the transverse spin wave transmits perfectly only when the momentum kkk of this mode coincides with $\ifmmode\pm\else\textpm\fi{}q$. At $k=\ifmmode\pm\else\textpm\fi{}q$, the wave function of this spin wave has the same form as the condensate wave function in the current-carrying state, so that the mechanism of this perfect transmission is found to be the same as tunneling of the supercurrent. Using this fact, the perfect transmission of the spin wave is proved for a generic barrier potential. We show that such perfect transmission does not occur in the quadrupolar mode. Further, we consider the effects of potentials breaking U(1) and spin-rotation symmetries on the transmission properties of excitations. Our results would be useful for understanding excitation properties of spinor BEC's, as well as the anomalous tunneling phenomenon in Bose superfluids.
We investigate tunneling properties of collective spin-wave excitations in the polar state of a spin-1 spinor Bose-Einstein condensate. Within the mean-field theory at T = 0, we show that when the condensate is in the critical supercurrent state, the spin wave mode exhibits perfect transmission through a nonmagnetic potential barrier in the low energy limit, unless the strength of a spin-independent interaction co equals that of a spin-dependent interaction co Such an anomalous tunneling behavior is absent in the case of a magnetic barrier. We also clarify a scaling law of the transmission probability as a function of the mode energy.
We investigate the tunneling properties of collective excitations through a domain wall in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate. Within the mean-field theory at T=0T=0T=0, we show that the transverse spin wave undergoes perfect reflection in the low-energy limit. This reflection property differs considerably from that of a domain wall in a Heisenberg ferromagnet where spin-wave excitations exhibit perfect transmission at arbitrary energy. When the Bogoliubov mode is scattered from this domain wall soliton, the transmission and reflection coefficients exhibit pronounced nonmonotonicity. In particular, we find perfect reflection of the Bogoliubov mode at energies where bound states appear. This is in stark contrast to the perfect transmission of the Bogoliubov mode with arbitrary energy through a dark soliton in a scalar Bose-Einstein condensate.
We investigate tunneling properties of Bogoliubov mode in a Bose-Einstein condensate. Using an exactly solvable model with a $\ensuremath{\delta}$-functional barrier, we show that each component in the two-component wave function (u,v)(u,v)(u,v) of low-energy Bogoliubov phonon has the same form as the condensate wave function in the supercurrent state. As a result, the currents Ju{J}_{u}Ju​ and Jv{J}_{v}Jv​ associated with uuu and vvv, respectively, have the same tunneling properties as those of supercurrent carried by condensate. Thus, the tunneling of low-energy Bogoliubov phonon described by the tunneling of these two currents shows perfect transmission. We also show that the supercurrent behaviors of Bogoliubov phonon still exist in the presence of supercurrent carried by condensate, except in the critical supercurrent state. In the critical current state, the perfect transmission is absent, because Ju{J}_{u}Ju​ or Jv{J}_{v}Jv​ exceeds their upper limit given by the critical value of the supercurrent associated with the condensate. Our results consistently explain the recently proposed two tunneling phenomena associated with Bogoliubov phonon, namely, the anomalous tunneling effect (perfect transmission in the low-energy limit) and the breakdown of the perfect transmission in the critical supercurrent state.
We investigate tunneling of excitations across a potential barrier separating two spin-1 Bose--Einstein condensates. Using mean-field theory at absolute zero temperature, we determine the transmission coefficients of excitations in the saturated magnetization state and unsaturated magnetization states. All excitations, except the quadrupolar spin mode in the saturated magnetization state, show the anomalous tunneling phenomenon characterized as perfect tunneling in the low-momentum limit through a potential barrier. The quadrupolar spin mode in the saturated magnetization state, whose spectrum is massive, shows total reflection. We discuss properties common between excitations showing the anomalous tunneling phenomenon. Excitations showing perfect tunneling have a gapless spectrum in the absence of the magnetic field, and their wave functions in the low-energy limit are the same as the condensate wave function.
The Nambu-Goldstone (NG) mode in a Bose-Einstein condensate (BEC) transmits a potential barrier with probability 1 in the zero-energy limit, which is known as the anomalous tunneling. In this paper, we investigate the tunneling properties of quasiparticles in a dynamically unstable BEC. We prepare a multi-component BEC (binary and spin-1 BEC) in a dynamically unstable state and solve the tunneling problem of the spin-wave excitation from the condensate. We find that the perfect transmission occurs even when the BEC is dynamically unstable if the spin-wave is the NG mode. Here, the mode that exhibits the perfect transmission is the dynamically unstable spin-wave mode, which is a pure-imaginary-eigenvalue solution of the Bogoliubov-de Gennes equation. Hence, we should take the zero-energy limit along not the real axis but the imaginary axis. We also demonstrate the existence of the perfect reflection of a dynamically unstable mode at the point where the imaginary part of the eigenvalue takes its maximum. In this case, the incident and reflected waves destructively interfere, and the amplitude of the quasiparticle wave function is strongly suppressed. We numerically confirm that the perfect reflection is a generic nature of dynamically unstable modes and not related to the NG mode.