Journal of Physics Conference Series

Anomalous Tunneling of Spin Wave in Polar State of Spin-1 BEC

Shohei Watabe, Yusuke S. Kato, Yoji Ohashi

Published Dec 17, 2012• 3 citations

Abstract

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.

DOI: 10.1088/1742-6596/400/1/012079

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Journal of Physics Conference Series

Anomalous Tunneling of Spin Wave in Polar State of Spin-1 BEC

Shohei Watabe, Yusuke S. Kato, Yoji Ohashi

Published Dec 17, 2012• 3 citations

Publisher

Abstract

DOI: 10.1088/1742-6596/400/1/012079

Related papers

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

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.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.

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Tunneling properties of Bogoliubov mode and spin-wave modes in supercurrent states of a spin-1 ferromagnetic spinor Bose-Einstein condensate

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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 $T=0$ , 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 $q$ , 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 $k$ 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 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 $T=0$, 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 $q$, 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 $k$ 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.

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Anomalous scattering of low-lying excitations in a spin-1 Bose-Einstein condensate

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We study the scattering of the transverse spin wave by an impurity potential in the ferromagnetic spin-1 Bose-Einstein condensate (BEC) by using the mean-field theory. We present a simpler framework of anomalous tunneling effect, the perfect transmission in the low-energy limit through an external potential barrier. The transverse spin wave obeys a Schrödinger-type equation; yet, the effects of the potential barrier on its transmission coefficient and on its scattering cross-section vanish in the low-energy limit. The modulus of the order parameter alone determines its transmission coefficient. The momentum p -dependence of the scattering cross-section σ exhibits a Rayleigh scattering type ( σ ∝ p 4 ) . These properties are common to the transverse spin wave and the Bogoliubov mode, which belong to different types of Nambu-Goldstone modes.We study the scattering of the transverse spin wave by an impurity potential in the ferromagnetic spin-1 Bose-Einstein condensate (BEC) by using the mean-field theory. We present a simpler framework of anomalous tunneling effect, the perfect transmission in the low-energy limit through an external potential barrier. The transverse spin wave obeys a Schrödinger-type equation; yet, the effects of the potential barrier on its transmission coefficient and on its scattering cross-section vanish in the low-energy limit. The modulus of the order parameter alone determines its transmission coefficient. The momentum p -dependence of the scattering cross-section σ exhibits a Rayleigh scattering type ( σ ∝ p 4 ) . These properties are common to the transverse spin wave and the Bogoliubov mode, which belong to different types of Nambu-Goldstone modes.

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Supercurrent behavior of low-energy Bogoliubov phonons and the anomalous tunneling effect in a Bose-Einstein condensate

Yoji Ohashi, Shunji Tsuchiya

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 $(u,v)$ of low-energy Bogoliubov phonon has the same form as the condensate wave function in the supercurrent state. As a result, the currents ${J}_{u}$ and ${J}_{v}$ associated with $u$ and $v$ , 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 ${J}_{u}$ or ${J}_{v}$ 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 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 $(u,v)$ of low-energy Bogoliubov phonon has the same form as the condensate wave function in the supercurrent state. As a result, the currents ${J}_{u}$ and ${J}_{v}$ associated with $u$ and $v$, 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 ${J}_{u}$ or ${J}_{v}$ 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.

arXiv:0806.0470Physical Review AOct 3, 200815 citations

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.

T=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

q

, 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

k

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 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=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.

(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

{J}_{u}

and

{J}_{v}

associated with

u

and

v

, 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

{J}_{u}

{J}_{v}

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.