Transmission of excitations in a spin-1 Bose-Einstein condensate through a barrier

Abstract

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. SHOHEI WATABE AND YUSUKE KATOPHYSICAL REVIEW A 83, 053624 (2011) where the sums with respect to i, j , i , and j are taken over the magnetic sublevels ±1 and 0.ˆ i (r) is the Bose field operatorThe sum with respect to k is taken over the Cartesian coordinates x, y, and z; m is the mass, g is the Landé's g factor, µ B is the Bohr magneton, and B( 0) is the strength of a magnetic field (with the z axis being taken as the direction of the magnetic field). The interaction strengths are given by c 0 = 4πh 2 (2a 2 + a 0 )/(3m), and c 1 = 4πh 2 (a 2 − a 0 )/(3m), where a S tot is the s-wave scattering length for a collision process with total spin S tot . The spin matrices of the spin-1 system are given by

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

“…In this paper, we further extend our previous studies [13][14][15][16] to the polar phase of a spin-1 spinor BEC. Recently, two of the authors [15] clarified that the spin wave in this phase also exhibits perfect transmission in the absence of superflow.…”

“…Recently, two of the authors [15] clarified that the spin wave in this phase also exhibits perfect transmission in the absence of superflow. In this paper, we examine how this anomalous tunneling behavior is affected by supercurrent.…”

“…Perfect transmission through a potential barrier, which is frequently referred to as the anomalous tunneling phenomenon, is now widely recognized as a fundamental property of the Bogoliubov excitation in a Bose superfluid [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. This phenomenon is quite different from the simple tunneling problem discussed in one-particle quantum mechanics, where the transmission probability always vanishes in the low-energy limit.…”

“…[13][14][15][16], we extended the previous work for the anomalous tunneling behavior of the Bogoliubov mode to spin-wave excitations in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate (BEC). We clarified that, in the low-energy limit, not only does the Bogoliubov mode exhibit perfect transmission, but so does the gapless transverse spin-wave.…”

Counting rule of Nambu–Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach

“…The corresponding perturbation theory for a large Jordan block is given in Appendix F. We give a general treatment of "massive" NGMs [50,51,52,53] in Bogoliubov theory in Subsec. 7.2.2 and Appendix G. The resulting perfect tunneling properties [54,55,56,57,58,59,60,61] of these NGMs are discussed in Subsec. 7.2.3. This paper is organized as follows.…”