Focusing on a quantum-limit behavior, we study a single vortex in a clean s-wave type-II superconductor by selfconsistently solving the Bogoliubov-de Gennes equation. The discrete energy levels of the vortex bound states in the quantum limit is discussed. The vortex core radius shrinks monotonically up to an atomic-scale length on lowering the temperature T , and the shrinkage stops to saturate at a lower T . The pair potential, supercurrent, and local density of states around the vortex exhibit Friedel-like oscillations. The local density of states has particle-hole asymmetry induced by the vortex. These are potentially observed directly by STM. PACS number(s): 74.60. Ec, 61.16.Ch, Growing interest has been focused on vortices both in conventional and unconventional superconductors from fundamental and applied physics points of view. This is particularly true for high-T c cuprates, since it is essential that one understands fundamental physical properties of the vortices in the compounds to better control various superconducting characteristics of some technological importance. Owing to the experimental developments, it is not difficult to reach low temperatures of interest where distinctive quantum effects associated with the discretized energy levels of the vortex bound states are expected to emerge. The quantum limit is realized at the temperature where the thermal smearing is narrower than the discrete bound state levels [1]: T /T c ≤ 1/(k F ξ 0 ) with ξ 0 =v F /∆ 0 the coherence length (∆ 0 the gap at T = 0) and k F (v F ) the Fermi wave number (velocity). For example, in a typical layered type-II superconductor NbSe 2 with T c = 7.2 K and k F ξ 0 ∼ 70, the quantum limit is reached below T < 50 mK. As for the high-T c cuprates, the corresponding temperature is rather high: T < 10 K for YBa 2 Cu 3 O 7−δ (YBCO).Important microscopic works to theoretically investigate the quasiparticle spectral structure around a vortex in a clean limit are put forth by Caroli et al. The purposes of the present paper are to reveal the quantum-limit aspects of the single vortex in s-wave superconductors and to discuss a possibility for the observation of them. The present study is motivated by the following recent experimental and theoretical situations: (1) The socalled Kramer and Pesch (KP) effect [1,3,7,8]; a shrinkage of the core radius upon lowering T (to be exact, an anomalous increase in the slope of the pair potential at the vortex center at low T ) is now supported by some experiments [9]. The T dependence of the core size is studied by µSR on NbSe 2 and YBCO [10], which is discussed later. The KP effect, if confirmed, forces us radically alter the traditional picture [11] for the vortex line such as a rigid normal cylindrical rod with the radius ξ 0 . (2) The scanning tunneling microscopy (STM) experiment on YBCO by Maggio-Aprile et al. [12], which enables us to directly see the spatial structure of the low-lying quasiparticle excitations around the vortex, arouses much interest. They claim that surprisingly enough, ...

It is shown theoretically that a persistent current can be continuously created in a Bose-Einstein condensate (BEC) of alkali atoms confined in a multiply connected region by making use of a spindegree of freedom of the order parameter of a BEC. We demonstrate that this persistent current is easily transformed into a vortex. Relaxation processes of these BEC after the confining field is turned off are also studied so that our analyses are compared with time of flight experiments. The results are shown to clearly reflect the existence of a persistent current.

The stability of doubly quantized vortices in dilute Bose-Einstein condensates of 23 Na is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards dissection into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments [A. E. Leanhardt et al. Phys. Rev. Lett. 89, 190403 (2002) The stability of single-quantum vortices has been studied extensively after such vortices were first observed in dilute alkali atom Bose-Einstein condensates (BECs) [1]. Since a single-valued complex order parameter describes the state of the condensate, its phase must undergo a 2πn change along a loop encircling a vortex, where n is the quantum number of the vortex. However, the creation of multiquantum vortices is impossible just by rotating the harmonic trapping potential at a high frequency, since the existence of many singly quantized vortices is energetically more favorable than a single multiquantum vortex [2]. Indeed, vortex lattices composed of single-quantum vortices were observed in such experiments [3].Verifying the proposal of topological phase engineering by Nakahara et al. [4], Leanhardt et al. [5] have recently succeeded in creating vortices simply by reversing the bias magnetic field used to trap the condensate. The vortices created display winding numbers with n = 2 (4π phase winding) or with n = 4 (8π phase winding), depending on the hyperfine spin states used for 23 Na condensates. It was confirmed that the axial angular momentum per particle is 2h (4h) for the doubly (quartically) quantized vortex.In this experiment, after creating a vortex it is held for ∼ 20 ms, watching the vortex core to split into singlequantum vortices. However, no splitting was observed in this time span. Since a doubly quantized vortex is expected to decay spontaneously into two singly quantized vortices owing to energetics, this observation seems to be puzzling. This motivates our investigation of the detailed dynamics of the decay process of multiply quantized vortices in view of the present experimental situation. In dilute BECs, these were the first experimentally realized double-quantum vortices which are known to exist in other superfluids, such as superfluid 3 He-A [6]. Therefore, we have a unique opportunity to examine the physics of multiply quantized vortices.There are several theoretical investigations on the instability of the doubly quantized vortex: The instability due to the bound state in the vortex core was pointed out by Rokhsar [7], who claimed that the decay of vortex states requires the presence of thermal atoms. On the other hand, Pu et al. [8] found that even in the absence of thermal atoms, i.e. in the non-dissipative system, appearance of the modes with...