Cooper pairs? magnetic moment in MCFL color superconductivity

We investigate the effect of the alignment of the magnetic moments of Cooper pairs of charged quarks that form at high density in three-flavor quark matter. The high-density phase of this matter in the presence of a magnetic field is known to be the Magnetic Color-Flavor-Locked (MCFL) phase of color superconductivity. We derive the Fierz identities of the theory and show how the explicit breaking of the rotational symmetry by the uniform magnetic field opens new channels of interactions and allows the formation of a new diquark condensate. The new order parameter is a spin-1 condensate proportional to the component in the field direction of the average magnetic moment of the pairs of charged quarks. The magnitude of the spin-1 condensate becomes comparable to the larger of the two scalar gaps in the region of large fields. The existence of the spin-1 condensate is unavoidable, as in the presence of a magnetic field there is no solution of the gap equations with nonzero scalar gaps and zero magnetic moment condensate. This is consistent with the fact that the extra condensate does not break any symmetry that has not already been broken by the known MCFL gaps. The spin-1 condensate enhances the condensation energy of pairs formed by charged quarks and the magnetization of the system. We discuss the possible consequences of the new order parameter on the issue of the chromomagnetic instability that appears in color superconductivity at moderate density.     

Topological Hall Effect of Spin-2 Condensate in a Time and Space-Dependent Magnetic Field

We simulate the dynamics of spin-2 ⁸⁷Rb condensate in a time and space-dependent magnetic field with a time-dependent variational approach. The topological Hall effect is observed, which has been realized in the experiment of spin-1 ²³Na condensate [Phys. Rev. Lett. 111, 245301 (2013)]. A driving-induced resonance behavior is observed.     

Fragmented and single condensate ground states of spin-1 bose Gas

We show that the ground state of a spin-1 Bose gas with an antiferromagnetic interaction is a fragmented condensate in uniform magnetic fields. The number fluctuations in each spin component change rapidly from being enormous (order N) to exceedingly small (order 1) as the magnetization of the system increases. A fragmented condensate can be turned into a single condensate state by magnetic field gradients. The conditions for existence and method of detecting fragmented states are presented.     

Polar-Core Spin Vortex of Quasi-2D Spin-2 Condensate in a Flat-Bottomed Optical Trap

Motivated by the recent experiments realized in a flat-bottomed optical trap [Science 347(2015) 167;Nat. Commun. 6(2015) 6162], we study the ground state of polar-core spin vortex of quasi-2D spin-2 condensate in a homogeneous trap plus a weak magnetic field. The exact spatial distribution of local spin is obtained and the vortex core are observed to decrease with the growth of the effective spin-spin interaction. For the larger effective spin-spin interaction, the spatial distribution of spin magnitude in spin-2 condensate we obtained agrees well with that of spin-1 condensate in a homogeneous trap, where a polar-core spin vortex was schematically demonstrated as a fully-magnetized planar spin texture with a zero-spin core. The effective spin-spin interaction is proportional to both the bare spin-spin interaction and the radius of the homogeneous trap, simultaneously. Thus the polar-core spin vortex we obtained can be easily controlled by the radius of the trap.     

Quantum dynamics of atomic coherence in a spin-1 condensate: Mean-field versus many-body simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a “ferromagnetic” state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.     

Beliaev theory of spinor Bose–Einstein condensates

By generalizing the Green’s function approach developed by Beliaev [S.T. Beliaev, Sov. Phys. JETP 7 (1958) 299; S.T. Beliaev, Sov. Phys. JETP 7 (1958) 289], we study effects of quantum fluctuations on the energy spectra of spin-1 spinor Bose–Einstein condensates, in particular, of a ⁸⁷Rb condensate in the presence of an external magnetic field. We find that due to quantum fluctuations, the effective mass of magnons, which characterizes the quadratic dispersion relation of spin-wave excitations, increases compared with its mean-field value. The enhancement factor turns out to be the same for two distinct quantum phases: the ferromagnetic and polar phases, and it is a function of only the gas parameter. The lifetime of magnons in a spin-1 ⁸⁷Rb spinor condensate is shown to be much longer than that of phonons due to the difference in their dispersion relations. We propose a scheme to measure the effective mass of magnons in a spinor Bose gas by utilizing the effect of magnons’ nonlinear dispersion relation on the time evolution of the distribution of transverse magnetization. This type of measurement can be applied, for example, to precision magnetometry.     

Influence of External Magnetic Fields on Tunneling of Spin-1 Bose Condensate

In this letter, we have studied the influence of the external magnetic fields on tunneling of the spin-1 Bose condensate. We find that the population transfer between spin-0 and spin-±1 exhibits the step structure under the external cosinusoidal magnetic field and a combination of static and cosinusoidal one, respectively. Compared with the longitudinal component of the external magnetic field, the smaller the transverse component of the magnetic field is, the larger the time scale of exhibiting the step structure does. The tunneling current may exhibit periodically oscillation behavior when the ratio of the transverse component of the magnetic field is smaller than that of the longitudinal component, otherwise it exhibits a damply oscillating behavior. This means that the dynamical spin localization can be adjusted by the external magnetic fields.     

扫描磁场中玻色-爱因斯坦凝聚体系的奇异自旋隧穿

用平均场的方法,研究了线性扫描磁场中自旋-1玻色-爱因斯坦凝聚体系的自旋隧穿.集中考虑⁸⁷Rb这种典型的碱金属原子凝聚体,根据外磁场扫描率的不同,研究了它的隧穿动力学.在慢扫描(即绝热条件)和快扫描条件下,体系无隧穿现象.对中等大小的扫描率,发现隧穿现象,且这个隧穿动力学对磁场扫描率非常的敏感,表现为看似混沌的隧穿区的存在.然而,把这个看似混沌的区域放大,发现在扫描率精度为10^-8T/s的量级上,隧穿率对磁场扫描率的关系实际是有规律的类周期结构.此外,还发现,实 关键词： 玻色-爱因斯坦凝聚 自旋 隧穿     

扫描磁场中玻色-爱因斯坦凝聚体系的奇异自旋隧穿

用平均场的方法，研究了线性扫描磁场中自旋-1玻色-爱因斯坦凝聚体系的自旋隧穿.集中考虑⁸⁷Rb这种典型的碱金属原子凝聚体，根据外磁场扫描率的不同，研究了它的隧穿动力学.在慢扫描(即绝热条件)和快扫描条件下，体系无隧穿现象.对中等大小的扫描率，发现隧穿现象，且这个隧穿动力学对磁场扫描率非常的敏感，表现为看似混沌的隧穿区的存在.然而，把这个看似混沌的区域放大，发现在扫描率精度为10^-8T/s的量级上，隧穿率对磁场扫描率的关系实际是有规律的类周期结构.此外，还发现，实     

Low-energy excitations of Yb As in a magnetic field

We discuss the effects of an applied magnetic field on the low-energy excitations in the low temperature phase of Yb₄As₃. We show also why the magnetic interaction of the Yb³⁺ ions is nearly of an isotropic Heisenberg spin-1/2 type. A small anisotropy due to an intrachain dipolar interaction leads to the opening of a gap when a magnetic field is applied. The model agrees with available experimental data. Simple experiments are suggested in order to further test the present theory. Received 3 February 1999     

Observation of spinor dynamics in optically trapped 87Rb Bose-Einstein condensates

We measure spin mixing of F=1 and F=2 spinor condensates of 87Rb atoms confined in an optical trap. We determine the spin mixing time to be typically less than 600 ms and observe spin population oscillations. The equilibrium spin configuration in the F=1 manifold is measured for different magnetic fields and found to show ferromagnetic behavior for low field gradients. An F=2 condensate is created by microwave excitation from the F=1 manifold, and this spin-2 condensate is observed to decay exponentially with time constant 250 ms. Despite the short lifetime in the F=2 manifold, spin mixing of the condensate is observed within 50 ms.     

Dynamic magnetic properties in the kinetic mixed spin-2 and spin-5/2 Ising model under a time-dependent magnetic field

We extend the recent paper [W. Jiang, V-C. Lo, B-D. Bai, J. Yang, Physica A 389 (2010) 2227-2233] to present a study, within a mean-field approach, the dynamic magnetic properties of the mixed spin-2 and spin-5/2 Ising ferrimagnetic system, which corresponds the molecular-based magnetic materials AFe^IIFe^III(C₂O₄)₃ [ A=N(n-C_nH_2n+1)₄, n=3-5], by using the Glauber-type stochastic dynamics. This mixed Ising ferrimagnetic system is used on a layered honeycomb lattice in which Fe^II (S=5/2) and Fe^III (σ=2) occupy sites. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first-or second-order) phase transitions. We also present the dynamic phase diagrams and study the dynamic magnetic hysteresis loop behaviors of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system. The results are compared with some experimental and theoretical works and a good overall agreement is found.     

Nematic order by disorder in spin-2 Bose-Einstein condensates

We show that quantum and thermal fluctuations in spin-2 Bose-Einstein condensates lift the accidental degeneracy of the mean-field phase diagram. Fluctuations select the uniaxial (square biaxial) nematic state for scattering lengths a4>a2 (a4相似文献   

Direct nondestructive imaging of magnetization in a spin-1 Bose-Einstein gas

Polarization-dependent phase-contrast imaging is used to resolve the spatial magnetization profile of an optically trapped ultracold gas. This probe is applied to Larmor precession of degenerate and nondegenerate spin-1 87Rb gases. Transverse magnetization of the Bose-Einstein condensate persists for the condensate lifetime, with a spatial response to magnetic field inhomogeneities consistent with a mean-field model of interactions. In comparison, the magnetization of the non-condensed gas decoheres rapidly. Rotational symmetry implies that the Larmor frequency of a spinor condensate be density independent, and thus suitable for precise magnetometry with high spatial resolution.     

Unusual field-induced transitions in exactly solved mixed spin-(1/2, 1) Ising chain with axial and rhombic zero-field splitting parameters

The mixed spin-(1/2, 1) Ising chain with axial and rhombic zero-field splitting parameters in the presence of the longitudinal magnetic field is exactly solved within the framework of decoration-iteration transformation and transfer-matrix method. Our particular emphasis is laid on an investigation of the influence of the rhombic term, which is responsible for an onset of quantum entanglement between two magnetic states S_k^z=±1 of the spin-1 atoms. It is shown that the rhombic term gradually destroys a classical ferrimagnetic order in the ground state and simultaneously causes diversity in magnetization curves including intermediate plateau regions, regions with a continuous change in the magnetization as well as several unusual field-induced transitions accompanied with magnetization jumps. Another interesting findings concern with an appearance of the round minimum in the temperature dependence of susceptibility times temperature data, the double-peak zero-field specific heat curves and the enhanced magnetocaloric effect. The temperature dependence of the specific heat with three separate maxima may also be detected when driving the system through the axial and rhombic zero-field splitting parameters close enough to a phase boundary between the ferrimagnetic and disordered states and applying sufficiently small longitudinal magnetic field.     

Spinor dynamics in an antiferromagnetic spin-1 condensate

We observe coherent spin oscillations in an antiferromagnetic spin-1 Bose-Einstein condensate of sodium. The variation of the spin oscillations with magnetic field shows a clear signature of nonlinearity, in agreement with theory, which also predicts anharmonic oscillations near a critical magnetic field. Measurements of the magnetic phase diagram agree with predictions made in the approximation of a single spatial mode. The oscillation period yields the best measurement to date of the sodium spin-dependent interaction coefficient, determining that the difference between the sodium spin-dependent s-wave scattering lengths a(f=2) - a(f=0) is 2.47+/-0.27 Bohr radii.     

Quantum quenches in a spinor condensate

We discuss the ordering of a spin-1 condensate when quenched from its paramagnetic phase to its ferromagnetic phase by reducing the magnetic field. We first elucidate the nature of the equilibrium quantum phase transition. Quenching rapidly through this transition reveals XY ordering either at a specific wave vector, or the "light-cone" correlations familiar from relativistic theories, depending on the end point of the quench. For a quench proceeding at a finite rate the ordering scale is governed by the Kibble-Zurek mechanism. The creation of vortices through growth of the magnetization fluctuations is also discussed. The long-time dynamics again depends on the end point, conserving the order parameter in a zero field, but not at a finite field, with differing exponents for the coarsening of magnetic order. The results are discussed in the light of a recent experiment by Sadler et al.     

Decomposition of the SU(2) Gauge Field and Circulation Condition of the Bose-Einstein Condensate

Using decomposition of the SU(2) gauge field in terms of unit vector field, we have discussed circulation condition of the spin-1/2 Bose-Einstein dendensate. For the two-component Bose-Einstein condensate,the SU/(2) symmetry of the internal states leads to a generalization of Mermin-Ho relation as a topological constrain of the superfluid velocity.     

The spin evolution of spin-3 52Cr Bose–Einstein condensate

This paper studies theoretically the spin evolution of a Bose--Einstein condensate starting from a mixture of two or three groups of ⁵²Cr (spin-3) atoms in an optical trap. The initial state is so chosen that the condensate has total magnetization zero so that the system does not distinguish up and down. It is assumed that the system is very dilute (particle number is very small), the temperature is very low, and the frequency of the harmonic trap is large enough. In these situations, the deviation caused by the neglect of the dipole--dipole interaction and by using the single-mode approximation is reduced. A theoretical calculation beyond the mean field theory is performed and the numerical results are helpful for the evaluation of the unknown strength g0.     

Vortex and droplet in holographic D-wave superconductors

We investigate non-trivial localized solutions of the condensate in a (2+1$2+1$)-dimensional D-wave holographic superconductor model in the presence of a background magnetic field. The calculation is done in the context of the (3+1$3+1$)-dimensional dual gravity theory of a charged massive spin-2 field in an AdS black hole background. By using numeric techniques, we find both vortex and droplet solutions. These solutions are important for studying the full phase diagram of D-wave superconductors.