Matter-Wave Solitons in an F=1 Spinor Bose-Einstein Condensate

Following our previous work [J. Ieda, T. Miyakawa, M. Wadati, cond-mat/0404569] on a novel integrable model describing soliton dynamics of an F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of the multi-component system with spin-exchange interactions. The exact multiple bright soliton solutions are obtained for the system where the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction is ferromagnetic (c_2 < 0). A complete classification of the one-soliton solution with respect to the spin states and an explicit formula of the two-soliton solution are presented. For solitons in polar state, there exists a variety of different shaped solutions including twin peaks. We show that a "singlet pair" density can be used to distinguish those energetically degenerate solitons. We also analyze collisional effects between solitons in the same or different spin state(s) by computing the asymptotic forms of their initial and final states. The result reveals that it is possible to manipulate the spin dynamics by controlling the parameters of colliding solitons.Comment: 12 pages, 9 figures, to appear in J. Phys. Soc. Jpn. Vol.73 No.11 (2004

Conserving Gapless Mean-Field Theory of a Multi-Component Bose-Einstein Condensate

We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from T=0 up to $T_{c}$ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.Comment: 8 pages, 7 figures Minor errors remove

Spin-Nematic Squeezed Vacuum in a Quantum Gas

Using squeezed states it is possible to surpass the standard quantum limit of measurement uncertainty by reducing the measurement uncertainty of one property at the expense of another complementary property. Squeezed states were first demonstrated in optical fields and later with ensembles of pseudo spin-1/2 atoms using non-linear atom-light interactions. Recently, collisional interactions in ultracold atomic gases have been used to generate a large degree of quadrature spin squeezing in two-component Bose condensates. For pseudo spin-1/2 systems, the complementary properties are the different components of the total spin vector , which fully characterize the state on an SU(2) Bloch sphere. Here, we measure squeezing in a spin-1 Bose condensate, an SU(3) system, which requires measurement of the rank-2 nematic or quadrupole tensor as well to fully characterize the state. Following a quench through a nematic to ferromagnetic quantum phase transition, squeezing is observed in the variance of the quadratures up to -8.3(-0.7 +0.6) dB (-10.3(-0.9 +0.7) dB corrected for detection noise) below the standard quantum limit. This spin-nematic squeezing is observed for negligible occupation of the squeezed modes and is analogous to optical two-mode vacuum squeezing. This work has potential applications to continuous variable quantum information and quantum-enhanced magnetometry

Multicomponent Bright Solitons in F = 2 Spinor Bose-Einstein Condensates

We study soliton solutions for the Gross--Pitaevskii equation of the spinor Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses are made in two ways: by assuming single-mode amplitudes and by generalizing Hirota's direct method for multi-components. We obtain one-solitons of single-peak type in the ferromagnetic, polar and cyclic states, respectively. Moreover, twin-peak type solitons both in the ferromagnetic and the polar state are found.Comment: 15 pages, 8 figure

Coherent multi-flavour spin dynamics in a fermionic quantum gas

Microscopic spin interaction processes are fundamental for global static and dynamical magnetic properties of many-body systems. Quantum gases as pure and well isolated systems offer intriguing possibilities to study basic magnetic processes including non-equilibrium dynamics. Here, we report on the realization of a well-controlled fermionic spinor gas in an optical lattice with tunable effective spin ranging from 1/2 to 9/2. We observe long-lived intrinsic spin oscillations and investigate the transition from two-body to many-body dynamics. The latter results in a spin-interaction driven melting of a band insulator. Via an external magnetic field we control the system's dimensionality and tune the spin oscillations in and out of resonance. Our results open new routes to study quantum magnetism of fermionic particles beyond conventional spin 1/2 systems.Comment: 9 pages, 5 figure

Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices

Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-T$_c$ superconductivity and unconventional magnetism. In contrast, phenomena in superfluids -- especially in ultracold quantum gases -- are commonly well described by the lowest orbital and a real order parameter. Here, we report on the observation of a novel multi-orbital superfluid phase with a {\it complex} order parameter in binary spin mixtures. In this unconventional superfluid, the local phase angle of the complex order parameter is continuously twisted between neighboring lattice sites. The nature of this twisted superfluid quantum phase is an interaction-induced admixture of the p-orbital favored by the graphene-like band structure of the hexagonal optical lattice used in the experiment. We observe a second-order quantum phase transition between the normal superfluid (NSF) and the twisted superfluid phase (TSF) which is accompanied by a symmetry breaking in momentum space. The experimental results are consistent with calculated phase diagrams and reveal fundamentally new aspects of orbital superfluidity in quantum gas mixtures. Our studies might bridge the gap between conventional superfluidity and complex phenomena of orbital physics.Comment: 5 pages, 4 figure

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate

A central goal in condensed matter and modern atomic physics is the exploration of many-body quantum phases and the universal characteristics of quantum phase transitions in so far as they differ from those established for thermal phase transitions. Compared with condensed-matter systems, atomic gases are more precisely constructed and also provide the unique opportunity to explore quantum dynamics far from equilibrium. Here we identify a second-order quantum phase transition in a gaseous spinor Bose-Einstein condensate, a quantum fluid in which superfluidity and magnetism, both associated with symmetry breaking, are simultaneously realized. $^{87}$Rb spinor condensates were rapidly quenched across this transition to a ferromagnetic state and probed using in-situ magnetization imaging to observe spontaneous symmetry breaking through the formation of spin textures, ferromagnetic domains and domain walls. The observation of topological defects produced by this symmetry breaking, identified as polar-core spin-vortices containing non-zero spin current but no net mass current, represents the first phase-sensitive in-situ detection of vortices in a gaseous superfluid.Comment: 6 pages, 4 figure

Physics with Coherent Matter Waves

This review discusses progress in the new field of coherent matter waves, in particular with respect to Bose-Einstein condensates. We give a short introduction to Bose-Einstein condensation and the theoretical description of the condensate wavefunction. We concentrate on the coherence properties of this new type of matter wave as a basis for fundamental physics and applications. The main part of this review treats various measurements and concepts in the physics with coherent matter waves. In particular we present phase manipulation methods, atom lasers, nonlinear atom optics, optical elements, interferometry and physics in optical lattices. We give an overview of the state of the art in the respective fields and discuss achievements and challenges for the future