A set of collective spin states is derived for a trapped Bose-Einstein condensate in which atoms have three internal hyperfine spins. These collective states minimize the interaction energy among condensate atoms, and they are characterized by strong spin correlations. We also examine the internal dynamics of an initially spin-polarized condensate. The time scale of spin mixing is predicted.[S0031-9007 (98)07921-6] PACS numbers: 03.75.Fi Bose-Einstein condensates (BEC) of atoms with internal degrees of freedom are new forms of macroscopically coherent matter which exhibit rich quantum structures. In the case of BEC with two internal spin states [1,2], theoretical studies have predicted interesting phenomena such as quantum entanglement of spins [3], suppression of quantum phase diffusion [4], and interference effects [5]. Recently, Stamper-Kurn et al. [6] have realized an optically trapped BEC in which all three hyperfine states in the lowest energy manifold of sodium atoms are involved. Such a three-component condensate raises new questions regarding the more complex ground state structure [7,8] and internal spin dynamics. One of the key features here is that there are spin exchange interactions which constantly mix different condensate spin components while the system as a whole remains in the ground state. For example, two atoms with respective hyperfine spins 11 and 21 interact and become two atoms with hyperfine spin 0. Therefore an important problem is to determine how atoms organize their spins in the ground state and how a spin-polarized BEC loses its polarization because of spin exchange interactions.In this paper we approach the questions using an algebraic method found in quantum optics. By excluding effects of noncondensate atoms, we identify the fact that the interaction between spin components in a BEC is analogous to 4-wave mixing in nonlinear optics. However, since the trap is like a matter wave cavity, a more appropriate optical analogy is the 4-wave mixing in a high finesse cavity (i.e., a cavity QED system). With the help of the methods developed in a related cavity QED problem [9,10], we are able to study the organization of spins in the condensate ground state. We find that there exists a class of quantum superposition states which minimize the interaction energy. These quantum states are recognized as collective spin states which are characterized by strong correlations among different spin components, and in some cases we find that the number of atoms in an individual spin component shows large fluctuations. In this paper we also examine the internal dynamics of the spin-mixing process arising from the nonlinear interactions between condensate atoms [11]. For an initially spin-polarized BEC, we predict the time scale at which spins become strongly mixed.To begin we consider a dilute gas of trapped bosonic atoms with hyperfine spin f 1. The second quantized Hamiltonian of the system is given by ͑h 1͒ H X a Z d 3 xĈ y a √ 2 = 2 2M 1 V T !Ĉ a 1 X a,b,m,n V abmn ZĈ y aĈ y bĈmĈn d 3 x , (1) wher...

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

Continuous quantum nondemolition monitoring of a collective atomic spin with an off-resonant laser beam has been performed. Squeezed atomic spin states have thereby been produced with spin noise reduction to 70% below the standard quantum limit expected for a coherent spin state.

We present theoretical studies of a two-species Bose condensate. Using a new numerical method, we have calculated ground state wave functions and show that, due to interspecies interactions, the condensate mixture displays novel behavior not found in a pure condensate. We compared our results with those of the Thomas-Fermi approximation (TFA) and find that under a broad range of conditions the TFA can be reliably used to predict many qualitative features of the condensates. Using our technique, we have modeled a recent JILA experiment on dual spin-state 87 Rb condensate. Finally, collective excitations of double condensates are discussed. [S0031-9007(97)

We show that the accuracy of atomic interferometry can be improved by using QND measurements of the atomic populations at the inputs to the interferometer. The accuracy of such a scheme surpasses the standard quantum limit of phase measurement δφSQL = 1/ √ N and could reach the Heisenberg limit δφ ∼ 1/N . We propose to perform QND measurements of atomic populations with an off-resonant laser field. The conditions necessary for this kind of QND measurement could be fulfilled in a variety of ways with current experimental techniques, including magneto-optical traps and atomic cells.

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We consider the intrinsic stability of the vortex states of a pure Bose-Einstein condensate confined in a harmonic potential under the effects of coherent atom-atom interaction. We find that stable vortices can be supported, and that vortex stability can be controlled by changing the inter-particle interaction strength. At unstable regimes, a vortex will spontaneously disintegrate into states with different angular momenta even without external perturbations, with the lifetime determined by its imaginary excitation frequencies.pacs numbers: 03.75.Fi, 05.30.Jp

We present a new theoretical treatment of the collective excitation spectrum of a two-species BoseEinstein condensate confined in a magnetic trap. We show that the interspecies interaction significantly modifies the excitation spectrum and gives rise to a rich set of new phenomena. We identify a novel metastable state of the double condensate and show that under external perturbation there can be a macroscopic quantum transition between this metastable state and the true ground state of the double condensate system. [S0031-9007 (97)05175-2] PACS numbers: 03.75.Fi, 05.30.JpSince the first observation of Bose-Einstein condensation (BEC) in a dilute alkali vapor [1], substantial effort has been made to study the properties of these weakly interacting trapped degenerate Bose gases. As theory and experiment have advanced, a new rich phenomenology has appeared in which new conditions arise, conditions which are not accessible in other BEC systems. One of the most stunning of these has been the recent experimental demonstration of a condensate mixture composed of two spin states of 87 Rb [2]. This observation has prompted significant interest in the physics of a new class of quantum fluids: the two-species Bose Einstein condensate (TBEC). Fundamental issues distinguish the trapped TBEC from the single species BEC, and at the heart of many of these issues is the presence of interspecies interactions and the resulting coupling of the two condensates. Previous theoretical treatments have shown that due to interspecies interactions, the ground state density distribution of a TBEC can display novel structures that do not exist in a one-species condensate [3,4]. In support of this, in the recent 87 Rb experiments, the measured density profiles of the two-spin state condensates indicated that there were observable consequences of the interactions between the two condensates. However, due to gravitational effects, the trap centers of each of the condensates were separated and a detailed theoretical analysis of the data was needed before the condensate coupling effect could be placed on firm grounds [5].To better understand the properties of the TBEC, important questions remain to be answered. For example: How do the interactions affect the excitation spectra and stability of the condensates? How will the condensates evolve under external perturbations? These questions are the subject of the present Letter.One of the fundamental properties of the confined condensate lies in the nature of the collective excitations. For single species alkali BEC, two research groups have experimentally measured some of the excitation frequencies [6], and theoretical calculations based on the Bogoliubov-Hartree theory [7,8] have shown excellent agreement with many of the experimental results. As a natural starting point to our TBEC investigation, we have numerically calculated the excitation spectra of a TBEC confined in an isotropic harmonic trap. We find that the spectra are significantly modified by the coupling between different species: the m...