Collisions in a thermal gas are perceived as random or incoherent as a consequence of the large numbers of initial and final quantum states accessible to the system. In a quantum gas, e.g. a Bose-Einstein condensate or a degenerate Fermi gas, the phase space accessible to low energy collisions is so restricted that collisions become coherent and reversible. Here, we report the observation of coherent spin-changing collisions in a gas of spin-1 bosons. Starting with condensates occupying two spin states, a condensate in the third spin state is coherently and reversibly created by atomic collisions. The observed dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. The spin-dependent scattering length is determined from these oscillations to be -1.45(32) Bohr. Finally, we demonstrate coherent control of the evolution of the system by applying differential phase shifts to the spin states using magnetic fields.PACS numbers:

We revisit the topic of the mean field ground state of a spin-1 atomic condensate inside a uniform magnetic field (B) under the constraints that both the total number of atoms (N ) and the magnetization (M) are conserved. In the presence of an internal state (spin component) independent trap, we also investigate the dependence of the so-called single spatial mode approximation (SMA) on the magnitude of the magnetic field and M. Our result indicate that the quadratic Zeeman effect is an important factor in balancing the mean field energy from elastic atom-atom collisions that are known to conserve both N and M.

We investigate in detail, using both analytical and numerical tools, the decoherence of electron spins in quantum dots ͑QDs͒ coupled to a bath of nuclear spins in magnetic fields or with various initial bath polarizations, focusing on the longitudinal relaxation in low and moderate field and polarization regimes. An increase of the initial polarization of nuclear-spin bath has the same effect on the decoherence process as an increase of the external magnetic field, namely, the decoherence dynamics changes from smooth decay to damped oscillations. This change can be observed experimentally for a single QD and for a double-QD setup.Our results indicate that substantial increase of the decoherence time requires very large bath polarizations, and the use of other methods ͑dynamical decoupling or control of the nuclear spins distribution͒ may be more practical for suppressing decoherence of QD-based qubits.

We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean field theory and adopting the single spatial mode approximation (SMA), the condensate spin dynamics is found to be well described by that of a nonrigid pendulum, and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate. Bose-Einstein condensation (BEC) has been one of the most active topics in physics for over a decade, and yet interest in this field remains impressively high. Recent experiments showcase the rich versatility of control over the atomic superfluid, e.g. the BEC-BCS crossover [1,2], quantized vortices [3,4,5], condensates in optical lattices [6], and low dimensional quantum gases [7,8]. While most of these efforts involve condensates of atoms in a single Zeeman state, activities in spinor condensates [9,10] have recently received significant boost with the addition of three new spin-1 experiments [11,12,13,14].In a spinor condensate, atomic hyperfine spin degree of freedom becomes accessible with the use of a far-off resonant optical trap instead of a magnetic trap. For atoms in the F = 1 ground state manifold, the presence of Zeeman degeneracy and spin dependent atom-atom interactions [9,10,11,15,16,17,18,19] leads to interesting condensate spin dynamics. In this article, we study spin mixing inside a spin-1 condensate [17,19,20], focusing on the interaction-driven coherent oscillations within a mean field description. Unlike the pioneering studies on this subject as in Refs. [17,19], we will highlight the important role of an external magnetic field, which is present in all experiments to date.Recently, a beautiful experiment has finally observed the long predicted Josephson type coherent nonlinear oscillations with a scalar condensate in a spatial double well potential [21].Although spin mixing driven by the internal spindependent interaction (not of the nature of a Rabi oscillation as driven by an external field [22,23]), has been observed in both F = 1 and F = 2 condensates [9,12,14,24], the coherence of this process has not yet been investigated. Over-damped single oscillations in spin populations have been observed in earlier experiments [24] although their interpretation has been limited because evolution from the initial (meta-stable) states was noise-driven. The main experimental obstacles to observe more oscillations are the dissipative atomic collisions among the condensed atoms and the decoherence collisions with noncondensed atoms [12,24]. A promising future direction relies on increased atomic detection sensitivity, thus the use of smaller condensates as in the experiment of Ref. [21], with lower number densities and at lower temperatures, two favorable conditions for the single spatial mode approximation (SMA) [17,19].The initial atomic population distribution in Fig. 1 corresponds to the (equi...