We experimentally study spin dynamics in a sodium antiferromagnetic spinor condensate with off-resonant microwave pulses. In contrast to a magnetic field, a microwave dressing field enables us to explore rich spin dynamics under the influence of a negative net quadratic Zeeman shift qnet. We find an experimental signature to determine the sign of qnet, and observe harmonic spin population oscillations at every qnet except near each separatrix in phase space where spin oscillation period diverges. In the negative and positive qnet regions, we also observe a remarkably different relationship between each separatrix and the magnetization. Our data confirms an important prediction derived from the mean-field theory: spin-mixing dynamics in spin-1 condensates substantially depends on the sign of the ratio of qnet and the spin-dependent interaction energy. This work may thus be the first to use only one atomic species to reveal mean-field spin dynamics, especially the separatrix, which are predicted to appear differently in spin-1 antiferromagnetic and ferromagnetic spinor condensates. [1,9,11,12], and quantum spin-nematic squeezing [14]. Such systems have been successfully described with a classical two-dimensional phase space [1, 2, 15-17], a rotor model [18], or a quantum model [13,17].In this paper, we experimentally study spin-mixing dynamics in a F =1 sodium spinor condensate starting from a nonequilibrium initial state, as a result of antiferromagnetic spin-dependent interactions and the quadratic Zeeman energy q M induced by an off-resonant microwave pulse. In contrast to a magnetic field, a microwave dressing field enables us to explore rich spin dynamics under the influence of a negative net quadratic Zeeman energy shift q net . A method to characterize the microwave dressing field is also explained. In both negative and positive q net regions, we observe spin population oscillations * yingmei.liu@okstate.edu resulted from coherent collisional interconversion among two |F = 1, m F = 0 atoms, one |F = 1, m F = +1 atom, and one |F = 1, m F = −1 atom. In every spin oscillation studied in this paper, our data shows that the population of the m F = 0 state averaged over time is always larger (or smaller) than its initial value as long as q net < 0 (or q net > 0). This observation provides an experimental signature to determine the sign of q net . We also find a remarkably different relationship between the total magnetization m and a separatrix in phase space where spin oscillation period diverges: the position of the separatrix moves slightly with m in the positive q net region, while the separatrix quickly disappears when m is away from zero in the negative q net region. Our data confirms an important prediction derived by Ref. [17]: the spin-mixing dynamics in F =1 spinor condensates substantially depends on the sign of R = q net /c. This work may thus be the first to use only one atomic species to reveal mean-field spin dynamics, especially the separatrix, which are predicted to appear differently in F =1 an...
We experimentally demonstrate that spin dynamics and the phase diagram of spinor condensates can be conveniently tuned by a two-dimensional optical lattice. Spin population oscillations and a lattice-tuned separatrix in phase space are observed in every lattice where a substantial superfluid fraction exists. In a sufficiently deep lattice, we observe a phase transition from a longitudinal polar phase to a broken-axisymmetry phase in steady states of lattice-confined spinor condensates. The steady states are found to depend sigmoidally on the lattice depth and exponentially on the magnetic field. We also introduce a phenomenological model that semi-quantitatively describes our data without adjustable parameters.PACS numbers: 67.85. Fg, 03.75.Kk, 03.75.Mn, 05.30.Rt A spinor Bose-Einstein condensate (BEC) confined in optical lattices has attracted much attention for its abilities to systematically study, verify, and optimize condensed matter models [1][2][3]. For instance, it can quantum simulate the Laughlin-type wavefunctions appearing in the fractional quantum Hall systems [4,5]. A better understanding of these models may directly lead to engineering revolutionary materials. An optical lattice has been a versatile technique to enhance interatomic interactions and control the mobility of atoms [6][7][8]. Atoms held in a shallow lattice can tunnel freely among lattice sites and form a superfluid (SF) phase. The tunneling rate is exponentially suppressed while the on-site atomatom interaction is increased in a deeper lattice. This may result in a transition from a SF phase to a Mottinsulator (MI) phase at a critical lattice depth, which has been confirmed in various scalar BEC systems [6][7][8][9]. In contrast to a scalar BEC, a spinor BEC has unique advantages due to an additional spin degree of freedom. The SF-MI phase transition is predicted to be remarkably different in spinor BECs, i.e., the transition may be first (or second) order around the tip of each Mott lobe for an even (or odd) occupation number in lattice-trapped antiferromagnetic spinor BECs [1,10].Spin-mixing dynamics and phase diagrams of spinor BECs in free space, as a result of spin-dependent interactions and quadratic Zeeman energy q B , have been well studied with sodium atoms [11][12][13][14][15][16][17] and rubidium atoms [18][19][20][21]. Richer spin dynamics are predicted to exist in lattice-trapped spinor BECs, which allow for a number of immediate applications. These include constructing a novel quantum-phase-revival spectroscopy driven by a competition between spin-dependent and spin-independent interactions, understanding quantum magnetism, directly detecting spin-dependent three-body and higher-body interactions, and realizing massive entanglement [1,3,22]. However, dynamics of latticetrapped spinor BECs have remained to be less explored, and most of such experimental studies have been carried out in ferromagnetic 87 Rb spinor BECs [23][24][25][26].In this paper, we experimentally demonstrate that a two-dimensional (2D) optical latt...
We experimentally study two quantum phase transitions in a sodium spinor condensate immersed in a microwave dressing field. We also demonstrate that many previously unexplored regions in the phase diagram of spinor condensates can be investigated by adiabatically tuning the microwave field across one of the two quantum phase transitions. This method overcomes two major experimental challenges associated with some widely used methods, and is applicable to other atomic species. Agreements between our data and the mean-field theory for spinor Bose gases are also discussed.PACS numbers: 67.85. Hj, 03.75.Mn, 67.85.Fg, 03.75.Kk A spinor Bose-Einstein condensate (BEC) is a multicomponent BEC with an additional spin degree of freedom, which has provided exciting opportunities to study quantum magnetism, superfluidity, strong correlations, spin-squeezing, and massive entanglement [1][2][3][4][5]. The interesting interactions in spinor BECs are interconversions among multiple spin states and magnetic field interactions (or microwave dressing field interactions) characterized by q net , the net quadratic Zeeman energy. The interplay of these interactions leads to oscillations among multiple spin populations, which has been experimentally confirmed in F =123 Na spinor BECs [6][7][8][9][10][11][12], and in both F =1 and F =287 Rb spinor condensates [13][14][15][16][17].Several groups demonstrated the mean-field (MF) ground states of spinor BECs by holding BECs in a fixed magnetic field and letting spin population oscillations damp out over a few seconds [8][9][10][11]. The required damping time, determined by energy dissipation, may in some cases exceed the BEC lifetime. The exact mechanism involved in energy dissipation requires further study, although it has been shown that energy dissipates much faster in high magnetic fields [10]. For F =1 BECs, a magnetic field introduces only a positive q net , while a microwave field has a distinct advantage since it can induce both positive and negative q net [1,7,12,18,19]. As shown in Ref. [12], the same physics model explains spin-mixing dynamics observed in both microwave fields and magnetic fields. One would assume that, if given a long enough exposure to a microwave field, a spinor BEC could also reach its MF ground states. However, experimental studies on ground states of spinor BECs in microwave fields have proven to be very difficult, since these fields are created by near-resonant microwave pulses. Two major experimental challenges associated with microwave fields are atom losses and variations in magnetization m. Microwave-induced changes in both m and the atom number N can be detrimental, especially when a spinor BEC is exposed to a large microwave field for a prolonged time [7,12]. As a result, the phase diagram of F =1 BECs has not been well explored in the q net ≤ 0 region, where applying microwave fields may be necessary.In this paper, we demonstrate a new method to overcome the aforementioned experimental challenges and report the observation of two quantum phase ...
We present a simple and optimal experimental scheme for an all-optical production of a sodium spinor Bose-Einstein condensate (BEC). With this scheme, we demonstrate that the number of atoms in a pure BEC can be greatly boosted by a factor of 5 in a simple setup that includes a single-beam optical trap or a crossed optical trap. This optimal scheme avoids technical challenges associated with some all-optical BEC methods, and can be applied to other optically trappable atomic species. In addition, we find a good agreement between our theoretical model and data. The upper limit for the efficiency of evaporative cooling in all-optical BEC approaches is also discussed.
Heterogeneous integration of materials systems for devices and circuits is becoming of increasing interest, particularly for the wide bandgap nitrides in both optoelectronic and electronic applications. However, typical high growth temperatures of GaN by metalorganic vapor phase epitaxy prevent the growth of GaN on wafers with temperature sensitive materials. This work presents a flow modulation epitaxy (FME) growth scheme which allows for step-flow growth of GaN at temperatures below 600 • C. The utilization of a pulsed growth scheme such as FME allows for the mitigation of challenges associated with limited motion of adatoms at lower growth temperatures. Factors such as temperature, precursor flow rate, cycle time, and film thickness were explored. Under optimized conditions, step-flow growth of GaN films at 550 • C was demonstrated. In addition to an improved surface morphology over layers grown in the conventional continuous growth mode, the carbon and oxygen residual impurity concentrations in the FME grown layers were significantly lower, with carbon and oxygen contents of 9 × 10 17 cm −3 and 8 × 10 16 cm −3 , respectively. Although the growth rate of the low temperature growth was very slow, ~0.006 Å/s, the flow modulation growth scheme developed here provides a pathway towards further integration of GaN with temperature sensitive materials.
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