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.
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.
We experimentally study spin dynamics in a sodium antiferromagnetic spinor condensate as a result of spin-dependent interactions c and microwave dressing field interactions characterized by the net quadratic Zeeman effect qnet. In contrast to magnetic fields, microwave dressing fields enable us to access both negative and positive values of 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. No spin domains and spatial modes are observed in our system. Our data in the negative qnet region exactly resembles what is predicted to occur in a ferromagnetic spinor condensate in the positive qnet region. This observation agrees with an important prediction derived from the mean-field theory: spin dynamics in spin-1 condensates substantially depends on the sign of qnet/c. This work uses only one atomic species to reveal mean-field spin dynamics, especially the remarkably different relationship between each separatrix and the magnetization, of spin-1 antiferromagnetic and ferromagnetic spinor condensates.
Entanglement lies at the core of emergent quantum technologies such as quantum-enhanced metrology, quantum communication and cryptography, and quantum simulation and computing. Spinor Bose-Einstein condensates (BECs) offer a promising platform for the generation and application of entangled states. For example, a spin-1 BEC has served for the proof-of-principle demonstration of a quantum-enhanced atomic clock. Ferromagnetic spin-1 BECs with zero magnetization exhibit three ground-state quantum phases with different entanglement properties. The control parameter can be tuned by a magnetic field or by microwave dressing. As already experimentally demonstrated, an entangled ground state can be reached from a well accessible, non-entangled one by driving the control parameter across quantum phase transitions (QPTs). We investigate which of the entangled ground states afford quantum-enhanced interferometry. The interferometric usefulness is quantified by the quantum Fisher information (QFI), which we analyze throughout all ground-state phases. A large QFI at about half the Heisenberg limit, and thus far above the standard quantum limit, is attained by the well-known Twin-Fock state and by the central broken-axisymmetry (CBA) state. We detail how the CBA state can be used as a probe for quantum-enhanced interferometry. Furthermore, we observe that the large QFI of the CBA state can be traced back to enclosed macroscopic superposition states (MSSs). Measuring the atom number in one out of three modes generates, with high probability and heralded by the measurement outcome, a MSS similar to a NOON state. Our proposal promises NOON-like MSSs of unprecedentedly many atoms. Both proposed applications of the adiabatically prepared CBA state depend only on existent technology. Our numerical results show that they tolerate a reasonably swift quasiadiabatic passage in the presence of atom loss as well as uncertainties of atom counting. Excited-state quantum phase transitions (ESQPTs) extend the concept of QPTs beyond the ground state. While they have been extensively investigated theoretically, there are only few experimental results. From the perspective of quantum-state engineering, it is furthermore surprising how rarely order parameters of ESQPTs are discussed in the literature. Mean-field models for spinor BECs imply ESQPTs, to which some experimental observations on the mean-field dynamics can be attributed. However, so far, neither theoretical nor experimental studies have specifically addressed ESQPTs in spinor BECs. We extend the ground-state phase diagram of ferromagnetic spin-1 BECs with zero magnetization across the spectrum. There are three excited-state phases, corresponding to one ground-state phase each. The ESQPTs are signaled by a diverging density of states. The mean-field phase-space trajectories can be characterized by a winding number that is in one-to-one correspondence to the excited-state phases. We derive a closely related order parameter encoded in the dynamics of coherent states and discuss how this order parameter can be interferometrically measured in current experiments. Remarkably, the mean-field model governing the ESQPTs in spin-1 BECs with zero magnetization is encountered also, e. g., in molecular and nuclear physics. Because of the superior experimental control, spinor BECs can be considered as simulators of the ESQPTs in those systems. Our results contribute to quantum-state engineering and quantum-enhanced interferometry in spinor BECs and to the characterization of excited-state quantum phases. The latter may, in turn, lead on to applications in quantum-state engineering.
23Na spin-1 Bose-Einstein condensates are used to experimentally demonstrate that mean-field physics beyond the single-mode approximation can be relevant during the nonequilibrium dynamics. The experimentally observed spin oscillation dynamics and associated dynamical spatial structure formation confirm theoretical predictions that are derived by solving a set of coupled mean-field Gross-Pitaevskii equations [J. Jie et al., Phys. Rev. A 102, 023324 (2020)]. The experiments rely on microwave dressing of the f=1 hyperfine states, where f denotes the total angular momentum of the 23Na atom. The fact that physics beyond the single-mode approximation at the mean-field level, i.e., spatial mean-field dynamics that distinguishes the spatial density profiles associated with different Zeeman levels, can, in certain parameter regimes, have a pronounced effect on the dynamics when the spin healing length is comparable to or larger than the size of the Bose-Einstein condensate has implications for using Bose-Einstein condensates as models for quantum phase transitions and spin squeezing studies as well as for nonlinear SU(1,1) interferometers.
Spinor condensates immersed in a microwave dressing field, which access both negative and positive values of the net quadratic Zeeman effect, have been realized in a recent experiment. In this report, we study the ground state properties of a spinor condensate with a microwave dressing field which enables us to access both negative and positive values of quadratic Zeeman energy. The ground state exhibits three different phases by varying the magnetization and the net quadratic Zeeman energy for both cases of ferromagnetic and antiferromagnetic interactions. We investigate the atomic-number fluctuations of the ground state and show that the hyperfine state displays super-Poissonian and sub-Poissonian distributions in the different phases. We also discuss the dynamical properties and show that the separatrix has a remarkable relation to the magnetization.
This thesis discusses non-equilibrium phenomena in antiferromagnetic spinor quantum gases. We investigate, both experimentally and theoretically, the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition. A microwave dressing field was used as a novel tool to access the polar to antiferrmagnetic quantum phase transition at the quadratic Zeeman shift, q=0. By performing instantaneous quenches across the phase transition,a dynamical instability was induced in the atomic cloud. This lead to pair formation and rapid amplification of spin +/-1 atoms through spin-mixing collisions. The spatial ordering kinetics in the vicinity of the phase transition was quantified by performing the local spin measurement. The coarsening dynamics was observed for the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud. Rich nonequilibrium behavior was observed in the form of growth and decay of both nematic and magnetic spin waves, following the quench. The spatiotemporal evolution was characterized through two particle correlations between atoms in each pair of spin states, which revealed dramatic differences between the dynamics of the spin correlations and those of the spin populations. \nFinally, we demonstrate the remarkable influence of linear Zeeman term on non-equilibrium dynamics of spinor Bose-Einstein condensates. We show that contrary to prior understanding magnetic field gradient actually suppresses the tendency of spin 0 state to separate into spin +/-1 state. This reconciles the Bogoliubov discrepancies and leads to a dramatic sharpening of the transition point, resulting in a resolution at the 1 Hz level. Our results point to the use of dynamics, rather than equilibrium quantities for high precision measurements of phase transitions in quantum gases.
We have experimentally observed the dynamics of an antiferromagnetic sodium Bose-Einstein condensate quenched through a quantum phase transition. Using an off-resonant microwave field coupling the F = 1 and F = 2 atomic hyperfine levels, we rapidly switched the quadratic energy shift q from positive to negative values. At q = 0, the system undergoes a transition from a polar to antiferromagnetic phase. We measured the dynamical evolution of the population in the F = 1, mF = 0 state in the vicinity of this transition point and observed a mixed state of all 3 hyperfine components for q < 0. We also observed the coarsening dynamics of the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud.