Spinor Condensates Research Articles

Parametric excitation and squeezing in a many-body spinor condensate.

Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states.

Universal few-body physics in resonantly interacting spinor condensates

Optical trapping techniques allow for the formation of bosonic condensates with internal degrees of freedom, so-called spinor condensates. Mean-field models of spinor condensates highlight the sensitivity of the quantum phases of the system to the relative strength of the two-body interaction in the different spin-channels. Such a description captures the regime where these interactions are weak. In the opposite and largely unexplored regime of strongly correlated spinor condensates, three-body interactions can play an important role through the Efimov effect, producing possible novel phases. Here, we study the three-body spinor problem using the hyperspherical adiabatic representation for spin-1, -2 and -3 condensates in the strongly-correlated regime. We characterize the Efimov physics for such systems and the relevant three-body mean-field parameters. We find that the Efimov effect can strongly affect the spin dynamics and three-body mean-field contributions to the possible quantum phases of the condensate through universal contributions to scattering observables.

Spin-dependent Bragg spectroscopy of a spinor Bose gas

We develop a general theory of spin-dependent Bragg spectroscopy for spinor Bose-Einstein condensates. This spectroscopy involves using a density and spin-coupled optical probe to excite the system. We show that within the linear response regime the momentum or energy transferred by the probe is determined by a set of density and spin-density dynamic structure factors. We derive a set of $f$-sum rules that provide rigorous constraints for the first energy moments of these structure factors. As an application we compute the dynamic structure factors for cases within all four distinct phases of a spin-1 condensate using Bogoliubov theory. Our results demonstrate that spin-dependent Bragg spectroscopy can be used to selectively investigate the various phonon and magnon excitation branches and will be a useful tool for advancing our understanding of spinor condensates.

Spin squeezing in dipolar spinor condensates

We study the effect of dipolar interactions on the level of squeezing in spin-1 Bose-Einstein condensates by using the single mode approximation. We limit our consideration to the $\mathfrak{su}(2)$ Lie subalgebra spanned by spin operators. The biaxial nature of dipolar interactions allows for dynamical generation of spin-squeezed states in the system. We analyze the phase portraits in the reduced mean-filed space in order to determine positions of unstable fixed points. We calculate numerically spin squeezing parameter showing that it is possible to reach the strongest squeezing set by the two-axis countertwisting model. We partially explain scaling with the system size by using the Gaussian approach and the frozen spin approximation.

The synchronization and stability of spinor polariton condensates

By taking account of the spin degree of freedom with varying the Zeeman splitting, we explore the possible synchronized states of spinor polariton condensates formed in a semiconductor microcavity. The interplay among nonlinear interactions, spin-flipping rates and energy splitting is theoretically investigated. Besides a minimum transverse-field induced spin-flipping rate required to form the synchronized state, we find that the interaction effect between polaritons is the dominant factor. Therefore, with the manipulation of the energy splitting between the two spin states, the spinor condensate initially synchronized with “elliptical” polarization may become two separated desynchronized and “circularly” polarized condensates. Moreover, the region and stability of synchronized states are discussed for various asymmetric pumping configurations.

Dynamical instability in theS=1Bose-Hubbard model

We study the dynamical instabilities of superfluid flows in the S=1 Bose-Hubbard model. The time evolution of each spin component in a condensate is calculated based on the dynamical Gutzwiller approximation for a wide range of interactions, from a weakly correlated regime to a strongly correlated regime near the Mott-insulator transition. Owing to the spin-dependent interactions, the superfluid flow of the spin-1 condensate decays at a different critical momentum from a spinless case when the interaction strength is the same. We furthermore calculate the dynamical phase diagram of this model and clarify that the obtained phase boundary has very different features depending on whether the average number of particles per site is even or odd. Finally, we analyze the density and spin modulations that appear in association with the dynamical instability. We find that spin modulations are highly sensitive to the presence of a uniform magnetic field.

Universal Coarsening Dynamics of a Quenched Ferromagnetic Spin-1 Condensate.

We demonstrate that a quasi-two-dimensional spin-1 condensate quenched to a ferromagnetic phase undergoes universal coarsening in its late time dynamics. The quench can be implemented by a sudden change in the applied magnetic field and, depending on the final value, the ferromagnetic phase has easy-axis (Ising) or easy-plane (XY) symmetry, with different dynamical critical exponents. Our results for the easy-plane phase reveal a fractal domain structure and the crucial role of polar-core spin vortices in the coarsening dynamics.

Magnetic tensor gradiometry using Ramsey interferometry of spinor condensates

We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate $^{87}$Rb spin-1 condensates in freefall and infer their relative Larmor phase -- and thus the differential magnetic field strength -- with a common-mode phase noise suppression exceeding $50\,\mathrm{dB}$. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure the magnetic field gradient tensor of ambient and applied magnetic fields with a nominal precision of $30\,\mathrm{\mu G\,cm^{-1}}$ and a sensor volume of $2\times10^{-5}\,\mathrm{mm}^3$. We predict a spin-projection noise limited magnetic energy resolution of order $\hbar$ for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle inherent to BEC experiments.

Spinor Condensates on a Cylindrical Surface in Synthetic Gauge Fields.

We show that by modifying the setup of the recent experiment that creates a "Dirac string" one can engineer a quasi-2D spinor Bose-Einstein condensate on a cylindrical surface, with a synthetic magnetic field normal to the surface. Because of the muticonnectivity of the surface, there are two types of vortices (called A and B) with the same vorticity. This is very different from the planar case, which only has one kind of vortex for fixed circulation. As the strength of the synthetic gauge field increases, the ground states will form a necklace of alternating AB vortices surrounding the lateral midpoint of the cylinder, and will split into two A and B necklaces at higher synthetic gauge fields. The fact that even the basic vortex structure of a Bose-Einstein condensate is altered in a cylindrical surface implies that richer phenomena are in store for quantum gases in other curved surfaces.

Polariton spin whirls

We report on the observation of spin whirls in a radially expanding polariton condensate formed under non-resonant optical excitation. Real space imaging of polarization- and time-resolved photoluminescence reveal a spiralling polarization pattern in the plane of the microcavity. Simulations of the spatiotemporal dynamics of a spinor condensate reveal the crucial role of polariton interactions with a spinor exciton reservoir. Harnessing spin dependent interactions between the exciton reservoir and polariton condensates allows for the manipulation of spin currents and the realization of dynamic collective spin effects in solid state systems.

Phase diagram and spin mixing dynamics in spinor condensates with a microwave dressing field.

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.

Spinor Bose-Einstein condensates of rotating polar molecules

We propose a scheme to realize a pseudospin-$1/2$ model of the $^{1}\Sigma(v=0)$ bialkali polar molecules with the spin states corresponding to two sublevels of the first excited rotational level. We show that the effective dipole-dipole interaction between two spin-$1/2$ molecules couples the rotational and orbital angular momenta and is highly tunable via a microwave field. We also investigate the ground state properties of a spin-$1/2$ molecular condensate. A variety of nontrivial quantum phases, including the doubly-quantized vortex states, are discovered. Our scheme can also be used to create spin-$1$ model of polar molecules. Thus, we show that the ultracold gases of bialkali polar molecules provide a unique platform for studying the spinor condensates of rotating molecules.

Analytic models for the density of a ground-state spinor condensate

We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the ground-state densities of ferromagnetic BECs are obtained from the Thomas-Fermi approximation (TFA) to this decoupled equation. Similarly, for the ground states of spin-1 anti-ferromagnetic and spin-2 anti-ferromagnetic and cyclic BECs, some of the spin component densities are zero which reduces the coupled GP equation to a simple reduced form. Analytic models for ground state densities are also obtained for anti-ferromagnetic and cyclic BECs from the TFA to the respective reduced GP equations. The analytic densities are illustrated and compared with the full numerical solution of the GP equation with realistic experimental parameters.

Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate.

We report on the observation of half-quantum vortices (HQVs) in the easy-plane polar phase of an antiferromagnetic spinor Bose-Einstein condensate. Using insitu magnetization-sensitive imaging, we observe that pairs of HQVs with opposite core magnetization are generated when singly charged quantum vortices are injected into the condensate. The dynamics of HQV pair formation is characterized by measuring the temporal evolutions of the pair separation distance and the core magnetization, which reveals the short-range nature of the repulsive interactions between the HQVs. We find that spin fluctuations arising from thermal population of transverse magnon excitations do not significantly affect the HQV pair formation dynamics. Our results demonstrate the instability of a singly charged vortex in the antiferromagnetic spinor condensate.

Antiferromagnetic Spinor Condensates in a Two-Dimensional Optical Lattice.

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 semiquantitatively describes our data without adjustable parameters.

Spontaneous spin textures in dipolar spinor condensates: A Dirac string gas approach

We study the spontaneous spin textures induced by magnetic dipole-dipole interaction in ferromagnetic spinor condensates under various trap geometries. At the mean-field level, we show the system is dual to a Dirac string gas with a negative string tension in which the ground state spin texture can be easily determined. We find that three-dimensional condensates prefer a meron-like vortex texture, quasi one-dimensional condensates prefer the axially polarized flare texture, while condensates in quasi two dimensions exhibit either a meron texture or an in-plane polarized texture.

Spin-Thermodynamics of Ultra-Cold Spin-1 Atoms

The spin-thermodynamics of a \(N\)-body spin-1 condensate containing only the spin-degrees of freedom is studied via a theory in which \(N\), the total spin \(S\) and its Z-component \(M\) are exactly conserved. The magnetic field \(B\) is considered as zero at first. Then the effect of a residual \(B\) is evaluated. A temperature \(T_3\) is defined as below that all the spatial degrees of freedom can be considered as being frozen and, accordingly, a pure spin-system will emerge. Effort is made to evaluate \(T_3\). When \(T\) goes up from zero, the internal energy \(U\) and the entropy \(S_E\) experience sharp changes in two narrow domains of \(T\) surrounding two turning temperatures \(T_1\) and \(T_2\), the latter is higher. When \(T T_2\), \(U\) and \(S_E\) remain unchanged. Whereas when \(T_1<T<T_2\), \(U\propto T\) and \(S_E\propto \ln T\). It was found that \(T_1\) and \(T_2\) originate from the gap \(E_{\mathrm{gap},1}\) (the energy difference between the ground state (g.s.) and the first excited state) and the width (the energy difference between the g.s. and the highest state without spatial excitation) of the spectra, respectively. Thus their appearance is a common feature in spin-thermodynamics. In fact, \(T_1\) marks the lowest excitation of the spin-modes, while \(T_2\) marks the maximization of the entropy in the spin-space. In particular, the T-dependent population density is defined so that the theory can be checked by experimental data. Two kinds of condensates are notable: (i) the strongly trapped systems with a very small \(N\), they can work as pure spin-systems at relatively higher temperature; (ii) the systems with a high magnetization (say, \(N-|M|\le 4\)), the dimensions of their spin-spaces are very low. Furthermore, a larger \(\omega \) together with a large N (for Rb) or a large \(|M|\) (for Na) will lead to a sufficiently large \(E_{\mathrm{gap},1}\) so that a real g.s. can be experimentally created at a higher temperature. The spin-thermodynamics would remain valid whenever the spatial modes decouple from the spin-modes. This can occur at a higher temperature as demonstrated in Pechkis et al. (Phys Rev Lett 111:025301, 2013).

Modulational Instability of Spinor Condensates in an Optical Lattice* *Supported by the National Natural Science Foundation of China under Grant No. 11274095 and the Program of USTITSPHP under Grant No. 13IRTSTHN016

We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-one-dimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.

Mobile vector soliton in a spin–orbit coupled spin-1 condensate

We study the formation of bound states and three-component bright vector solitons in a quasi-one-dimensional spin–orbit-coupled hyperfine spin f = 1 Bose–Einstein condensate using numerical solution and variational approximation of a mean-field model. In the antiferromagnetic domain, the solutions are time-reversal symmetric, and the component densities have multi-peak structure. In the ferromagnetic domain, the solutions violate time-reversal symmetry, and the component densities have single-peak structure. The dynamics of the system are not Galelian invariant. From an analysis of Galelian invariance, we establish that the single-peak ferromagnetic vector solitons are true solitons and can move maintaining constant component densities, whereas the antiferromagnetic solitons cannot move with constant component densities.

A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate

We report the observation of coherent circulation in a macroscopic Bose-Einstein condensate of polaritons in a ring geometry. Because they are spinor condensates, half-quanta are allowed in where there is a phase rotation of π in connection with a polarization vector rotation of π around a closed path. This half-quantum behavior is clearly seen in the experimental observations of the polarization rotation around the ring. In our ring geometry, the half-quantum state that we see is one in which the handedness of the spin flips from one side of the ring to the other side in addition to the rotation of the linear polarization component; such a state is allowed in a ring geometry but will not occur in a simply connected geometry. This state is lower in energy than a half-quantum state with no change of the spin direction and corresponds to a superposition of two different elementary half-quantum states. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise from one shot to the next; this fluctuation corresponds to spontaneous breaking of time-reversal symmetry in the system. This type of macroscopic polariton ring condensate allows for the possibility of direct control of the circulation to excite higher quantized states and the creation of Josephson junction tunneling barriers.