We show that spinor Bose gases subject to a quadratic Zeeman effect exhibit coexisting superfluidity and spin superfluidity, and study the interplay between these two distinct types of superfluidity. To illustrate that the basic principles governing these two types of superfluidity are the same, we describe the magnetization and particle-density dynamics in a single hydrodynamic framework. In this description spin and mass supercurrents are driven by their respective chemical potential gradients. As an application, we propose an experimentally accessible stationary state, where the two types of supercurrents counterflow and cancel each other, thus resulting in no mass transport. Furthermore, we propose a straightforward setup to probe spin superfluidity by measuring the in-plane magnetization angle of the whole cloud of atoms. We verify the robustness of these findings by evaluating the four-magnon collision time, and find that the time scale for coherent (superfluid) dynamics is separated from that of the slower incoherent dynamics by one order of magnitude. Comparing the atom and magnon kinetics reveals that while the former can be hydrodynamic, the latter is typically collisionless under most experimental conditions. This implies that, while our zero-temperature hydrodynamic equations are a valid description of spin transport in Bose gases, a hydrodynamic description that treats both mass and spin transport at finite temperatures may not be readily feasible.
We show that spinor Bose gases subject to a quadratic Zeeman effect exhibit coexisting superfluidity and spin superfluidity, and study the interplay between these two distinct types of superfluidity. To illustrate that the basic principles governing these two types of superfluidity are the same, we describe the magnetization and particle-density dynamics in a single hydrodynamic framework. In this description spin and mass supercurrents are driven by their respective chemical potential gradients. As an application, we propose an experimentally accessible stationary state, where the two types of supercurrents counterflow and cancel each other, thus resulting in no mass transport. Furthermore, we propose a straightforward setup to probe spin superfluidity by measuring the in-plane magnetization angle of the whole cloud of atoms. We verify the robustness of these findings by evaluating the four-magnon collision time, and find that the time scale for coherent (superfluid) dynamics is separated from that of the slower incoherent dynamics by one order of magnitude. Comparing the atom and magnon kinetics reveals that while the former can be hydrodynamic, the latter is typically collisionless under most experimental conditions. This implies that, while our zero-temperature hydrodynamic equations are a valid description of spin transport in Bose gases, a hydrodynamic description that treats both mass and spin transport at finite temperatures may not be readily feasible.
Spinor Bose gases may exhibit both phase and ferromagnetic order. Consequently, they may support superflow of both mass and spin currents. In this thesis we utilize a stochastic Gross-Pitaevskii model to investigate the superfluid properties of a two-dimensional spin-1 Bose gas with ferromagnetic interactions. Owing to the low dimensionality, the superfluidity of this system can not be attributed to the presence of a Bose-Einstein condensate, with thermal fluctuations precluding long-range order. Rather, mass and spin superfluidity emerge via respective Berezinskii-Kosterlitz-Thouless (BKT) transitions. Such transitions are characterized by the emergence of quasi-long-range order, driven by the binding of topological defect pairs. First, we consider an easy-plane ferromagnetic gas. We find the system superfluidity may be understood by direct application of existing BKT theory. In particular, mass and spin superfluidity are respectively associated with quasi-long-range order in the global phase and local magnetization. The former arises from the binding of mass vortex pairs, while the latter arises from the binding of polar-core spin vortex pairs. Following this, we introduce axial magnetization, and consider a gas in the broken-axisymmetric phase. We find axial magnetization acts to couple mass and spin superflows via a mechanism analogous to the superfluid drag exhibited by two-component superfluids. This coupling renders invalid the direct applicability of existing BKT theory: here mass and spin superfluidity may each be associated with both phase and magnetic order. We remedy this with a generalization making concrete the relation between superfluidity and quasi-long-range order in this system. In addition, through variations of the quadratic Zeeman energy and axial magnetization we identify three distinct superfluid phases, which serve as finite-temperature generalizations of the polar, broken-axisymmetric, and easy-axis ferromagnetic ground states.
The paper investigates the coexistence and interplay of spin and mass superfluidity in a ferromagnetic spin-1 Bose-Einstein condensate. Superfluidity is possible only in the presence of uniaxial anisotropy (linear and quadratic Zeeman effect). This follows from the topology of the order-parameter space (vacuum manifold). According to the Landau criterion, the critical phase gradients, both for mass and spin supercurrents, vanish at the phase transition from the easy-plane to the easy-axis anisotropy. However, mass superfluidity is still possible at the phase transition. This is because the Landau criterion signals instability only with respect to nonsingular vortices with special ratio between circulations of mass and spin currents. Phase slips produced by these vortices are not sufficient for complete decay of supercurrents. Full decay of supercurrents requires phase slips with vortices of another topological class and larger energy. These phase slips are suppressed by energetic barriers up to the upper critical velocity (gradient) exceeding the Landau critical velocity. The upper critical velocity does not vanish nor has any anomaly in the critical point at the phase transition from the easy-plane to the easy-axis anisotropy.
Spinor Bose-Einstein condensates (BECs) are multi-component superfluids with magnetic interactions, formed from dilute gases of atoms in the Zeeman sublevels mF of a single hyperfine ground state F. Spinor BECs are inherently magnetic quantum objects, and exhibit a multitude of features such as spin domains, magnon excitations, and distinct magnetic phases. At the heart of the magnetic nature of a spinor BEC is the spin-dependent collisional interaction c, which determines the overall magnetic behaviour of the superfluid. In conjunction with the quadratic Zeeman shift q, the magnitude and sign of c give rise to an intricate magnetic phase diagram. The magnetic phase of a spinor BEC is tunable, and c and q are the knobs. In addition to realising quantum simulators of magnetism, spinor BECs are also precise magnetic sensors. Atomic magnetometry measures the Larmor precession frequency of atoms, which is proportional to the magnetic field strength. The sensitivity of an atomic magnetometer is principally dependent on the duration of the measurement (interrogation time) and number of atoms participating in the measurement. BECs are highly suitable as atomic magnetometers, allowing for long interrogation times and high atomic density, with microscopic sensor volumes. The latter is an important consideration, as measurement of small magnetic sources demand equally microscopic sensors. Established forms of magnetometry (such as warm vapour magnetometers) use large sensing volumes and are not trivially miniaturised. The exquisite sensitivity of a spinor BEC to magnetic fields becomes a liability when one studies low energy (~ 1 Hz) spinor physics over long evolution times (100 ms) in a typical laboratory environment. To first order, the spin-collisional interaction is independent of the magnetic field. However, spatially inhomogeneous magnetic fields are problematic, exerting mechanical forces on the magnetically sensitive spin components, suppressing spin collisions and possibly introducing relaxation mechanisms that confound the observation of intrinsic equilibration. Precise characterisation of magnetic field gradients and their cancellation is thus of paramount importance. In this thesis, the interaction of a spinor BEC with its environment is studied. The construction, operation and optimisation of a BEC machine is described in detail, as well as the quantum state preparation and control techniques used. Spin-mixing collisions were studied by observing population oscillations, the characteristic hallmark of such coherent phenomena. The observed population dynamics showed strong evidence of the deleterious effects of magnetic field gradients. A series of experiments were performed using spin-echo pulse sequences to decouple the evolving spinor condensate from the inhomogeneous magnetic environment with encouraging results, but which posed further questions. The fidelity of spin-echo pulses in the strong radiative coupling regime was also studied. Spinor condensates were then employed as sensitive magnetometers to characterise the magnetic landscape they inhabit. A new method of measuring magnetic field gradients was developed, using a pair of spinor BECs separated in space that are simultaneously addressed by a Ramsey interferometry sequence. Combined with a re-orientable magnetic bias field, the resulting gradiometer was used to measure the magnetic field gradient tensor in vacuo. This scheme can be extended to realise a high-precision vector co-magnetometer, with spatiotemporal sensitivity comparable to established forms of magnetometry. Vector light shifts (VLSs) are optically-induced energy shifts that result in effective magnetic fields, which in our case originate from the laser beams used to trap the atoms. The VLS vanishes for purely linearly polarised light, which is experimentally difficult to obtain in vacuo. Small elliptical polarisation imperfections originating from birefringent optics and the glass vacuum cell result in a non-zero shift that contaminates magnetometry measurements. The VLS is spatially varying due to the intensity gradient of the trapping light. Due to gravitational sag of the trapping potential, the spatial variation of the VLS is accentuated, resulting in an effective magnetic field gradient that contributes to dephasing and component separation. The simultaneous Ramsey interferometry experiments are then adapted to measure the VLS-induced Zeeman shift and diagnose its elimination. Up to 99.96% of the VLS is eliminated using this method, and extensions to the technique are described.
The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter -- is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in ^3He-B. This superfluid current of spins -- spin supercurrent -- is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid ^4He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves -- magnons. We discuss different states of magnon superfluidity with different types of spin-orbit coupling: in bulk ^3He-B; magnetically traped "Q-balls" at very low temperatures; in ^3He-A and ^3He-B immerged in deformed aerogel; etc. Some effects in normal ^3He can also be treated as a magnetic BEC of fermi liquid. A very similar phenomena can be observed also in a magnetic systems with dinamical frequensy shift, like MnC03. We will discuss the main experimental signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex -- a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken U(1) symmetry -- phonons in the spin-superfluid magnon gas; etc. For recent review see Yu. M. Bunkov and G. E. Volovik J. Phys. Cond. Matter. 22, 164210 (2010)
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.
Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of a collective quantum state in which a macroscopic number of particles occupy the lowest energy state and thus is governed by a single wavefunction. Here we highlight the BEC in a magnetic subsystem--the BEC of magnons, elementary magnetic excitations. The magnon BEC is manifested as the spontaneously emerging state of the precessing spins, in which all spins precess with the same frequency and phase even in an inhomogeneous magnetic field. The coherent spin precession was observed first in superfluid (3)He-B and this domain was called the homogeneously precessing domain (HPD). The main feature of the HPD is the induction decay signal, which ranges over many orders of magnitude longer than is prescribed by the inhomogeneity of magnetic field. This means that spins precess not with a local Larmor frequency, but coherently with a common frequency and phase. This BEC can also be created and stabilized by continuous NMR pumping. In this case the NMR frequency plays the role of a magnon chemical potential, which determines the density of the magnon condensate. The interference between two condensates has also been demonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. The main property is the existence of a spin supercurrent. This spin supercurrent flows separately from the mass current. Transfer of magnetization by the spin supercurrent by a distance of more than 1 cm has been observed. Also related phenomena have been observed: the spin current Josephson effect; the phase-slip processes at the critical current; and the spin current vortex--a topological defect which is the analog of a quantized vortex in superfluids and of an Abrikosov vortex in superconductors; and so on. It is important to mention that the spin supercurrent is a magnetic phenomenon, which is not directly related to the mass superfluidity of (3)He: it is the consequence of a specific antiferromagnetic ordering in superfluid (3)He. Several different states of coherent precession have been observed in (3)He-B: the homogeneously precessing domain (HPD); a persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. In compressed aerogel the coherent precession has been also found in (3)He-A. We demonstrate that the coherent precession of magnetization is a true BEC of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by spin-orbit coupling which is different for different states of the magnon BEC.