Long-lived coherent spin precession of 3He-B at low temperatures around 0.2 Tc is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulated experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.
Recently E. Sonin commented [1] on our preprint "Supercurrent in a room temperature Bose-Einstein magnon condensate" [2,3], arguing that our "claim of detection of spin supercurrent is premature and has not been sufficiently supported by presented experimental results and their theoretical interpretation." We consider the appearance of this Comment as a sign of significant interest into the problem of supercurrents in Bose-Einstein magnon condensates. Here, we explicitly address E. Sonin's comments and show that our interpretation of our experimental results as a detection of a magnon supercur…
Evolution of an overpopulated gas of magnons to a Bose-Einstein condensate and excitation of a magnon supercurrent, propelled by a phase gradient in the condensate wave function, can be observed at room-temperature by means of the Brillouin light scattering spectroscopy in an yttrium iron garnet material. We study these phenomena in a wide range of external magnetic fields in order to understand their properties when externally pumped magnons are transferred towards the condensed state via two distinct channels: A multistage Kolmogorov-Zakharov cascade of the weak-wave turbulence or a one-step…
A phenomenological theory is developed, that accounts for the collective dynamics of a Bose-Einstein condensate of magnons. In terms of such description we discuss the nature of spontaneous macroscopic interference between magnon clouds, highlighting the close relation between such effects and the well known Josephson effects. Using those ideas we present a detailed calculation of the Josephson oscillations between two magnon clouds, spatially separated in a magnonic Josephson junction.
Using a variational method, we derive an exact upper bound for one-magnon excitation energy in ferromagnetic spinor gases, which limits the quantum corrections to the effective mass of a magnon to be positive. We also derive an upper bound for one-magnon excitation energy in lattice systems. The results hold for both Bose and Fermi systems in $d$ dimensions as long as the interaction is local and invariant under spin rotation.
The emergence of a non-equilibrium Bose-Einstein-like condensation of magnons in rf-pumped magnetic thin films has recently been experimentally observed. We present here a complete theoretical description of the non-equilibrium processes involved. It it demonstrated that the phenomenon is another example of the presence of a Bose-Einstein-like condensation in non-equilibrium many-boson systems embedded in a thermal bath, better referred-to as Fröhlich-Bose-Einstein condensation. The complex behavior emerges after a threshold of the exciting intensity is attained. It is inhibited at higher inte…
Motivated by the recent experiment performed by the Berkeley group [G. E. Marti {\it et al.}, Phys. Rev. Lett. {\bf 113}, 155302 (2014)], we consider the dynamics of magnons in a spin-1 spinor-dipolar Bose-Einstein condensate, using mean-field theory. We show that the effective mass of a magnon is increased by the magnetic dipole-dipole interaction, as observed in the experiment. The magnon mass is also decreased by changing the direction of the magnetic field. The increase and decrease in the magnon mass manifest themselves in the acceleration of the magnons.
Thermalization of a parametrically driven magnon gas leading to the formation of a Bose-Einstein condensate at the bottom of a spin-wave spectrum was studied by time- and wavevector-resolved Brillouin light scattering spectroscopy. It has been found that the condensation is preceded by the conversion of initially pumped magnons into a second group of frequency degenerated magnons, which appear due to parametrically stimulated scattering of the initial magnons to a short-wavelength spectral region. In contrast to the first magnon group, which wavevectors are orthogonal to the wavevectors of the…
We observe the condensation of magnon excitations within an $F=1$ $^{87}$Rb spinor Bose-Einstein condensed gas. Magnons are pumped into a longitudinally spin-polarized gas, allowed to equilibrate to a non-degenerate distribution, and then cooled evaporatively at near-constant net longitudinal magnetization whereupon they condense. We find magnon condensation to be described quantitatively as the condensation of free particles in an effective potential that is uniform within the ferromagnetic condensate volume, evidenced by the number and distribution of magnons at the condensation transition. …
We introduce a system of phenomenological equations for Bose-Einstein condensates of magnons in the one-dimensional setting. The nonlinearly coupled equations, written for amplitudes of the right-and left-traveling waves, combine basic features of the Gross-Pitaevskii and complex Ginzburg-Landau models. They include localized source terms, to represent the microwave magnon-pumping field. With the source represented by the $δ$-functions, we find analytical solutions for symmetric localized states of the magnon condensates. We also predict the existence of asymmetric states with unequal amplitud…
We consider a two-component Bose-condensed mixture characterized by positive s-wave scattering lengths. We assume equal densities and intra-species interactions. By doing the Bogoliubov transformation of an effective Hamiltonian we obtain the lower energy magnon dispersion incorporating the superfluid entrainment between the components. We argue that p-wave pairing of distinct bosons should be accompanied by self-localization of magnons and formation of a magnetoroton. We demonstrate the effect on a model system of particles interacting via step potentials.
We clarify the condition for the occurrence of magnon Bose-Einstein condensation (BEC) in spin pumping systems without using external pumping magnetic fields. The Goldstone model is generalized and the stability of the vacuum is closely investigated. By applying the generalized Goldstone model to spin pumping systems, the condition for the experimental realization of the stable magnon BEC in spin pumping systems is theoretically proposed.
We report evidence for the existence of a supercurrent of magnons in a magnon Bose-Einstein condensate prepared in a room temperature yttrium-iron-garnet magnetic film and subject to a thermal gradient. The magnon condensate is formed in a parametrically populated magnon gas, and its temporal evolution is studied by time-, frequency- and wavector-resolved Brillouin light scattering spectroscopy. It has been found that local heating in the focal point of a probing laser beam enhances the temporal decrease in the density of the freely evolving magnon condensate after the termination of the pumpi…
Local temperature control of magnon frequency and direction of supercurrents in a magnon Bose-Einstein condensate
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道）；Weizmann Institute of Science（魏茨曼科学研究所）；Fraunhofer Institute for Industrial Mathematics ITWM（弗劳恩霍夫工业数学研究所）
The quanta of magnetic excitations - magnons - are known for their unique ability to undergo Bose-Einstein condensation at room temperature. This fascinating phenomenon reveals itself as a spontaneous formation of a macroscopic coherent state under the influence of incoherent stimuli. Spin currents have been predicted to offer electronic control of magnon Bose-Einstein condensates, but this phenomenon has not been experimentally evidenced up to now. Here we experimentally show that current-driven Bose-Einstein condensation can be achieved in nanometer-thick films of magnetic insulators with ta…
Magnon Bose-Einstein Condensates (BECs) and supercurrents are coherent quantum phenomena, which appear on a macroscopic scale in parametrically populated solid state spinsystems. One of the most fascinating and attractive features of these processes is the possibility of magnon condensation and supercurrent excitation even at room temperature. At the same time, valuable information about a magnon BEC state, such as its lifetime, its formation threshold, and coherency, is provided by experiments at various temperatures. Here, we use Brillouin Light Scattering (BLS) spectroscopy for the investig…
The Bose-Einstein condensation (BEC) of magnons created by a strong pumping in ferromagnetic thin films of yttrium iron garnet used as systems of finite size is considered analytically. Such a peculiarity, typical for this magnetic material, as the presence of a minimum in the spectrum of spin waves at a finite value of the wave vector is taken into account. The definition of hightemperature BEC is introduced and its characteristics are discussed. A role of boundary conditions for spin variables is analyzed, and it is shown that in the case of free spins on the boundary the magnon lattice can …
We measure the mass, gap, and magnetic moment of a magnon in the ferromagnetic $F=1$ spinor Bose-Einstein condensate of $^{87}$Rb. We find an unusually heavy magnon mass of $1.038(2)_\mathrm{stat}(8)_\mathrm{sys}$ times the atomic mass, as determined by interfering standing and running coherent magnon waves within the dense and trapped condensed gas. This measurement is shifted significantly from theoretical estimates. The magnon energy gap of $h\times 2.5(1)_\mathrm{stat}(2)_\mathrm{sys}\;\mathrm{Hz}$ and the effective magnetic moment of $-1.04(2)_\mathrm{stat}(8)\,μ_\textrm{bare}$ times the …
We theoretically investigate spin transfer between a system of quasiequilibrated Bose-Einstein condensed magnons in an insulator in direct contact with a conductor. While charge transfer is prohibited across the interface, spin transport arises from the exchange coupling between insulator and conductor spins. In normal insulator phase, spin transport is governed solely by the presence of thermal and spin-diffusive gradients; the presence of Bose-Einstein condensation (BEC), meanwhile, gives rise to a temperature-independent condensate spin current. Depending on the thermodynamic bias of the sy…
Using the Aharonov-Casher (A-C) phase, we present a microscopic theory of the Josephson and persistent spin currents in quasi-equilibrium Bose-Einstein condensates (BECs) of magnons in ferromagnetic insulators. Starting from a microscopic spin model that we map onto a Gross-Pitaevskii Hamiltonian, we derive a two-state model for the Josephson junction between the weakly coupled magnon-BECs. We then show how to obtain the alternating-current (ac) Josephson effect with magnons as well as macroscopic quantum self-trapping in a magnon-BEC. We next propose how to control the direct-current (dc) Jos…
We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion epsilon_k has two degenerate minima at finite wave-vectors q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2pi/q; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We…
We explore the formation and collective modes of Bose-Einstein condensate of Dirac magnons (Dirac BEC). While we focus on two-dimensional Dirac magnons, an employed approach is general and could be used to describe Bose-Einstein condensates with linear quasiparticle spectrum in various systems. By using a phenomenological multicomponent model of pumped boson population together with bosons residing at Dirac nodes, the formation and time evolution of condensates of Dirac bosons is investigated. The condensate coherence and its multicomponent nature are manifested in the Rabi oscillations whose …
We study the Josephson oscillation and self trapping dynamics of a cigar-shaped dipolar Bose-Einstein condensate of $^{52}$Cr atoms polarized along the symmetry axis of an axially-symmetric double-well potential using the numerical solution of a mean-field model, for dominating repulsive contact interaction (large positive scattering length a) over an anisotropic dipolar interaction. Josephson-type oscillation emerges for small and very large number of atoms, whereas self trapping is noted for an intermediate number of atoms. The dipolar interaction pushes the system away from self trapping to…
We report on experimental observation of BEC-like behaviour of quantized electron spin waves (magnons) in a dense gas of spin polarized atomic hydrogen. The magnons are trapped and controlled with inhomogeneous magnetic fields, and described by a Schrödinger-like wave equation, in analogy to the BEC experiments with neutral atoms. We have observed the appearance of a sharp feature in the ESR spectrum displaced from the normal spin wave spectrum. We believe that this observation corresponds to a sudden growth of the ground state population of the magnons and emergence of their spontaneous coher…
Enhancement of magnon flux toward a Bose-Einstein condensate
RPTU University Kaiserslautern-Landau（凯泽斯劳滕-兰道理工大学）；Fraunhofer Institute for Industrial Mathematics ITWM（弗劳恩霍夫工业数学研究所）；The Weizmann Institute of Science（魏茨曼科学研究所）
An easy-plane ferromagnetic insulator in a uniform external magnetic field and in contact with a phonon bath and a normal metal bath is studied theoretically in the presence of dc spin current injection via the spin Hall effect in the metal. The Keldysh path integral formalism is used to model the magnon gas driven into a nonequilibrium steady state by mismatched bath temperatures and/or electrical injection, and we analyze the magnon system in the normal (uncondensed) state, but close to the instability to Bose-Einstein condensation (BEC), within the self-consistent Hartree-Fock approximation…
We derive exact solitonic solutions of a class of Gross-Pitaevskii equations with time-dependent harmonic trapping potential and interatomic interaction. We find families of exact single-solitonic, multi-solitonic, and solitary wave solutions. We show that, with the special case of an oscillating trapping potential and interatomic interaction, a soliton can be localized indefinitely at an arbitrary position. The localization is shown to be experimentally possible for sufficiently long time even with only an oscillating trapping potential and a constant interatomic interaction.
We study the expansion of harmonically trapped bosons in a two-dimensional lattice after suddenly turning off the confining potential. We show that, in the presence of multiple occupancies per lattice site and strong interactions, the system exhibits a clear dynamical separation into slowly and rapidly expanding clouds. We discuss how this effect can be understood within a simple picture by invoking doublons and Bose enhancement. This picture is corroborated by an analysis of the momentum distribution function in the regions with slowly and rapidly expanding bosons.
Bose-Einstein condensation (BEC) of magnons is one of few macroscopic quantum phenomena observable at room temperature. Due to competition of the exchange and the magnetic dipole interactions the minimum-energy magnon state is doubly degenerate and corresponds to two antiparallel non-zero wavevectors. Correspondingly, magnon BEC differs essentially from other condensates, since it takes place simultaneously at +/-k_min. The degeneracy of BEC and interaction between its two components have significant impact on the condensate properties. Phase locking of the two condensates causes formation of …
Based on the mean-field approximation and the phase space analysis, we discuss the dynamics of Bose-Einstein condensates in a double-well potential. By applying a periodic modulation to the coupling between the condensates, we find the condensates can be trapped in the time-dependent eigenstates of the effective Hamiltonian, we refer to this effect as time-dependent self-trapping of BECs. A comparison of this self-trapping with the adiabatic evolution is made, finding that the adiabatic evolution beyond the traditional(linear) adiabatic condition can be achieved in BECs by manipulating the non…
We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low energy eigenspectr…
The problem of self-trapping of a Bose-Einstein condensate (BEC) and a binary BEC in an optical lattice (OL) and double well (DW) is studied using the mean-field Gross-Pitaevskii equation. For both DW and OL, permanent self-trapping occurs in a window of the repulsive nonlinearity $g$ of the GP equation: $g_{c1}<g<g_{c2}$. In case of OL, the critical nonlinearities $g_{c1}$ and $g_{c2}$ correspond to a window of chemical potentials $μ_{c1}<μ<μ_{c2}$ defining the band gap(s) of the periodic OL. The permanent self-trapped BEC in an OL usually represents a breathing oscillation of a stable statio…
Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons
The University of Osaka（大阪大学）；Kyoto University（京都大学）；Fukushima Medical University（福岛医科大学）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）
Considering a two-dimensional Bose-Hubbard spinor lattice with weak nearest neighbour interactions and no particle transfer between sites, we theoretically study the transport of energy from one initially excited dimer, to the rest of the lattice. Beyond a critical interaction strength, low energy on-site excitations are quickly dispersed throughout the array, while stronger excitations are self trapped, resulting in localized energy breathers and solitons. These structures are quasiparticle analogues to the discrete 2D solitons in photonic lattices. Full many-body simulations additionally dem…
We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $|ψ(0)\rangle=|\cdots 2020\cdots \rangle$ in the presence of a trapping potential. We compute the level spacing statistic, the time evolution of the number imbalance between the odd and the even sites, and the entanglement entropy in order to show that the system exhibits nonergodicity in a strongly interacting regime. The trapping potential enhances nonergodicity even when the trapping potential is weak compared to the the hopping energy. We d…
We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green's functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a 3D weakly-interacting gas the spectrum can be obtained by applying the Bogoliub…
We study the transverse expansion of arrays of ultracold $^{87}$Rb atoms weakly confined in tubes created by a 2D optical lattice, and observe that transverse expansion is delayed because of mutual atom interactions. A mean-field model of a coupled array shows that atoms become localized within a roughly square fort-like self-trapping barrier with time-evolving edges. But the observed dynamics is poorly described by the mean-field model. Theoretical introduction of random phase fluctuations among tubes improves the agreement with experiment, but does not correctly predict the density at which …
We report the thermodynamic properties of Bose and Fermi ideal gases immersed in periodic structures such as penetrable multilayers or multitubes simulated by one (planes) or two perpendicular (tubes) external Dirac comb potentials, while the particles are allowed to move freely in the remaining directions. Although the bosonic chemical potential is a constant for $T < T_c$, a non decreasing with temperature anomalous behavior of the fermionic chemical potential is confirmed and monitored as the tube bundle goes from 2D to 1D when the wall impenetrability overcomes a critical value. In the spe…
We revisit the coherent or delocalized to self-trapping transition in an interacting bosonic quantum fluid confined in a double well potential, in the context of full quantum calculations. We show that an $N$-particle Bose-Hubbard fluid reaches an stationary state through the two-body interactions. These stationary states are either delocalized or self-trapped in one of the wells, the former appearing as coherent oscillations in the mean-field approximation. By studying one- and two-body properties in the energy eigenstates and in a set of coherent states, we show that the delocalized to self-…
By generalizing the Green's function approach proposed by Beliaev [1, 2], we investigate the effect of quantum depletion on the energy spectra of elementary excitations in an F = 1 spinor Bose-Einstein condensate, in particular, of 87Rb atoms in an external magnetic field. We find that quantum depletion increases the effective mass of magnons in the spin-wave excitations with quadratic dispersion relations. The enhancement factor turns out to be the same for both ferromagnetic and polar phases, and also independent of the magnitude of the external magnetic field. The lifetime of these magnons …
We study the stability and dynamics of an ultra-cold bosonic gas trapped in a toroidal geometry and driven by rotation, in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a "disorder" potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the sy…
We experimentally study tunneling of Bose-condensed $^{87}$Rb atoms prepared in a quasi-bound state and observe a non-exponential decay caused by interatomic interactions. A combination of a magnetic quadrupole trap and a thin $1.3\mathrm{μm}$ barrier created using a blue-detuned sheet of light is used to tailor traps with controllable depth and tunneling rate. The escape dynamics strongly depend on the mean-field energy, which gives rise to three distinct regimes--- classical spilling over the barrier, quantum tunneling, and decay dominated by background losses. We show that the tunneling rat…
We study the ground state of frustrated spin-S chains in a strong magnetic field in the immediate vicinity of saturation. In strongly frustrated chains, the magnon dispersion has two degenerate minima at inequivalent momenta $\pm Q$, and just below the saturation field the system can be effectively represented as a dilute one-dimensional lattice gas of two species of bosons that correspond to magnons with momenta around $\pm Q$. We present a theory of effective interactions in such a dilute magnon gas that allows us to make quantitative predictions for arbitrary values of the spin. With the he…
We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the non-interacting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsacker (TF-vW) density functional. It is found …
We show that the adiabatic dynamics of a Bose-Einstein condensate (BEC) in a double well potential can be described in terms of a dark variable resulting from the combination of the population imbalance and the spatial atomic coherence between the two wells. By means of this dark variable, we extend, to the non-linear matter wave case, the recent proposal by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)] on adiabatic passage techniques to coherently control the population of two internal levels of an atom/molecule. We investigate the conditions to adiabatically split or transport a BEC as …
