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 a standing wave of the condensate density and quantized vortices. Additionally, interaction between the two components is believed to be important for stabilization of the condensate with respect to the real-space collapse. Thus, the possibility to create a non-degenerate, single-component condensate is decisive for understanding of underlying physics of magnon BEC. Here, we experimentally demonstrate an approach, which allows one to accomplish this challenging task. We show that this can be achieved by using a separation of the two components of the degenerate condensate in the real space by applying a local pulsed magnetic field, which causes their motion in the opposite directions. Thus, after a certain delay, the two clouds corresponding to different components become well separated in the real space. We find that the motion of the clouds can be described well based on the peculiarities of the magnon dispersion characteristics. Additionally, we show that, during the motion, the condensate cloud harvests non-condensed magnons, which results in a partial compensation of the condensate depletion.
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.
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…
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…
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 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…
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）
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 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…
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.
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.
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 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 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.
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 …
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…
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）
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…
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 …
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）
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…
Paul Scherrer Institute（保罗谢尔研究所）；Institut de Physique, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院物理系）；Nordita, Royal Institute of Technology, Stockholm University（诺迪塔，皇家理工学院，斯德哥尔摩大学）；University of Missouri（密苏里大学）；Laboratory of Nanoscale Magnetic Materials and Magnonics, Institute of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料研究所纳米磁性材料与磁振子实验室）；Institute of Microengineering, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院微工程学院）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料与能源中心）；INNOVENT e.V. Technologieentwicklung（INNOVENT技术开发协会）
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 pumpin…
Recently, magnons, which are quasiparticles describing the collective motion of spins, were found to undergo Bose-Einstein condensation (BEC) at room temperature in films of Yttrium Iron Garnet (YIG). Unlike other quasiparticle BEC systems, this system has a spectrum with two degenerate minima, which makes it possible for the system to have two condensates in momentum space. Recent Brillouin Light scattering studies for a microwave-pumped YIG film of thickness d=5 $μ$m and field H=1 kOe find a low-contrast interference pattern at the characteristic wavevector $Q$ of the magnon energy minimum. …
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 investigate the elastic scattering of Bose-Einstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the Bose-Einstein condensate such that the Bose-Einstein condensate gets depleted. As a precursor for the excitation of the Bose-Einstein condensate we observe wave chaos within a mean-field theory.
We discuss the comment [ arXiv:1102.2943] by E. Kozik about "Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein Condensates [arXiv:1007.4441]".
The dynamics of a Bose-Einstein condensate of atoms having attractive interactions is studied using quantum many-body simulations. The collapse of the condensate by quantum tunneling is numerically demonstrated and the tunneling rate is calculated. The correlation properties of the quantum many-body state are investigated.
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 report the formation of Bose-Einstein condensates into non-equilibrium states. Our condensates are much longer than equilibrium condensates with the same number of atoms, show strong phase fluctuations, and have a dynamical evolution similar to that of quadrupole shape oscillations of regular condensates. The condensates emerge in elongated traps as the result of local thermalization when the nucleation time is short compared to the axial oscillation time. We introduce condensate focusing as a powerful method to extract the phase-coherence length of Bose-Einstein condensates.
We study center-of-mass oscillations of a dipolar Bose-Einstein condensate in the vicinity of a superconducting surface. We show that the magnetic field of the magnetic dipoles induces eddy currents in the superconductor, which act back on the Bose-Einstein condensate. This leads to a shift of its oscillation frequency and to an anharmonic coupling of the Bose-Einstein condensate with the superconductor. The anharmonicity creates a coupling to one of the collective modes of the condensate that can be resonantly enhanced, if the parameters of the condensate are chosen properly. This provides a …
We discuss the effect of anomalous quantum-reflection of Bose-Einstein condensates as a screening effect, that is created by the condensate itself. We derive an effective, time-independent single-mode approach, that allows us to define different paths of reflection. We compare our theory with experimental results.
I present an interconversion currents algebra for an atom-molecule Bose-Einstein condensate model and use it to get the quantum dynamics of the currents. For different choices of the Hamiltonian parameters I get different currents dynamics.
Collapsing Bose-Einstein condensates are rich and complex quantum systems for which quantitative explanation by simple models has proved elusive. We present new experimental data on the collapse of high density Rb-85 condensates with attractive interactions and find quantitative agreement with the predictions of the Gross-Pitaevskii equation. The collapse data and measurements of the decay of atoms from our condensates allow us to put new limits on the value of the Rb-85 three-body loss coefficient K_3 at small positive and negative scattering lengths.
The role of complex potentials in single-body Schrődinger equation has been studied intensively. We study the quantum coherence for degenerate Bose gases in complex potentials, when the exchange symmetry of identical bosons is considered. For initially independent Bose-Einstein condensates, it is shown that even very weak imaginary potential can induce perfect quantum coherence between different condensates. The scheme to observe imaginary potential induced quantum coherence is discussed.
We theoretically study macroscopic entanglement between a magnetically trapped Bose-Einstein condensate and a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupling with the magnetic trap to generate macroscopic entanglement. The scheme also provides a platform to investigate interferometry with an entangled Bose Einstein condensate and to explore physics at the quantum-classical interface.
Preparation of molecular quantum gas promises novel applications including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing. Experimental preparation of colder and denser molecular samples, however, is frequently hindered by fast inelastic collisions that heat and deplete the population. Here we report the formation of two-dimensional Bose-Einstein condensates (BECs) of spinning $g-$wave molecules by inducing pairing interactions in an atomic condensate. The trap geometry and the low temperature of the molecules help reducing …
We describe the transition of $N$ weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and non-condensate thermalization, we derive a master equation for the condensate subsystem in the presence of the non-condensate environment under the inclusion of all two body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakl…
The condensate number distribution during the transition of a dilute, weakly interacting gas of N=200 bosonic atoms into a Bose-Einstein condensate is modeled within number conserving master equation theory of Bose-Einstein condensation. Initial strong quantum fluctuations occuring during the exponential cycle of condensate growth reduce in a subsequent saturation stage, before the Bose gas finally relaxes towards the Gibbs-Boltzmann equilibrium.
We calculate the condensate fraction and the condensate and non-condensate spatial and momentum distribution of the Bose-Hubbard model in a trap. From our results, it is evident that using approximate distributions can lead to erroneous experimental estimates of the condensate. Strong interactions cause the condensate to develop pedestal-like structures around the central peak that can be mistaken as non-condensate atoms. Near the transition temperature, the peak itself can include a significant non-condensate component. Using distributions generated from QMC simulations, experiments can map t…
The Bose-stimulated self-organization of a quasi-two dimensional non-equilibrium Bose-Einstein condensate in an in-plane potential is proposed. We obtained the solution of the nonlinear, driven-dissipative Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in an external asymmetric parabolic potential within the method of the spectral expansion. We found that, in sharp contrast to previous observations, the condensate can spontaneously acquire a soliton-like shape for spatially homogenous pumping. This condensate soliton performs oscillatory motion in a parabolic trap and, also, …
In certain field theoretical models, composite solitons consisting of a domain wall and vortex lines attached to the wall have been referred to as D-brane solitons. We show that similar composite solitons can be realized in phase-separated two-component Bose-Einstein condensates. We discuss the similarities and differences between topological solitons in the Abelian-Higgs model and those in two-component Bose-Einstein condensates. Based on the formulation of gauge theory, we introduce the "boojum charge" to characterize the "D-brane soliton" in Bose-Einstein condensates.
I introduce two family of exactly solvable models for multiatomic hetero-nuclear and homo-nuclear molecular Bose-Einstein condensates through the algebraic Bethe ansatz method. The conserved quantities of the respective models are also showed.
