Bose-Einstein condensation at finite momentum and magnon condensation in thin film ferromagnets

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion ϵ _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 2 π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.     

New non-Goldstone collective mode of BEC of magnons in superfluid 3He-B

Bose-Einstein condensation of magnons in superfluid 3He-B is experimentally manifested by various states where coherent spin precession is established spontaneously, even in nonhomogeneous magnetic fields. Once such a condensate with coherent spin precession is created, it occupies the state with minimal energy, the ground state. The application of an additional magnetic field to that condensate may cause its deflection from the energy minimum and the condensate responds by creating collective gapless oscillations known as Goldstone modes. This Letter reports the experimental observation of a new (non-)Goldstone mode, which can be viewed as an additional NMR mode of condensed magnons in a rotating frame of reference.     

QUIC阱中紧束缚状态下87Rb原子气体的玻色-爱因斯坦凝聚体相变的直接观测

在QUIC阱中经蒸发冷却获得了2×10⁵个|F=2,m_F=2〉态的⁸⁷Rb原子气体的玻色-爱因斯坦凝聚.验证了紧束缚状态下原子云的轴向尺寸的变化作为BEC相变的判据，观察了从热原子气体到玻色-爱因斯坦凝聚的相变过程，测量了自由膨胀过程中BEC的纵横比变化，并和理论预言进行了对比. 关键词： 玻色-爱因斯坦凝聚 激光冷却与囚禁     

Magnon BEC in superfluid <Superscript>3</Superscript>He-A

The new mode of magnetization precession in superfluid ³He-A in a squeezed aerogel has been recently reported. We consider this mode in terms of the Bose-Einstein condensation (BEC) of magnons. The difference between magnon BEC states in ³He-A and in ³He-B is discussed. The article is published in the original.     

Production of a bose einstein condensate of metastable helium atoms

We recently observed a Bose-Einstein condensate in a dilute gas of ⁴He in the 2³S₁ metastable state. In this article, we describe the successive experimental steps which led to the Bose-Einstein transition at 4.7 μK: loading of a large number of atoms in a MOT, efficient transfer into a magnetic Ioffé-Pritchard trap, and optimization of the evaporative cooling ramp. Quantitative measurements are also given for the rates of elastic and inelastic collisions, both above and below the transition. Received 15 October 2001     

Features of the Coupled Nuclear–Electron Spin Precession in the Bose–Einstein Condensate of Magnons

JETP Letters - The experimental detection of the Bose-Einstein condensate of magnons in coupled nuclear-electron spin precession in antiferromagnets brings the prospect of its use for magnonics and...     

Bose-Einstein condensation of rubidium atoms

A setup for preparing the Bose-Einstein condensate of rubidium atoms has been built. The condensate consists of 10⁵–10^{6 87}Rb atoms in the hyperfine state F _g = 2 of the ground electronic state. Three key indications of condensation—a sharp increase in the phase-space density of atoms, the threshold emergence of two fractions in the cloud, and anisotropic expansion of the condensate—have been observed.     

The Bose-Einstein condensation in a finite one-dimensional homogeneous system of noninteracting bosons

Condensation of the ideal Bose gas in a closed volume having the shape of a rectangular parallel-epiped of length L with a square base of side length l (L ? l) is theoretically studied within the framework of the Bose-Einstein statistics (grand canonical ensemble) and within the statistics of a canonical ensemble of bosons. Under the condition N(l/L)⁴ ? l, where N is the total number of gas particles, dependence of the average number of particles in the condensate on the temperature T in both statistics is expressed as a function of the ratio t=T/T ₁, where T ₁ is a certain characteristic temperature depending only on the longitudinal size L. Therefore, the condensation process exhibits a one-dimensional (1D) character. In the 1D regime, the average numbers of particles in condensates of the grand canonical and canonical ensembles coincide only in the limiting cases of t → 0 and t → ∞. The distribution function of the number of particles in the condensate of a canonical ensemble of bosons at t ≤1 has a resonance shape and qualitatively differs from the Bose-Einstein distribution. The former distribution begins to change in the region of t ～ 1 and acquires the shape of the Bose-Einstein distribution for t ? 1. This transformation proceeds gradually that is, the 1D condensation process exhibits no features characteristic of the phase transition in a 3D system. For N(l/L)⁴ ? 1, the process acquires a 3D character with respect to the average number of particles in the condensate, but the 1D character of the distribution function of the number of particles in the condensate of a canonical ensemble of bosons is retained at all N values.     

Self-trapping of magnon Bose-Einstein condensates in the ground state and on excited levels: from harmonic to box confinement

Long-lived coherent spin precession of (3)He-B at low temperatures around 0.2T(c) 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.     

Production and measurement of Bose-Einstein condensate of 87Rb atomic gas

The research platform for Bose-Einstein condensate in ⁸⁷Rb atomic gas, which is composed of a double MOT configuration and a QUIC trap, was reported. The properties of the condensate were measured both in time-of-flight and in tight confinement by the absorption imaging method. The measurements agreed with the criterions of Bose-Einstein condensation phase transition. About 2×10⁵ atoms were pure condensed. Supported by the National Natural Science Foundation of China (Grant No. 10334050) and the National Basic Research Program of China (Grant Nos. 2001CB309307 and 2006CB921202)     

Phonons in a magnon superfluid and symmetry-breaking field

Recent experiments [1,2] on the measurement of the spectrum of the Goldstone collective mode of a coherently precessing state in ³He-B are discussed using the presentation of the coherent-spin precession in terms of the Bose-Einstein condensation of magnons. The mass in the spectrum of the Goldstone boson—a phonon in the superfluid magnon liquid—is induced by the symmetry-breaking field, which is played by the RF magnetic field. The text was submitted by the author in English.     

Two-magnon Raman scattering in helical spin system

Two-magnon Raman scattering in the helical spin system at finite temperatures is studied by the two-time Green function method. The interaction between two magnons excited simultaneously by the incident light and the interaction between these magnons and other magnons excited thermally are included by use of a decoupling approximation similar to that of Callen. The temperature dependence of the line shape is calculated for the Γ⁺₄ and Γ⁺₅ modes in MnO₂ and VF₂.     

Beliaev theory of spinor Bose–Einstein condensates

By generalizing the Green’s function approach developed by Beliaev [S.T. Beliaev, Sov. Phys. JETP 7 (1958) 299; S.T. Beliaev, Sov. Phys. JETP 7 (1958) 289], we study effects of quantum fluctuations on the energy spectra of spin-1 spinor Bose–Einstein condensates, in particular, of a ⁸⁷Rb condensate in the presence of an external magnetic field. We find that due to quantum fluctuations, the effective mass of magnons, which characterizes the quadratic dispersion relation of spin-wave excitations, increases compared with its mean-field value. The enhancement factor turns out to be the same for two distinct quantum phases: the ferromagnetic and polar phases, and it is a function of only the gas parameter. The lifetime of magnons in a spin-1 ⁸⁷Rb spinor condensate is shown to be much longer than that of phonons due to the difference in their dispersion relations. We propose a scheme to measure the effective mass of magnons in a spinor Bose gas by utilizing the effect of magnons’ nonlinear dispersion relation on the time evolution of the distribution of transverse magnetization. This type of measurement can be applied, for example, to precision magnetometry.     

All-optical formation of molecules with spin degree of freedom in an atomic Bose-Einstein condensate

We have performed a two-photon photoassociation experiment in an atomic Bose-Einstein condensate of ⁸⁷Rb with the spin degree of freedom, which is created by an all-optical method with CO₂ lasers. The spinor character of the created molecules has been revealed by the photoassociation spectrum with a new structure. The hyperfine structure of the created molecules near the dissociation limit is identified by observations of the Zeeman and AC-Stark effects of the molecules. We have also demonstrated the spin-selective creation of molecules. This result would open the new possibility of research on novel molecular spinor BEC.     

Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar <Superscript>3</Superscript>He

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid ³He, experimentally observed in uniaxial aerogel ³He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.     

Two-photon correlations of luminescence at the Bose-Einstein condensation of dipolar excitons

Correlations of the luminescence intensity (the second-order correlation function g ⁽²⁾(τ)), where τ is the delay time between the photons detected in pairs) under the conditions of the Bose-Einstein condensation (BEC) of dipolar excitons has been studied in a temperature range of 0.45–4.2 K. Photoexcited dipolar excitons have been accumulated in a lateral trap in a GaAs/AlGaAs Schottky diode with a 25-nm wide single quantum well with an electric bias applied across the heterolayers. Two-photon correlations have been measured with the use of a two-beam intensity interferometer with a time resolution of }~0.4 ns according to the well-known classical Hanbury-Brown-Twiss scheme. The photon bunching has been observed at the onset of Bose-Einstein condensation manifested by the appearance of a narrow exciton condensate line in the luminescence spectrum at an increase in the optical pumping (the line width near the threshold is ?200 μeV). At the same time, the two-photon correlation function itself obeys the super-Poisson distribution, g ⁽²⁾(τ) > 1, at time scale τ_c ? 1 ns of the system coherence. The photon bunching is absent at a pumping level substantially below the condensation threshold. The effect of bunching also decreases at pumping significantly above the threshold, when the narrow exciton condensate line starts to dominate in the luminescence spectra, and finally disappears with the further increase in the optical excitation. In this region, the distribution of pair photon correlations is a Poisson distribution manifesting the united quantum coherent state of the exciton condensate. Under the same conditions, the first-order spatial correlation function g ⁽¹⁾(r) determined from the interference pattern of the luminescence signals from the spatially separated parts of the condensate at constant pumping remains noticeable at distances of no less than 4 μm. The discovered effect of photon bunching is very sensitive to temperature and decreases by several times with a temperature increase in the range of 0.45–4.2 K. Assuming that the luminescence of the dipolar excitons directly reflects the coherence properties of the gas of interacting excitons, the discovered photon bunching at the onset of condensation, where the fluctuations of the exciton density and, consequently, of the luminescence intensity are most significant, indicates a phase transition in the interacting Bose gas of excitons, which is an independent way of detecting the Bose-Einstein condensation of excitons.     

Experimental Setup for Observation the Bose–Einstein Condensation of Magnons in Solid Antiferromagnets CsMnF3 and MnCO3

The Bose–Einstein condensation of magnons was observed in 1984 in superfluid ³He–B. The same phenomena should exist in solid magnetic systems. We describe here a partly digital experimental setup for studying solid antiferromagnets CsMnF₃ and MnCO₃ by pulse and continuous wave nuclear magnetic resonance. With this equipment, the Bose–Einstein condensation of magnons was observed for the first time in these single crystals.     

The <Superscript>55</Superscript>Mn Spin Echo Test of Magnon BEC State in MnCO<Subscript>3</Subscript>

The coherent quantum state of magnons—Bose–Einstein condensate (BEC) has been observed in several types of antiferromagnets. According to the Bose statistics of magnons, BEC appears when the magnon density exceeds the critical density N _BEC and the magnon gas condenses to a quantum liquid. The BEC state is characterized by a coherent precession of the magnetization. In this paper, the first experiments showing the suppression of the spin echo signal by the magnon BEC is presented. These experiments confirm the coherence of magnetic excitations in the BEC state.     

Bose condensation in strongly monideal systems

The possibility of the formation of a condensate with a finite absolute value of the momentum k₀ in a strongly nonideal Bose system is considered. Such a condensate comes into existence when the one-particle spectrum of a normal system touches zero in the point k₀ ≠ 0. The form of a correlation function below the condensation point shows the appearance of a long-range order, but not the infinite long-range one. In the case of liquid ⁴He estimates show that $\text{k}{}_0\text{? 1}\text{A}\text{?}{}^{\mathrm{?1}}$, and at the temperature T>₀ ～ 1 K this unusual condensate with a finite magnitude of the momentum turns into the conventional Bose-Einstein condensate with the zero momentum. The properties of correlation functions in the spaces of different dimensions are discussed.