Permanent Bose–Einstein Condensate

International audience

The Bose–Einstein condensation (BEC) corresponds to the formation of a collective quantum state in which macroscopic number of particles is governed by a single wave function. The magnon BEC, the coherent state of a macroscopic number of magnons, manifests itself by coherent precession of magnetization even in an inhomogeneous magnetic field. The magnon BEC has many similarities with the atomic BEC. But it shows a great variety of properties in different magnetic materials. Here we will classify the different types of magnonic BECs.

Advances in quantum computing and telecommunications stimulate the search for classical systems allowing partial implementation of a similar functionality under less stringent environmental conditions. Here, we present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose–Einstein condensate (BEC) formed at opposite wavevectors in a room-temperature yttrium-iron-garnet ferrimagnetic film. Employing micromagnetic numerical simulations, we show the use of wavelength-selective parametric pumping to controllably initialize and manipulate the two-component BEC. Next, by modeling the interaction of this BEC with a pulse- and radio-frequency-driven dynamic magnonic crystal we translate the concept of Rabi-oscillations into the wavevector domain and demonstrate how to manipulate the magnon-BEC system regarding the polar and azimuthal angles in the Bloch sphere representation. We hope that our study provides a significant stimulus on the boundary between qubit functionality and classical systems of interacting BECs, which use a subset of qubit-based algorithms.

Room-temperature quantum computing and solid-state quantum simulations have been long-standing goals in the field of quantum information science. Magnon Bose-Einstein condensation at room temperature may provide a key advance towards these objectives. Normally, the magnon Bose-Einstein condensation is driven by microwave pumping and detected by light. Here, the authors propose a method to create stable magnon condensate using lasers in a magneto-optical cavity, opening new avenues for all-optical control in quantum magnonics.

Strong experimental evidences of the formation of quasi-equilibrium Bose-Einstein condensation (BEC) of magnons at room temperature in a film of yttrium iron garnet (YIG) excited by microwave radiation have been recently reported. Here we present a theory for the magnon gas driven by a microwave field far out of equilibrium showing that the nonlinear magnetic interactions create cooperative mechanisms for the onset of a phase transition leading to the spontaneous generation of quantum coherence and magnetic dynamic order in a macroscopic scale. The theory provides rigorous support for the formation of a BEC of magnons in a YIG film magnetized in the plane. We show that the system develops coherence only when the microwave driving power exceeds a threshold value and that the theoretical result for the intensity of the Brillouin light scattering from the BEC as a function of power agrees with the experimental data. The theory also explains quantitatively experimental measurements of microwave emission from the uniform mode generated by the confluence of BEC magnon pairs in a YIG film when the driving power exceeds a critical value.

We report magnetic susceptibility, specific heat, and neutron scattering measurements as a function of applied magnetic field and temperature to characterize the S = 1/2 quasi-two-dimensional (2D) frustrated magnet piperazinium hexachlorodicuprate (PHCC). The experiments reveal four distinct phases. At low temperatures and fields the material forms a quantum paramagnet with a 1 meV singlet triplet gap and a magnon bandwidth of 1.7 meV. The singlet state involves multiple spin pairs some of which have negative ground state bond energies. Increasing the field at low temperatures induces 3D long-range antiferromagnetic order at 7.5 Tesla through a continuous phase transition that can be described as magnon Bose–Einstein condensation. The phase transition to a fully polarized ferromagnetic state occurs at 37 Tesla. The ordered antiferromagnetic phase is surrounded by a renormalized classical region. The crossover to this phase from the quantum paramagnet is marked by a distinct anomaly in the magnetic susceptibility which coincides with closure of the finite temperature singlet–triplet pseudo gap. The phase boundary between the quantum paramagnet and the Bose–Einstein condensate features a finite temperature minimum at T = 0.2 K, which may be associated with coupling to nuclear spin or lattice degrees of freedom close to quantum criticality.

Magnon, the quanta of spin waves, can serve as an efficient spin information carrier for memory and logic applications, with the advantages of the Joule-heating free induced low power-dissipation property and the phase-coherent induced quantum phenomena. In analogy to spintronics, magnonics focuses on the excitation, detection, and manipulation of magnons (spin waves). In recent years, with the development of nanotechnology, abundant magnonic phenomena emerge in the nanoscale, such as the spin Seebeck effect, magnon-mediated electric current drag effect, magnon valve effect, magnon junction effect, magnon resonant transimission, magnon transfer torque, spin wave propagation, subterahertz spin wave excitation, magnon Bose–Einstein condensation, and so on. Here, we review the recent progresses in magnonics from physics, materials to devices, shedding light on the future directions for magnonics.

Recent experimental data on Bose-Einstein condensation of magnons in the spin-gap compound Yb_{2}Si_{2}O_{7} revealed an asymmetric Bose-Einstein condensation dome [G. Hester et al., Phys. Rev. Lett. 123, 027201 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.027201]. We examine modifications to the Heisenberg model on a breathing honeycomb lattice, showing that this physics can be explained by competing anisotropic perturbations. We employ a gamut of analytical and numerical techniques to show that the anisotropy yields a field driven phase transition from a state with broken Ising symmetry to a phase that breaks no symmetries and crosses over to the polarized limit.

Bose-Einstein condensation (BEC) of triplet excitations triggered by a magnetic field, sometimes called magnon BEC, in dimerized antiferromagnets gives rise to a long-range antiferromagnetic order in the plane perpendicular to the applied magnetic field. To explore the effects of spin-orbit coupling on magnon condensation, we study a spin model on a distorted honeycomb lattice with dimerized Heisenberg exchange ($J$ terms) and uniform off-diagonal exchange ($\Gamma'$ terms) interactions. Via variational Monte Carlo calculations and spin-wave theory, we find that an out-of-plane magnetic field can induce different types of long-range magnetic orders, no matter if the ground state is a non-magnetic dimerized state or an ordered N\'{e}el state. Furthermore, the critical properties of field-driven phase transitions in the presence of spin-orbit couplings, as illustrated from spin-wave spectrum and interpreted by effective field theory, can be different from the conventional magnon BEC. Our study is helpful to understand the rich phases of spin-orbit coupled antiferromagnets induced by magnetic fields.

Quantum magnets, which involve strong quantum fluctuation stemming from noncommutative properties of spin operators, have attracted much attention because of those fascinating properties. In this paper, we report detailed behaviors of the ferroelectricity, driven by the field-induced Bose-Einstein condensation of magnon quasiparticles in the quantum spin gap system ${\mathrm{TlCuCl}}_{3}$. Superposition of the wave functions inherent in a quantum magnet in its ground state plays a key role in the appearance of this ferroelectricity. The field dependence of the spontaneous electric polarization clearly demonstrates that the ferroelectricity is caused by the emergence of the vector spin chirality in the magnon Bose-Einstein condensate. The ferroelectricity is suggested to be significantly enhanced by quantum entanglement in the spin dimer. Furthermore, reflecting the isotropic nature of ${\mathrm{TlCuCl}}_{3}$, the ferroelectricity is very soft with a low electric coercive field ${E}_{\mathrm{r}}\ensuremath{\simeq}0.03$ MV/m. Our analysis indicates that vector components of the electric polarization, which are not caused by the spin current mechanism, appear in ${\mathrm{TlCuCl}}_{3}$.

We report the experimental realization of a space-time crystal with tunable periodicity in time and space in the magnon Bose-Einstein Condensate (BEC), formed in a room-temperature Yttrium Iron Garnet (YIG) film by radio-frequency space-homogeneous magnetic field. The magnon BEC is prepared to have a well defined frequency and non-zero wavevector. We demonstrate how the crystalline "density" as well as the time and space textures of the resulting crystal may be tuned by varying the experimental parameters: external static magnetic field, temperature, thickness of the YIG film and power of the radio-frequency field. The proposed space-time crystals provide a new dimension for exploring dynamical phases of matter and can serve as a model nonlinear Floquet system, that brings in touch the rich fields of classical nonlinear waves, magnonics and periodically driven systems.

Exchange interactions between S=1/2 sites in piperazinium hexachlorodicuprate produce a frustrated bilayer magnet with a singlet ground state. We have determined the field-temperature phase diagram by high field magnetization and neutron scattering experiments. There are two quantum critical points: Hc1=7.5 T separates a quantum paramagnet phase from a three dimensional, antiferromagnetically ordered state while Hc2=37 marks the onset of a fully polarized state. The ordered phase, which we describe as a magnon Bose-Einstein condensate (BEC), is embedded in a quantum critical regime with short range correlations. A low temperature anomaly in the BEC phase boundary indicates that additional low energy features of the material become important near Hc1.

In 1938 London [1,2] offered an explanation of the observation earlier that year of superfluid behavior in liquid 4He when it is cooled below a critical temperature of 2.17 °K. He argued that the superfluid transition was analogous to the Bose condensation of an (ideal) gas of non-interacting atoms obeying the same Bose-Einstein spin-statistics relation as 4He atoms. This relation requires the many-atom wave function to be completely symmetric in the atomic coordinates, resulting in a preference for the atoms to occupy the same single-particle states. For a finite system of atoms the momenta are quantized in spacings proportional to the inverse of the system size. At high temperatures the fraction of atoms occupying any one of the momentum states also scales as the inverse of the size. However, as the temperature is reduced below a critical Bose condensation temperature a significant fraction of the atoms, independent of the system size, begins to occupy the zero-momentum state. The Bose condensate fraction of an ideal gas approaches one at zero temperature. For 4He, by analogy, at high temperatures in the normal fluid the condensate fraction should be zero, but as temperatures are reduced below the superfluid transition temperature the condensate fraction should rise to a non-zero value. The effect of the strong interactions among the (non-ideal) 4He atoms is to deplete the zero temperature condensate fraction from one in an ideal gas to a value much less than one for 4He. While the analogy between superfluidity and Bose condensation is imperfect, the concept of a Bose condensate in the superfluid phase has survived. A variety of increasingly sophisticated many-body calculations have predicted a condensate fraction of about 10 % at zero temperature in superfluid 4He at SVP. Because of the importance of superfluidity and the related phenomenon of superconductivity to condensed matter physics, this simple prediction has motivated a more than twenty year effort involving up to one hundred scientists to measure the Bose condensate fraction in 4He.

We consider a general anisotropic spin-orbit coupling (SOC) and analyze the phase diagrams of both balanced and imbalanced Fermi gases for the entire BCS--Bose-Einstein condensate (BEC) evolution. In the first part, we use the self-consistent mean-field theory at zero temperature, and show that the topological structure of the ground-state phase diagrams is quite robust against the effects of anisotropy. In the second part, we go beyond the mean-field description, and investigate the effects of Gaussian fluctuations near the critical temperature. This allows us to derive the time-dependent Ginzburg-Landau theory, from which we extract the effective mass of the Cooper pairs and their critical condensation temperature in the molecular BEC limit.

Dynamical characteristics of internal and external states of a Bose-Einstein condensate are generally different and independent, thus requiring different experimental manipulation techniques. The spin-orbit coupling recently achieved in Bose-Einstein condensates essentially connects spin and motion degree of freedom, endowing spin states with the ability to respond to orbital manipulation, and vice versa. In this work, a dynamical response effect, induced by simultaneously manipulating the internal and external states of a spin-orbit-coupled Bose-Einstein condensate, is predicted. Here, the “simultaneously manipulating the internal and external states” means that the driving field combines the Zeeman field applied to the internal state of the atom and the orbital potential affecting the external states of the atom. Specifically, the Bose-Einstein condensate is assumed to be activated by an abruptly applied Zeeman field and a sudden shake of the trapping potential. After some reasonable simplification and approximation of the model (i.e. neglecting the inter-atomic interactions and modelling the shake of the trapping potential by a short time-dependent pulse), an analytical relationship connecting spin frequency spectrum and the parameters of the driving fields is derived. The numerical calculations based on directly integrating the Gross-Pitaevskii equation are in good agreement with the results from the analytical relationship. The physical origin of the predicted spin dynamical response can be traced back to the quantum interference among different spin-orbit states. Due to the fact that a series of characteristic parameters of the condensate can be manifested in the spin frequency spectrum, the dynamical response effect predicted here provides a candidate method for determining and calibrating various system parameters by measuring the spin frequency spectrum.