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Ground-state and non-ground-state Bose-Einstein condensation of magnons in superfluid 3He-B

S. Autti, Yu. M. Bunkov, V. B. Eltsov, P. J. Heikkinen, J. J. Hosio, Pierre Hunger, M. Krusius, Григорий Ефимович Воловик

Published Feb 8, 2010• 0 citations
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Abstract

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.

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Magnon Bose-Einstein -kondensaatit 3He-B -supranesteessä

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In this thesis we study Bose-Einstein condensates of trapped magnon quasiparticles in superfluid 3He-B. These condensates form in the trap provided by the order-parameter texture and applied magnetic field profile. We provide numerical description of two properties of the condensates, both observed in experiments: One of these properties is the ability to interact with the trapping potential, which draws an analogy to Q-balls of high energy physics. The other is an extra relaxation mechanism owing to interaction with vortices of broken symmetry. We construct a three-dimensional model of magnon Q-balls. The spatial variation of the order parameter in equilibrium is solved in a quasi-three-dimensional model by minimizing the total free energy. Eigenstates of the resulting potential found by solution of the Schr odinger equation in three dimensions. We discuss the formation and properties of Q-balls of magnons, which are "true" Q-balls in the sense that the trapping potential is forced to follow the movement of the magnon condensate. In high energy physics Q-balls are non-topological solitons that are stable owing to the charge conservation. In the case of magnon BECs the approximately conserved magnon number represents the Q-ball charge. We calculate the NMR signal using a realistic model of the measurement circuit, and show that in the case of the magnon Q-ball the signal is not generally proportional to the transverse magnetization when the condensate moves in space. The calibration of experimental signal amplitude is further used in the description of rocking oscillations of the broken-symmetry vortex cores and related dissipation of the magnon condensate. These oscillations are driven by the precessing magnetization of the magnon condensate.

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Martin Kupka, Peter Skyba

States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid ${}^{3}$He-$B$ represent the macroscopic examples of the Bose-Einstein condensates of magnons. Once the magnons form one of these states, this many-magnon coherent quantum state is described by a ``single-magnon wave function'' (or an order parameter). A suitable external perturbation may cause the condensate to oscillate around the state of coherent precession, which demonstrates a collective rigidity of the condensate against scattering a single magnon out of it. The states corresponding to a free coherent precession of magnetization are degenerate in the phase of precession, so there exist oscillations around such states with a gapless dispersion relation, known as the Goldstone modes. Here, we present both experimental and theoretical results of the study of the spin density oscillations superposed on a homogeneously precessing domain in superfluid ${}^{3}$He-$B$ in the presence of a high-frequency excitation field ${B}_{\text{rf}}$. We show that the presence of this field lifts the degeneracy of the precessing state with respect to the phase of precession, that is, it violates the symmetry of the magnon condensate, and former Goldstone modes become non-Goldstone ones, as they acquire the energy gap in their spectrum.

Physical Review B•May 31, 2012•14 citations
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.
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.
In this thesis we study Bose-Einstein condensates of trapped magnon quasiparticles in superfluid 3He-B. These condensates form in the trap provided by the order-parameter texture and applied magnetic field profile. We provide numerical description of two properties of the condensates, both observed in experiments: One of these properties is the ability to interact with the trapping potential, which draws an analogy to Q-balls of high energy physics. The other is an extra relaxation mechanism owing to interaction with vortices of broken symmetry. We construct a three-dimensional model of magnon Q-balls. The spatial variation of the order parameter in equilibrium is solved in a quasi-three-dimensional model by minimizing the total free energy. Eigenstates of the resulting potential found by solution of the Schr odinger equation in three dimensions. We discuss the formation and properties of Q-balls of magnons, which are "true" Q-balls in the sense that the trapping potential is forced to follow the movement of the magnon condensate. In high energy physics Q-balls are non-topological solitons that are stable owing to the charge conservation. In the case of magnon BECs the approximately conserved magnon number represents the Q-ball charge. We calculate the NMR signal using a realistic model of the measurement circuit, and show that in the case of the magnon Q-ball the signal is not generally proportional to the transverse magnetization when the condensate moves in space. The calibration of experimental signal amplitude is further used in the description of rocking oscillations of the broken-symmetry vortex cores and related dissipation of the magnon condensate. These oscillations are driven by the precessing magnetization of the magnon condensate.
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.
Under suitable experimental conditions, collective spin-wave excitations, magnons, form a Bose–Einstein condensate (BEC), where the spins precess with a globally coherent phase. Bose–Einstein condensation of magnons has been reported in a few systems, including superfluid phases of 3He, solid state systems, such as yttrium-iron-garnet films, and cold atomic gases. The superfluid phases of 3He provide a nearly ideal test bench for coherent magnon physics owing to experimentally proven spin superfluidity, the long lifetime of the magnon condensate, and the versatility of the accessible phenomena. We first briefly recap the properties of the different magnon BEC systems, with focus on superfluid 3He. The main body of this review summarizes recent advances in the application of magnon BEC as a laboratory to study basic physical phenomena connecting to diverse areas from particle physics and cosmology to vortex dynamics and new phases of condensed matter. This line of research complements the ongoing efforts to utilize magnon BECs as probes and components for potentially room-temperature quantum devices. In conclusion, we provide a roadmap for future directions in the field of applications of magnon BEC to fundamental research.
Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of the collective quantum state, in which the macroscopic number of particles occupies the lowest energy state and thus is governed by a single wave function. Here we highlight the BEC in a magnetic subsystem -- the BEC of magnons, elementary magnetic excitations. 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 the inhomogeneous magnetic field. We consider this phenomenon on example of spin precession in superfluid phases of 3^33He. The magnon BEC in these phases has all the properties of spin superfluidity. The states of the phase-coherent precession belong to the class of the coherent quantum states, which manifest themselves by superfluidity, superconductivity, quantum Hall effect, Josephson effect and many other macroscopic quantum phenomena.
States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid 3{}^{3}3He-BBB represent the macroscopic examples of the Bose-Einstein condensates of magnons. Once the magnons form one of these states, this many-magnon coherent quantum state is described by a ``single-magnon wave function'' (or an order parameter). A suitable external perturbation may cause the condensate to oscillate around the state of coherent precession, which demonstrates a collective rigidity of the condensate against scattering a single magnon out of it. The states corresponding to a free coherent precession of magnetization are degenerate in the phase of precession, so there exist oscillations around such states with a gapless dispersion relation, known as the Goldstone modes. Here, we present both experimental and theoretical results of the study of the spin density oscillations superposed on a homogeneously precessing domain in superfluid 3{}^{3}3He-BBB in the presence of a high-frequency excitation field Brf{B}_{\text{rf}}Brf​. We show that the presence of this field lifts the degeneracy of the precessing state with respect to the phase of precession, that is, it violates the symmetry of the magnon condensate, and former Goldstone modes become non-Goldstone ones, as they acquire the energy gap in their spectrum.