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arXiv:1204.3423 · Journal of Experimental and Theoretical Physics Letters

Bose analogs of the MIT bag model of hadrons in coherent precession

S. Autti, V. B. Eltsov, Григорий Ефимович Воловик

Published Jul 1, 2012• 9 citations
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Abstract

It has recently been demonstrated that magnon condensation in the trap exhibits the phenomenon of self-localization [1]. When the number of magnons in the textural trap increases, they drastically modify the profile of the gap and highly increase its size. The trap gradually transforms from the initial harmonic one to the box with walls almost impenetrable for magnons. The resulting texture-free “cavity” filled with the magnon condensate wavefunction becomes the bosonic analog of the MIT bag, in which hadron is seen as a cavity surrounded by the QCD vacuum, in which the free quarks are confined in the ground or excited state. Here, we consider the bosonic analog of the MIT bag with quarks on the ground and excited levels.

DOI
10.1134/s0021364012100049

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It has recently been demonstrated that magnon condensation in the trap exhibits the phenomenon of self-localization [1]. When the number of magnons in the textural trap increases, they drastically modify the profile of the gap and highly increase its size. The trap gradually transforms from the initial harmonic one to the box with walls almost impenetrable for magnons. The resulting texture-free “cavity” filled with the magnon condensate wavefunction becomes the bosonic analog of the MIT bag, in which hadron is seen as a cavity surrounded by the QCD vacuum, in which the free quarks are confined in the ground or excited state. Here, we consider the bosonic analog of the MIT bag with quarks on the ground and excited levels.
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.
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.
I review free and trapped Bose‐Einstein condensates (BECs) [1, 2, 3, 4, 5]. In an isotropic harmonic potential V(r) = 12Mω2r2, the single‐particle ground state introduces a new intrinsic scale of length [the ground‐state size d = ℏ/(Mω)] and energy [the ground‐state energy E0 = 32ℏω]. When the trap rotates [6, 7, 8], there is a critical angular velocity for the appearance of one or a few quantized vortices. For more rapid rotation [9, 10, 11, 12, 13] the condensate contains a vortex array. The resulting centrifugal forces expand the condensate radially and shrink it axially; thus the condensate becomes effectively two‐dimensional. If the external rotation speed approaches the frequency of the radial harmonic confining potential, the condensate enters the “lowest‐Landau‐level” regime, and a simple description again becomes possible [14, 15]. Eventually, the system is predicted to make a quantum phase transition to a highly correlated state analogous to the fractional quantum Hall states of electrons in a strong magnetic field [16, 17, 18, 19, 20].
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.
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.
Trapped Bose-Einstein condensates (BECs) differ considerably from the standard textbook example of a uniform Bose gas. In an isotropic harmonic potential V(r) = ½Mω2 r 2, the single-particle ground state introduces a new intrinsic scale of length [the ground-state size d = √ℏ/(Mω)] and energy [the ground-state energy E 0 = 32 \frac{3} {2} 23​ ℏω]. When the trap rotates at a low angular velocity, the behavior of a single vortex illustrates the crucial role of discrete quantized vorticity. For more rapid rotation, the condensate contains a vortex array. The resulting centrifugal forces expand the condensate radially and shrink it axially; thus, the condensate becomes effectively two dimensional. If the external rotation speed approaches the frequency of the radial harmonic confining potential, the condensate enters the “lowest-Landau-level” regime, and a simple description again becomes possible. Eventually, the system is predicted to make a quantum phase transition to a highly correlated state analogous to the fractional quantum Hall states of electrons in a strong magnetic field.