A great effort has been devoted to formulate a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in order to connect classical and quantum theories rests in finding a parameter which plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneer works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi [Phys. Rev. Lett. 52, 2009 (1984)]. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail. 1A great effort has been devoted to formulate a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in order to connect classical and quantum theories rests in finding a parameter which plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneer works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi [Phys. Rev. Lett. 52, 2009 (1984)]. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail. 1

Jan 1, 19987 citations

Experiments on Spin Precession

D. Dubbers, H.‐J. Stöckmann

Graduate texts in physicsJan 1, 20130 citations

Spin Precession — A Dynamical Discussion

Julian Schwinger

World Scientific series in 20th century physicsMay 1, 20001 citation

Optically driven spin-alignment precession

Anatoly A. Fomin, M. Yu. Petrov, Anatoly S. Pazgalev +2 more

The effect of optically driven spin precession discovered by Bell and Bloom [W. E. Bell and A. L. Bloom, Phys. Rev. Lett. 6, 280 (1961)] is widely used nowadays as a basis for numerous experiments in fundamental physics and for diverse applications. In this paper we consider a much less popular version of the light-induced spin precession that does not imply coherent precession of the spin-system magnetization and is excited by linearly (rather than circularly) polarized light. Pump-probe measurements performed on the ${D}_{2}$ line of cesium vapor show that the magnitude of the signal of the optically driven spin-alignment precession, in ``vacuum'' cells (with no buffer gas) is close to that of classical spin-orientation precession. In the presence of buffer gas, however, the signal of spin-alignment precession appears to be strongly suppressed. The discovered effect is ascribed to spin mixing of excited states of cesium atoms in the cycle of optical pumping.The effect of optically driven spin precession discovered by Bell and Bloom [W. E. Bell and A. L. Bloom, Phys. Rev. Lett. 6, 280 (1961)] is widely used nowadays as a basis for numerous experiments in fundamental physics and for diverse applications. In this paper we consider a much less popular version of the light-induced spin precession that does not imply coherent precession of the spin-system magnetization and is excited by linearly (rather than circularly) polarized light. Pump-probe measurements performed on the ${D}_{2}$ line of cesium vapor show that the magnitude of the signal of the optically driven spin-alignment precession, in ``vacuum'' cells (with no buffer gas) is close to that of classical spin-orientation precession. In the presence of buffer gas, however, the signal of spin-alignment precession appears to be strongly suppressed. The discovered effect is ascribed to spin mixing of excited states of cesium atoms in the cycle of optical pumping.

arXiv:2309.11123Physical Review AOct 16, 20234 citations

Magnon Bose–Einstein condensation and spin superfluidity

Yu. M. Bunkov, Григорий Ефимович Воловик

Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of a collective quantum state in which a macroscopic number of particles occupy the lowest energy state and thus is governed by a single wavefunction. Here we highlight the BEC in a magnetic subsystem--the BEC of magnons, elementary magnetic excitations. The 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 an inhomogeneous magnetic field. The coherent spin precession was observed first in superfluid (3)He-B and this domain was called the homogeneously precessing domain (HPD). The main feature of the HPD is the induction decay signal, which ranges over many orders of magnitude longer than is prescribed by the inhomogeneity of magnetic field. This means that spins precess not with a local Larmor frequency, but coherently with a common frequency and phase. This BEC can also be created and stabilized by continuous NMR pumping. In this case the NMR frequency plays the role of a magnon chemical potential, which determines the density of the magnon condensate. The interference between two condensates has also been demonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. The main property is the existence of a spin supercurrent. This spin supercurrent flows separately from the mass current. Transfer of magnetization by the spin supercurrent by a distance of more than 1 cm has been observed. Also related phenomena have been observed: the spin current Josephson effect; the phase-slip processes at the critical current; and the spin current vortex--a topological defect which is the analog of a quantized vortex in superfluids and of an Abrikosov vortex in superconductors; and so on. It is important to mention that the spin supercurrent is a magnetic phenomenon, which is not directly related to the mass superfluidity of (3)He: it is the consequence of a specific antiferromagnetic ordering in superfluid (3)He. Several different states of coherent precession have been observed in (3)He-B: the homogeneously precessing domain (HPD); a persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. In compressed aerogel the coherent precession has been also found in (3)He-A. We demonstrate that the coherent precession of magnetization is a true BEC of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by spin-orbit coupling which is different for different states of the magnon BEC.Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of a collective quantum state in which a macroscopic number of particles occupy the lowest energy state and thus is governed by a single wavefunction. Here we highlight the BEC in a magnetic subsystem--the BEC of magnons, elementary magnetic excitations. The 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 an inhomogeneous magnetic field. The coherent spin precession was observed first in superfluid (3)He-B and this domain was called the homogeneously precessing domain (HPD). The main feature of the HPD is the induction decay signal, which ranges over many orders of magnitude longer than is prescribed by the inhomogeneity of magnetic field. This means that spins precess not with a local Larmor frequency, but coherently with a common frequency and phase. This BEC can also be created and stabilized by continuous NMR pumping. In this case the NMR frequency plays the role of a magnon chemical potential, which determines the density of the magnon condensate. The interference between two condensates has also been demonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. The main property is the existence of a spin supercurrent. This spin supercurrent flows separately from the mass current. Transfer of magnetization by the spin supercurrent by a distance of more than 1 cm has been observed. Also related phenomena have been observed: the spin current Josephson effect; the phase-slip processes at the critical current; and the spin current vortex--a topological defect which is the analog of a quantized vortex in superfluids and of an Abrikosov vortex in superconductors; and so on. It is important to mention that the spin supercurrent is a magnetic phenomenon, which is not directly related to the mass superfluidity of (3)He: it is the consequence of a specific antiferromagnetic ordering in superfluid (3)He. Several different states of coherent precession have been observed in (3)He-B: the homogeneously precessing domain (HPD); a persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. In compressed aerogel the coherent precession has been also found in (3)He-A. We demonstrate that the coherent precession of magnetization is a true BEC of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by spin-orbit coupling which is different for different states of the magnon BEC.

Journal of Physics Condensed MatterMar 30, 201065 citations

The Generalized Spin Precession Equation

D. Dubbers, H.‐J. Stöckmann

Graduate texts in physicsJan 1, 20130 citations

{D}_{2}

line of cesium vapor show that the magnitude of the signal of the optically driven spin-alignment precession, in ``vacuum'' cells (with no buffer gas) is close to that of classical spin-orientation precession. In the presence of buffer gas, however, the signal of spin-alignment precession appears to be strongly suppressed. The discovered effect is ascribed to spin mixing of excited states of cesium atoms in the cycle of optical pumping.