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Communications in Theoretical Physics

Physical Effects of U(1)-Induced Gauge Field and Their Non-Adiabatic Corrections for the Cases with Arbitrary Spin

Chang-Pu Sun, Mo‐Lin Ge, Qing Xiao

Published Jan 1, 1990• 4 citations
Publisher

Abstract

By making use of the improved Born-Oppenheimer approximate method, we deal with the separation of spin variable and space variable of neutral particle with arbitrary spin in inhomogeneous magnetic field and non-adiabatic corrections for the problems are thereby computed as perturbations. We also analysis the geometrical properties of loop phase of the induced gauge potential and point out its observable effects relating to Bitter and Dubbers' experiment. Finally, we discuss the transitions between the instantaneous spin states as non-;-adiabatic effects resulting from inhomogeneity of the magnetic field.

DOI
10.1088/0253-6102/13/1/63

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By making use of the improved Born-Oppenheimer approximate method, we deal with the separation of spin variable and space variable of neutral particle with arbitrary spin in inhomogeneous magnetic field and non-adiabatic corrections for the problems are thereby computed as perturbations. We also analysis the geometrical properties of loop phase of the induced gauge potential and point out its observable effects relating to Bitter and Dubbers' experiment. Finally, we discuss the transitions between the instantaneous spin states as non-;-adiabatic effects resulting from inhomogeneity of the magnetic field.
By extending the Born-Oppenheimer approximation improved by Wilczek et al. to deal with separation of the spin and space coordinates of a particle in an external field, we generally discuss the direct effects of an induced gauge field and the higher-order corrections to the problem. It is shown that Bitter and Dubbers's experiment about Berry's phase is directly explained as an effect of the induced gauge potential in terms of the first-order approximation in this paper. The higher-order effects appearing in this experiment are also pointed out when the adiabatic conditions are broken.
The effects of entanglement and spin-spin collisions on the gauge fields in ultracold atoms are presented in this paper. Two gauge fields are calculated and discussed. One of the fields comes from space dependent spin-spin collisions in ultracold atoms, while the other results from the usual Born-Oppenheimer method, which separates the center-of-mass motion from the relative motion in the two-body problem. Adiabatic conditions that lead to the key results of this paper are also presented and discussed. Entanglement shared between the two atoms is shown to affect the atomic motion. In the presence of entanglement, the additional scalar potential disappears; this is different from the case of atoms in separable states.
In non-adiabatic cases the topological action associated with Berry's phase and the corresponding effective Hamiltonian are obtained by path-integral method. We also give the non-adiabatic transition probability amplitude in the first-order approximation. It is thereby shown that the Berry's phase and the induced gauge structure have universality of existence. As an example, dynamics of induced monople relating to the Bitter-Dubber's experiment is analysed in terms of induced gauge field.
The effects of entanglement and spin-spin collision on the gauge field in ultracold atoms are presented in this paper. Two gauge fields are calculated and discussed. One of the fields comes from space dependent spin-spin collisions in ultra-cold atoms, while another results from the usual Born-Oppenheimer method, which separates the center-of-mass motion from the relative motion in the two-body problem. Adiabatic conditions that lead to the key results of this paper are also presented and discussed. Entanglement shared between the two atoms is shown to affect the atomic motion. In the presence of entanglement, the additional scalar potential disappears, this is different from the case of atoms in separable states.
By invoking the use of a space-spin coupling transformation, the exact Schrödinger evolution wavefunction is fortunately obtained for a neutron moving in a helical magnetic field. This result just enjoys the effect of Berry's phase or its induced gauge field in Bitter-Dubbers experiment as its limiting case with strong field. It is also predicted from the exactly-dynamical analysis that a pulse of polarized neutrons with monotonous momentum will be split into two pulses with different momentum shifts accompanying the spin-down and spin-up states respectively.
The effect of the motion of mass center of a two-level atom on its transition in a quantized radiation field is studied in this paper by generalizing the Jaynes–Cummings model to include the coupling depending on space degrees of freedom. As an additional geometrical phase—Berry's phase in the oscillation, the effect of the induced gauge field resulting from the Born–Oppenheimer (BO) approximation explicitly exists in the transition probability between the up and down states of atomic quasispin. It is shown that when the atom's kinetic energy is small enough that the BO adiabatic approximation holds for the case with small atom's momentum or large detuning, the adiabatically approximate solutions are applicable and it is possible to localize an atom in the cavity.