A Summary: Parallels Between Bosonic and Fermionic Quantization

Marion Delehaye, Sébastien Laurent, Igor Ferrier-Barbut +2 more

Summary form only given. Superfluidity is amongst the most impressive macroscopic manifestations of quantum behavior. Frictionless flow has been observed in several low-temperature quantum systems, such as liquid helium [1, 2], or more recently ultracold gases [3-5]. Several hallmarks of superfluidity such as critical velocity, quantized vortices, and second sound have been observed [6-11], in both liquid helium and ultracold gases, and in both Bose and Fermi systems.Here, we use the high level of tunability offered by ultracold gases to control their interactions and obtain a double Bose-Fermi superfluid of fermionic 6Li and bosonic ,Li. We have typically Nf = 3.5 . 105 fermionic atoms and Nb = 4 . 104 bosonic atoms at a temperature of about 100 nK, which is below the critical temperature for superfluidity for both the Bose and the Fermi cloud [13].

Hong-Yi Fan

A Weyl–Wigner quantization scheme for Fermi system which is parallel to the bosonic case is established. We prove a new theorem: Weyl ordering of Fermi operators is invariant under fermionic similar transformations. Comparing with the preceding paper,1 we see the Bose–Fermi supersymmetry in this aspect. As an application of the theorem, we construct a generalized fermionic squeezed state.

H. C. Yen

Avinash Sharma

Essential contents on quantization of fields and second quantization, which are necessary for undergraduate and graduate level, are presented in this chapter. An innovative approach is used for the presentations and the discussions on field quantization and second quantization for systems of Bosons and Fermions. The chapter covers field operators, the procedure of second quantization and its use for the Schrödinger equation for both Bosons and Fermions, matrix representation of Fermionic operators, number operators for both Bosons and Fermions, and systems of weakly interacting Bosons and Fermions. A good number of solved examples and unsolved exercises clarify the basic concepts behind quantization of fields and second quantization.