We have assumed that atoms are placed in given positions of the standing wave of cavity. Based on modern optical achievements it is possible to localize a small number of emitters (atoms, ions, molecules and even nuclei) in various geometrical systems like optical cavities, quantum dots, optical lattices and dielectric or disordered media. It is supposed that at initial moment t = 0 pair of atoms is prepared in superposition of ground state |g⟩, first excited |e1⟩, second |e2⟩ and third excited |e3⟩ states and quantized cavity field in coherent state |ξ⟩. By using exact analytical solution for statevector of the coupled atom-field system found with the help of Schrodinger equation quantum-statistical properties of the quantized cavity field are examined as a function of the |ξ| parameter. Exact analytical solutions for the atomic population inversion ⟨Sz⟩, mean photon number ⟨n⟩ and their fluctuations σ are obtained by using this solution. In this situation quantum statistics of cavity field has the tendency towards oscillations, but exact periodicity of these oscillations is violated by the analogy with the micromaser model [2] and two-photon JCM of a threelevel atom [3].We have assumed that atoms are placed in given positions of the standing wave of cavity. Based on modern optical achievements it is possible to localize a small number of emitters (atoms, ions, molecules and even nuclei) in various geometrical systems like optical cavities, quantum dots, optical lattices and dielectric or disordered media. It is supposed that at initial moment t = 0 pair of atoms is prepared in superposition of ground state |g⟩, first excited |e1⟩, second |e2⟩ and third excited |e3⟩ states and quantized cavity field in coherent state |ξ⟩. By using exact analytical solution for statevector of the coupled atom-field system found with the help of Schrodinger equation quantum-statistical properties of the quantized cavity field are examined as a function of the |ξ| parameter. Exact analytical solutions for the atomic population inversion ⟨Sz⟩, mean photon number ⟨n⟩ and their fluctuations σ are obtained by using this solution. In this situation quantum statistics of cavity field has the tendency towards oscillations, but exact periodicity of these oscillations is violated by the analogy with the micromaser model [2] and two-photon JCM of a threelevel atom [3].

Jan 1, 20150 citations

Interaction of an atom with a quantized field

Dipankar Bhattacharyya, Jyotirmoy Guha

Institute of Physics eBooksJan 1, 20220 citations

Third quantization of the electromagnetic field

J. D. Franson

We consider an approach in which the usual wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in the quadrature representation of mode $j$ of the electromagnetic field is further quantized to produce a field operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j}).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schr\"odinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.We consider an approach in which the usual wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in the quadrature representation of mode $j$ of the electromagnetic field is further quantized to produce a field operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j}).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schr\"odinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.

arXiv:2103.00596Physical Review ADec 1, 20213 citations

We consider an approach in which the usual wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in the quadrature representation of mode

j

of the electromagnetic field is further quantized to produce a field operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j}).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schr\"odinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.