Abstract
We will start our discussion with the most simple system: a single two-level atom interacting with an electromagnetic field.
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- 1.
For convenience, we will use both the decay rate \(\Gamma \) and half-decay rate \(\gamma \) at different points in this Thesis.
- 2.
A density operator can be used to describe a statistical mixed state of quantum states that cannot be described by one single state vector, \(\rho =\sum _i p_i \left| \Psi _i \right\rangle \!\left\langle \Psi _i \right| \).
- 3.
The mass of the positively charged atom core (nucleus plus core electrons) is very much larger than the electron and so is assumed to be unmoved by the electric field.
- 4.
The signs of \(\kappa _{\Lambda }\) and \(\tilde{\kappa }_{\Lambda }\) in Eq. (12.1.28) of [1] differ to those here. However, the quantities of interest are \(|\kappa _{\Lambda }|^2\) and \(|\tilde{\kappa }_{\Lambda }|^2\) and so a sign difference is not important.
- 5.
The choice of ground state energy is arbitrary, since \(E_e\) is defined relative to \(E_g\).
- 6.
The EM field part of the Hamiltonian has no effect on the atomic operator, and vice versa.
- 7.
It is still assumed that we sum over the two polarisations as well.
- 8.
If \(\text {d}y(t)/\text {d}t = x(t)y(t)\) then \(\int _0^t \dot{y}(t_1)\text {d}t_1 = \int _0^t x(t_1) y(t_1) \text {d}t_1 = \int _0^t x(t_1) y(0) \text {d} t_1 + \int _0^t x(t_1) \left( \int _0^{t_1} \dot{y}(t_{2})\text {d} t_2\right) \text {d} t_1\).
- 9.
We do not remove the oscillation of the EM field as this is no longer operator-valued.
- 10.
\(\sin (\omega t) = \cos (\omega t - \pi /2)\).
References
C. Gardiner, P. Zoller, The Quantum World of Ultra-Cold Atoms and Light: Book 1 Foundations of Quantum Optics, 1st edn. (Imperial College Press, London, 2014)
C. Gardiner, P. Zoller, The Quantum World of Ultra-Cold Atoms and Light: Book 2 The Physics of Quantum-Optical Devices, 1st edn. (Imperial College Press, London, 2015)
C. Cohen-Tannoudji, J.D.-R. Gilbert Grynberg, Atom-Photon Interactions (Wiley, New Jersey, 2004)
J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1963)
T. Werlang, A. Dodonov, E. Duzzioni, C. Villas-Bôas, Rabi model beyond the rotating-wave approximation: generation of photons from vacuum through decoherence. Phys. Rev. A 78, 053805 (2008)
R. Friedberg, J.T. Manassah, Effects of including the counterrotating term and virtual photons on the eigenfunctions and eigenvalues of a scalar photon collective emission theory. Phys. Lett. A 372, 2514 (2008)
Y. Li, J. Evers, W. Feng, S.Y. Zhu, Spectrum of collective spontaneous emission beyond the rotating-wave approximation. Phys. Rev. A 87, 053837 (2013)
J. Dalibard, Y. Castin, K. Mølmer, Wave-function approach to dissipative processes in quantum optics. Phys. Rev. Lett. 68, 580 (1992)
D.C. Burnham, R.Y. Chiao, Coherent resonance fluorescence excited by short light pulses. Phys. Rev. 188, 667 (1969)
A.A. Svidzinsky, J.T. Chang, M.O. Scully, Cooperative spontaneous emission of N atoms: many-body eigenstates, the effect of virtual Lamb shift processes, and analogy with radiation of N classical oscillators. Phys. Rev. A 81, 053821 (2010)
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Bettles, R. (2017). Single Two-Level Atom. In: Cooperative Interactions in Lattices of Atomic Dipoles. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-62843-1_2
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