A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field

Abstract

We consider $N_a$ three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the configurations $\Xi$, $\Lambda$ and $V$, with and without detuning. The semi-classical and exact quantum calculations for both the expectation values of the total number of excitations $\mathcal{M}=⟨\mathbf{M}⟩$ and photon number $n=⟨\mathbf{n}⟩$ have an excellent correspondence as functions of the control parameters. We prove that the ground state of the collective regime obeys sub-Poissonian statistics for the $\mathcal{M}$ and $n$ distribution functions. Therefore, their corresponding fluctuations are not well described by the semiclassical approximation. We show that this can be corrected by projecting the variational state to a definite value of $\mathcal{M}$.

28 pages

References in corpus (3)

• Phase transitions and dark-state physics in two-color superradiance
• Coherent State Description of the Ground State in the Tavis-Cummings Model and its Quantum Phase Transitions
• Quantum phase transitions of three-level atoms interacting with a one-mode electromagnetic field

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