How ‘cold’ can a Markovian dissipative cavity QED system be?

Abstract

We consider the cavity quantum electrodynamics (QED) system described by the Rabi Hamiltonian, composed of a two-level atom and a single cavity field mode, subject to Markovian damping and dephasing mechanisms. It is shown that without the rotating wave approximation the asymptotic mean photon number and the atomic excitation probability are above the thermal values due to the anti-resonant term in the Rabi Hamiltonian, and are always greater than zero. These quantities are evaluated approximately for two different master equations and compared to exact numerical results, showing good agreement. We discuss the origin of this phenomenon and show that it also persists for an empty dissipative cavity if one uses a quite general form of the Markovian master equation.

Dissipation and ultrastrong coupling in circuit QED

“…Additionally, modulations of the qubit transition frequency can be used to generate red and blue sidebands, or as a parametric oscillator inducing squeezing. Finally, while this means that noise in σ z can generate photons [23,57,58], our model reasonably shows that these spurious excitations cannot be generated at zero temperature. In this appendix, we derive in the dressed basis the Lindbladian corresponding to coupling to the X and σ x baths.…”

Detecting ground-state qubit self-excitations in circuit QED: A slow quantum anti-Zeno effect

“…23,24 However, the form of those dissipative terms is questionable in non-RWA setups, and furthermore, there is no justification to equate the sparse measurement setup in this paper to a particular dissipative model. This lack of equivalence between models manifests in the fact that, as we have seen numerically, the sparsely repeated measurements can hit certain resonances that invalidate the anti-Zeno dynamics.…”

“…One popular approach 23,24 is to combine the usual photon leakage mechanism from quantum optics models L(ρ) ∼ 2aρa † − a † aρ − ρa † a with the qubit-cavity Hamiltonian. Note that, in such a combination, the asymptotic states of the dissipation (the vacuum) and of the interaction (populated cavity) are incompatible, and one may find excitations induced by the dissipative terms, an infinite stream of photons leaking out of the cavity and other controversial phenomena.…”

Mean excitation numbers due to the anti-rotating term in cavity QED under Lindbladian dephasing

“…[2, 3] for microscopic deduction) and hence store an infinite amount of energy, so the additional system energy is continuously supplied by the environment and the First Law of Thermodynamics is not violated (for the discussion concerning the Second Law of Thermodynamics in systems subject to frequent quantum measurements see [5]). Although the phenomenon of photon generation due to decoherence was explained qualitatively in [1,8], no satisfactory analysis was carried out to derive analytically whether for the pure Markovian dephasing the average photon number de facto increases linearly with time and whether this growth saturates for large times. So the aim of this paper is to investigate analytically the behavior of Mean Excitation Numbers due to Anti-Rotating Term (MENDART), such as mean photon number and its variance or atomic excitation probability, and investigate their asymptotic characteristics in the simplest case of Markovian dephasing.…”

“…We shall show that for any initial state in the asymptotic limit the mean photon number n indeed increases linearly with time, the average value of the photon number second moment n 2 grows quadratically with time, and the atomic excitation probability P e attains a constant value. So this paper provides the missing mathematical explanation for the phenomenon of steady photon generation due to Lindblad-type decoherence in the presence of the anti-rotating term.Our starting point is the Markovian master equation for the density matrix ρ that takes into account both the atomic and cavity field phase-damping (dephasing) [2,3,8,9] (1) where γ a (γ c ) is the atomic (cavity) dephasing rate and H is the Rabi Hamiltonian [10, 11] (we set = 1)that includes the anti-rotating term (aσ − + a † σ + ). Here a and a † are the cavity annihilation and creation operators, n ≡ a † a is the photon number operator, and ω, Ω and g are the cavity frequency, the atomic transition frequency and the atom-field coupling constant, respectively.…”