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

Abstract

We study the photon generation from arbitrary initial state in cavity QED due to the combined action of the anti-rotating term present in the Rabi Hamiltonian and Lindblad-type dephasing. We obtain a simple set of differential equations describing this process and deduce useful formulae for the moments of the photon number operator, demonstrating analytically that the average photon number increases linearly with time in the asymptotic limit. PACS numbers: 42.50.Pq, 42.50.Ct, 42.50.Hz In the 2008-th paper by Werlang et al.[1] a puzzling quantum effect was noticed from numerical simulations: when a two-level atom interacts with a single mode of the radiation field in a cavity by means of the Rabi Hamiltonian, while subject to standard Markovian dephasing mechanism, the average intracavity photon number exhibits a linear growth with time. Such asymptotic photon generation due to decoherence occurs because for pure dephasing processes the environment may be viewed as a unmonitored detector making random nondemolition measurements of the number of quanta in the atom-field system [2,3], whilst in [4][5][6] it was shown that nondemolition measurements can pump energy into the system via the destruction of quantum coherence provided the anti-rotating term is kept in the light-matter interaction Hamiltonian (i.e., without performing the Rotating Wave Approximation [7]). Besides, the pure dephasing reservoirs always possess a finite temperature (see, e.g. [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]...

Effective Landau-Zener transitions in the circuit dynamical Casimir effect with time-varying modulation frequency

“…Moreover, we do not restrict our analysis to a specific model for the reservoirs' spectral densities and make the simplest assumption that the dissipation rates are zero for < 0 and take on constant values κ, γ and γ φ for ≥ 0. Since our primary goal is to study the photon generation from vacuum, such assumption is the most conservative with regards to the spurious generation of excitations due to dephasing [54,57,58]. Besides, eventual random fluctuations in the modulation frequency may be treated as additional dephasing noise [54,57], so the simultaneous inclusion of κ, γ and γ φ covers the most common experimental situations.…”

О Связи Неэрмитова Гамильтониана Со Стохастическим Дифференциальным Уравнением В Теории Открытых Систем

“…Исследования многих задач теории открытых систем и квантовой термодинамики сейчас начинаются с формулировки в качестве исходного уравнения кинетического уравнения в форме Линдблада [34][35][36]. Как и в представленном анализе, так и в случае общих уравнений Линдблада мы неявно имеем реальный " распадный" физический процесс (поле), приводящий к появлению неэрмитовой части гамильтониана и/или определяющий линдбладовские операторы релаксации.…”

“…В ряде задач ионизации в классическом поле [13] интерференционными слагаемыми можно пренебречь в силу их малого вклада в вероятности переходов в сильных полях. В других задачах [34,35] c феноменологическим учетом процессов релаксации фазы осцилляторов учет [38] интерференционных слагаемых позволяет избежать парадоксальных результатов [34,35], противоречащих началам термодинамики. А в случае описания процесса затухания моды высокодобротного резонатора учет интерференции поля резонатора и вакуумного поля, определяющего сбой атомной фазы, определяет механизм запирания моды резонатора [39].…”