The effect of a permanent dipole moment on the polar molecule cavity quantum electrodynamics

Abstract

Abstract. A dressed-state perturbation theory beyond the rotating wave approximation (RWA) is presented to investigate the interaction between a two level electronic transition of the polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground-and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments (PDM) and the counter-rotating wave term (CRT) can be shown separately. The validity of these explicit results is discussed by comparing with the direct numerical simulation. Comparing to CRT coupling, PDM results in the coupling of more dressed states and the energy shift proportional to the square of the normalized permanent dipole difference, and a greater Bloch-Siegert shift could be produced in giant dipole molecule cavity QED. In addition, our method could also be extended to the solution of two-level atom Rabi model Hamiltonian beyond the RWA.

Parity chain and parity chain breaking in the two-level cavity quantum electrodynamics system

“…By comparison, we have found that the perturbation results are in good agreement with the numerical simulation in the steady state [23] . Here, the system is initially prepared in its excited state, and the cavity field is in the vacuum state, i.e., jΨð0Þi ¼ je; 0i.…”

“…Recent progresses draw the extensive attention to the ultrastrong-coupling (USC) regime in the superconducting circuit cavity QED with the normalized coupling strength λ∕ω c reaching 0.1 [18,19] , where the CRT of the interaction is no longer ignored and induces the BlochSiegert (B-S) shift, and the population dynamics no longer show strictly periodic Rabi oscillation, but complicated chaotic behavior instead [20][21][22] . Moreover, in the strongcoupling regime, we have demonstrated that the permanent dipole moment (PDM) term comparable with the CRT cannot be neglected in the molecule-cavity coupling system [23] . In the USC regime, the parity symmetry shows the advantage in the aspect of the generation and reconstruction of arbitrary states [24] .…”

“…As a unique property of the polar molecule, the PDM has been studied and measured experimentally [28] . The effects of both the PDM and CRT on the energy level and stationary state wave function of the system have been studied in our earlier work [23] . In this Letter, based on the dressed-state perturbation theory, we study the effects of the CRT and PDM terms on the transitions between dressed-state energy levels, the parity symmetry, and the dynamical evolution of a twolevel cavity QED system beyond the RWA.…”

“…According to the Schrödinger equation and the dressedstate perturbation theory, where the interaction Hamiltonian of both the PDM and the CRT are viewed as a perturbation term [23] , we have obtained the analytical energy levels E g;0 , E AE n and the wave function jΨ g;0 i, jΨ AE n i of the ground state and excited states in the perturbation case, where jΨ AE n i (E AE n ) is the summation of the zero-order perturbation term jψ AE n i (ε AE n ) and the kth-order perturbation term jψ AEðkÞ n i (ε AEðkÞ n ). By comparison, we have found that the perturbation results are in good agreement with the numerical simulation in the steady state [23] .…”

“…[23]. To simplify the problem concerned, here we consider the wave function up to the first-order perturbation and the energy up to the second-order perturbation.…”