The effects of counter-rotating terms on ground states (GS) of a lambda-type three-level atomic system coupled with two fields are examined. The GS, which are dark states in rotating wave approximation (RWA), can be expressed by a simple formula including the excited states. When the coupling strength is less than 0.2 of the maximum energy splitting in the atomic system, the component coefficients of excited states in the GS can be described by the formula similar as that in a two-level system and have linear relationship with their coupling constant. Further increasing the coupling strength will increase the excited components in the GS more rapidly, very different from the two-level system. OCIS codes: 270.1670. doi: 10.3788/COL201210.S12701.
The effects of counter-rotating terms on ground states (GS) of a lambda-type three-level atomic system coupled with two fields are examined. The GS, which are dark states in rotating wave approximation (RWA), can be expressed by a simple formula including the excited states. When the coupling strength is less than 0.2 of the maximum energy splitting in the atomic system, the component coefficients of excited states in the GS can be described by the formula similar as that in a two-level system and have linear relationship with their coupling constant. Further increasing the coupling strength will increase the excited components in the GS more rapidly, very different from the two-level system. OCIS codes: 270.1670. doi: 10.3788/COL201210.S12701.
Recalling that the rotating wave approximation (RWA) is only valid in the weak coupling regimes, the purpose of this paper is to study the Hamiltonian dynamics describing the full quantum mechanical approach of the interaction between various configurations of three-level atoms Lambda, V and ladder distinctly with a two-mode radiation field, while the RWA is not considered; the counter-rotating terms (CRTs) are taken into account. Generally, the presence of CRTs in the Hamiltonian prevents one to achieve an analytical solution. Moreover, as we will show in the present work, using the perturbation theory, analytical solvable Hamiltonians can be successfully obtained. According to our calculations, the contribution of CRTs within the ordinary Hamiltonian is equivalent to the replacement of the constant detuning with a specific intensity dependent detuning in the first order, and the constant atom field coupling with a particular intensity dependent (f deformed) coupling in the second order of the associated perturbation parameter. Moreover, noticing that according to the initial expression of the Hamiltonian, each mode of the field interacts only with a specific pair of the allowed transitions of each type of the three-level atom, it is surprisingly observed that via applying the mentioned approach, the obtained intensity dependent coupling functions depend on both modes of the field, f(na,nb). In this way, it is seen that the CRTs are removed with the price of arriving at some intermixed intensity dependent atom field coupling functions of the two modes of the field. In this way, the obtained final Hamiltonians are analytically solvable. At last, by determining the time evolution of the atom field wave function, we study the effects of CRTs on a few nonclassical properties of the state of the system, including the atomic population inversion and photon statistics.
A four-level double-Λ atomic scheme, i.e. two Λ systems sharing the same two ground levels, that interacts with four laser light fields is studied theoretically. The peculiarity is that each of the two ground states can be coupled to each excited state by two laser light fields. A certain energy difference exists between excited-state levels. We consider this energy small enough so that a laser resonant to either transition can also couple the other transition. We test whether coupling of the more detuned laser is not non-negligible. Multiply connected states were also recently analyzed (and a comparison with experiment was presented), but for the simpler, two- and three-level atomic schemes (Stacey et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 085502). Theoretical treatment of the double-Λ atomic scheme is commonly done by solving optical Bloch equations (OBEs). When the rotating-wave approximation (RWA) is applied, OBEs become, by their form, a set of linear differential equations with constant coefficients. Theoretical treatment of the interaction scheme treated here leads to OBEs with coefficients that are not constant, but oscillate with time, even after RWA is applied. Under certain assumptions, the approximation can be used where the time-dependent coefficients are averaged over their periods. The method yields a new system of equations (similar to standard OBEs), but with more independent variables, and can also be solved in the usual way. The results presented here analyze the validity of this approximation by comparing the results for the double-Λ atomic scheme with single- and two-fold coupled transitions. We test whether in the limit of large-energy splitting between excited-state levels both approaches lead to similar results.
The eigenenergy spectrum of the Jaynes–Cummings (JC) model with and without the rotating-wave approximation (RWA) is investigated. The numerical analysis indicates that the non-RWA spectrum can only be approximated by the RWA in the range of sufficiently small coupling constant and detuning. In other region, the counter-rotating terms remarkably change the nature of the RWA energy spectrum. A simple expression with high accuracy for ground eigenenergy and eigenvector for non-RWA is available. The ground eigenvector for non-RWA shows that the ground state is not a dark state and very different from that of RWA which is a dark state.
In this article, by using the perturbation theory, we analytically solve the eigenvalue problem for the Hamiltonian describing the interaction of a Λ -type three-level atom with a single-mode radiation field without the rotating wave approximation (RWA). For this purpose, the atom–field interaction Hamiltonian, which contains the counter-rotating terms (CRTs), is transformed to an analytically solvable Hamiltonian by applying three successive unitary transformations. According to our calculations, the contribution of CRTs within the transformed Hamiltonian is in fact replaced by transforming the 'constant detuning' with the 'intensity-dependent detuning' in the first order, and the 'constant atom–field coupling' with the intensity-dependent coupling in the second order of the perturbation parameters. Then, by solving the eigenvalue problem for the transformed Hamiltonian, the eigenvector of the considered atom–field Hamiltonian is obtained analytically. Finally, after achieving the state vector of the atom–field system at an arbitrary time, a few nonclassical properties of the system state are investigated numerically. Meanwhile, we compare our results with the presence of RWA, from which the role of CRTs will be established.
We study the effects of the non-rotating wave approximation (non-RWA) on the spontaneous emission of a Λ-type three-level atom, where the metastable states are coupled to a common excited state by a weak laser field and the lower-level doublet is driven by a strong microwave field. When the non-RWA is applied to the interaction of the atom with the microwave field, the spontaneous emission spectrum is comprised of a series of ultrasharp lines. The physical interpretation of the spectral characteristics is given in light of the dressed states.
Abstract We report the remarkable phenomena caused by high-order interaction of counter-rotating-wave terms in a three-level Λ-type system coupled with two laser fields. With the low-order interaction of the rotating-wave terms, transparency induced by Autler−Townes splitting is obtained. When the high-order interaction of the counter-rotating-wave terms is considered, some sideband peaks show up and the probe field is amplified without population inversion. The stronger the coupling, the larger the amplification. The gain of probe photons comes mainly from the loss of the control field through a one-photon or two-photon process.