Optical Manipulation Of Quantum Coherence And Quantum Correlation In Rydberg Atoms

Rydberg atoms with high principal quantum numbers have exaggeratedproperties including long radiative lifetimes and large dipole moment, etc.. Thesefeatures that any other atoms don’t have are the effective resources for a wide rangof quantum information tasks. For example, it was proposed to take advantage ofthese properties to optically manipulate the long-rang dipole-dipole interactionbetween Rydberg atoms and to prepare quantum entanglement. Particularly, thedipole-dipole interaction can result in the so-called dipole blockade effect,prohibiting the excitation of two or more atoms into a highly excited Rydbergstate within a mesoscopic volume. Dipole blockade is the basis of manypromising proposals for coherently preparing quantum entangled state, generatingreliable single photons, and simulating many-body quantum systems. In this thesis,we mainly use the optical means such as electromagnetically inducedtransparency (EIT) and stimulated Raman adiabatic passage (STIRAP) techniquesto manipulate the quantum interference effect and atomic excitation behaviors,and to realize the coherent generation of quantum correlations involvingentanglement between cold atoms and two-photon correlation in the rigid dipoleblockade regime and the antiblockade regime.In the third chapter, we study the steady optical response of a five-levelatomic system in the parametric region where resonant two-photon transitions aremuch stronger than far-detuned single-photon transitions. We find that theconcurrent absorption of two weak probe fields can be well suppressed in anarrow spectral region to attain electromagnetically induced transparency (EIT)via quantum destructive interference between different two-photon transition pathways. To gain a deeper insight into relevant physics, we adiabatically reducethis five-level system with trivial single-photon transitions into a three-levelsystem with vanishing single-photon transitions by deriving an effectiveHamiltonian. The two systems have almost the same two-photon absorptionspectra exhibiting typical EIT features but are a little different in fine details. Thismeans that most characteristics of two-photon quantum destructive interferenceare reserved after the adiabatic elimination approximation. In addition, we verifyby numerical calculations that the two-photon EIT spectra are insensitive to thedipole-dipole interaction of cold Rydberg atoms when the uppermost level has ahigh principle quantum number.In the fourth chapter, we study the transmitted intensity and correlationproperties of a probe field traveling through a sample of interacting cold87Rbatoms driven into the inverted Y configuration. Two windows ofelectromagnetically induced transparency are found in the transmission spectrum,which are either sensitive or immune to the input probe intensity. This means thatone window is accompanied by normal cooperative optical nonlinearity while theother is a result of a linear optical response. Moreover, we find sufficientlysuppressed two-photon correlation within the nonlinear window and greatlyenhanced two-photon correlation between the linear and nonlinear windows. Inthe case of the degenerate window, however, it is viable to conceal the cooperativeoptical nonlinearity behind the linear optical response. This then allows usconsiderable flexibility to manipulate the propagation and evolution of a quantumlight field.In the fifth chapter, we study the transmission properties of a probe fieldpassing through a sample of N-type cold atoms possessing a high Rydberg state.Due to the conditioned dipole blockade of Rydberg excitation, this atomic samplemight exhibit a nonlinear optical response in terms of electromagnetically induced transparency (EIT) as manifested by the sensitivity of the transmitted probeintensity and correlation to input probe intensity and correlation. It is of particularinterest that the nonlinear EIT response can be opposite (both normal andabnormal) in two different regions of probe detuning, which is a striking featureof the four-level N system of interacting atoms. The former (latter) exhibitsnormal (abnormal) cooperative optical nonlinearity, in that the transmitted probeintensity and correlation are reduced (enhanced) as the input probe intensity orcorrelation is increased. The realization of both normal and abnormal nonlinearEIT effects in one atomic sample is expected to have wider applications inmanipulation of photonic statistics of weak light signals, e.g., to attain prominentphotonic bunching and/or antibunching in a dynamic quantum delay or memoryprocess.In the sixth chapter, we study a dilute sample of cold atoms to achieveefficient population transfer from a ground state to a Rydberg state. This sample isapproximately divided into many independent microspheres containing only twoatoms. Each pair of atoms in a microsphere may become quantum correlated viathe dipole-dipole interaction characterized by a van der Waals potential. Ournumerical results show that, by modulating detunings of a pump pulse and aStokes pulse applied in the counterintuitive order, we can drive the dilute sampleeither into the blockade regime or into the antiblockade regime. In the blockaderegime, only one atom is allowed to be coherently transferred into the Rydbergstate in a microsphere, which then results in a maximal entangled state. In theantiblockade regime, however, both atoms in a microsphere can be efficientlyexcited into the Rydberg state, which is not accompanied by quantumentanglement. A second maximal entangled state may also be generated if wework between the rigid blockade regime and the antiblockade regime. Note thatthe existence of a quasidark state is essential for exciting both atoms in a microsphere into the Rydberg state when the van der Waals potential is nonzero.In summary, we first study the steady optical response where the two-photonEIT spectra are insensitive to the dipole-dipole interaction due to a very smallpopulation of the Rydberg atoms in the weak field limit. Then we study the novelcooperative optical nonlinearity (normal and abnormal) mediated by thedipole-dipole interactions in the ultracold Rydberg atoms. In the case of denseratomic sample or stronger probe field, we find that the steady EIT spectra are verysensitive to the probe field. This indicates that the strong dipolar interactions maybe mapped onto the photonic statistic and quantum correlation. At last, we useanother effective technique called STIRAP to study the dynamical Rydbergexcitations and find that we can drive the system into the dipole blockade regimeor the antiblockade regime by simply modulating the parameters of laser. In thebasis of these two kinds of effects, we further generate the different maximalatomic entangled states.