Cooperative Optical Non-Linearity in a Blockaded Rydberg Ensemble

Abstract

This thesis describes the observation of a novel optical non-linearity mediated by the dipole-dipole interactions in a cold gas of Rydberg atoms. Electromagnetically induced transparency (EIT) is used to map the strong dipolar interactions onto an optical transition, resulting in a cooperative effect where the optical response of a single atom is modified by the surrounding atoms due to dipole blockade. This optical non-linearity is characterised as a function of probe power and density for both attractive and repulsive interactions, demonstrating a non-linear density dependence associated with cooperativity. For the case of repulsive interactions, excellent agreement is obtained at low densities between experimental data and an interacting three-atom model. The ability to tune the interactions with an external field is also verified.This cooperative effect can be used to manipulate light at the single photon level, which is relevant for applications in quantum information processing. A theoretical model is developed to show that the non-linearity can be used to obtain a highly correlated single-photon output from a coherent laser field interacting with a single blockade region. Progress towards observing this experimentally is described, including details of the construction of a new apparatus capable of confining atoms to within a blockade radius.

Observation of a large, resonant, cross-Kerr nonlinearity in a cold Rydberg gas

“…A distinguishing property of this Kerr nonlinearity is its dependence on r 3 b which, in turn is proportional to C 6 (n * ), making the phase proportional to (n * ) 5.5 when OD, ∆ EIT , Ω c are held constant. This scaling is dramatically different than what would be expected from a nonlinearity due to the AC Stark shift, which has no Rydberg level dependence, or superradiant cascade decay, which scales as (n * ) 2.5 [35]. Additionally, our Kerr-nonlinearity is cooperatively enhanced due to its quadratic dependence on atom density.…”

GKSL generators and digraphs: computing invariant states

“…Since L d | D = 0 it is tempting to write that L d cannot be written in GKSL form (2.1) (see e.g. section 4.1.1 of [20]). Regarding the coefficient matrix Γ of L d as acting of M N (C), however, we have that Γ| D ⊥ = 0 and Γ| D : D → D acts by…”

Stabilizing Rabi oscillation of a charge qubit via the atomic clock technique

“…To probe the offset-charge fluctuation with a high sensitivity and also extend the relaxation time of the Rabi oscillation, we choose  = 10 V 0 cm -1 , which is smaller than the first-avoided-crossing field [45], and T f =0.3 μs. For the typical atomic velocity of 350 m s -1 , we have the atom-field interaction length of 0.1 mm (see figure 3(a)).…”

“…t i is the initial time of the ith atom entering the capacitor C s and T f is the time duration of the atoms staying inside the capacitor region. cm) 2[45] is the static polarizability of ñ |R . To the first-order approximation, f i is expressed as f where we have defined the large phase shift induced by the main constant part N g0 of N g (t) The small phase fluctuation df i is given by…”