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arXiv:1102.0669 · Journal of Physics B Atomic Molecular and Optical Physics

Optical non-linearity in a dynamical Rydberg gas

Jonathan D. Pritchard, A. Gauguet, Kevin J. Weatherill, Charles S. Adams

Published Sep 14, 2011• 26 citations
arXivHTMLPDF

Abstract

We use the technique of electro-magnetically induced transparency (EIT) to probe the effect of attractive dipole-dipole interactions in a highly excited Rydberg gas. The transient character of the EIT response is investigated by rapidly scanning the probe laser through resonance. We characterize the resulting cooperative optical non-linearity as a function of probe strength, density and scan direction. For the 58D$_{5/2}$ Rydberg state, an atom density of $1.6\times10^{10} $cm$^{-3}$ and a positive frequency scan we measure a third-order non-linearity of $χ^{(3)}=5\times 10^{-7}$ m$^2$V$^{-2}$. For the reverse scan we observe a second order non-linearity of $χ^{(2)}=5\times 10^{-6}$ mV$^{-1}$. The contrasting behaviour can be explained in terms of motional effects and resonant excitation of Rydberg pairs.

DOI
10.1088/0953-4075/44/18/184019

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We use the technique of electro-magnetically induced transparency (EIT) to probe the effect of attractive dipole-dipole interactions in a highly excited Rydberg gas. The transient character of the EIT response is investigated by rapidly scanning the probe laser through resonance. We characterize the resulting cooperative optical non-linearity as a function of probe strength, density and scan direction. For the 58D5/2_{5/2}5/2​ Rydberg state, an atom density of 1.6×10101.6\times10^{10} 1.6×1010cm−3^{-3}−3 and a positive frequency scan we measure a third-order non-linearity of χ(3)=5×10−7χ^{(3)}=5\times 10^{-7}χ(3)=5×10−7 m2^22V−2^{-2}−2. For the reverse scan we observe a second order non-linearity of χ(2)=5×10−6χ^{(2)}=5\times 10^{-6}χ(2)=5×10−6 mV−1^{-1}−1. The contrasting behaviour can be explained in terms of motional effects and resonant excitation of Rydberg pairs.
We use the technique of electro-magnetically induced transparency (EIT) to probe the effect of attractive dipole-dipole interactions in a hi ghly excited Rydberg gas. The transient character of the EIT response is investigated by rapidly scanning the probe laser through resonance. We characterize the resulting cooperative optical non-linearity as a function of probe strength, density and scan direction. For the 58D5/2 Rydberg state, an atom density of 1.6 � 10 10 cm 3 and a positive frequency scan we measure a third-order non-linearity of � (3) = 5 � 10 7 m 2 V 2 . For the reverse scan we observe a second order non-linearity of � (2) = 5 � 10 6 mV 1 . The contrasting behaviour can be explained in terms of motional effects and resonant excitation of Rydberg pairs.
By coupling a probe transition to a Rydberg state using electromagnetically induced transparency (EIT) we map the strong dipole-dipole interactions onto an optical field. We characterize the resulting cooperative optical nonlinearity as a function of probe strength and density. We demonstrate good quantitative agreement between the experiment and an N-atom cooperative model for N=3 atoms per blockade sphere and the n=60 Rydberg state. The measured linewidth of the EIT resonance places an upper limit on the dephasing rate of the blockade spheres of <110 kHz.
We investigate the linear and nonlinear optical response to an optical pumping of a four-level atomic system with electromagnetically induced transparency (EIT) in a cold Rydberg atomic gas. It is found that the transient behavior (especially, the third- and fifth-order susceptibilities) of the probe field, and the steady-state EIT spectrum of the gas, depend crucially on the Rydberg atoms' interaction. Furthermore, we find that the response speed of the Rydberg interaction with EIT can be as much as six times faster than the EIT without the Rydberg interaction, and that the nonlinear response time of the fifth-order optical susceptibility is longer than that of the third-order susceptibility. It is established that the Rydberg blockade effect plays a significant role in increasing the response speed of the Rydberg with EIT.
Transmission properties of a weak probe field traveling through a sample of interacting cold 87Rb atoms driven into the three-level ladder configuration, which is a typical Rydberg electromagnetically induced transparency (EIT) system, are investigated. Rydberg atoms are considered to be a perfect platform in the research fields of quantum optics and quantum information processing due to some exaggerated properties of Rydberg atoms with high principal quantum number, especially, the dipole-dipole interaction between Rydberg atoms leads to the so-called dipole blockade effect accommodating at most one Rydberg excitation within a mesoscopic volume. The dipole blockade effect may be mapped onto the spectrum of EIT, and the EIT exhibits the cooperative optical nonlinearity which is usually characterized by two indicators, i.e., the probe intensity and the photonic correlation. The cooperative optical nonlinearity is also found here in the phase of transmission spectrum, and the phase can be regarded as the third indicator of nonlinearity in Rydberg EIT. However, there are tremendous differences between the phase and probe transmission (photonic correlation) though they both originate from the conditional polarization. Specifically, the phase is not sensitive to neither the incident probe intensity nor the initial photonic correlation at the resonant probe frequency under the condition of the Autler-Townes (AT) splitting where two other indicators exhibit significant cooperative nonlinearity. The nonlinearity in phase spectrum occurs only in the regime between the resonant probe frequency and the AT splitting and especially is remarkable at the frequency where the probe field is classical. Finally, influence of the principal quantum number and the atomic density on the transmitted phase are examined. In the nonlinear regime, the absolute value of the phase becomes smaller and smaller as the principal quantum number and the atomic density are raised. This indicates that the nonlinearity is strengthened by increasing them. The probe phase provides an attractive supplement to study in depth the cooperative optical nonlinearity in Rydberg EIT and offers us the considerable flexibility to manipulate the propagation and evolution of a quantum light field.
Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.
We predict a resonant enhancement of the nonlinear optical response of an interacting Rydberg gas under conditions of electromagnetically induced transparency. The enhancement originates from a two-photon process which resonantly couples electronic states of a pair of atoms dressed by a strong control field. We calculate the optical response for the three-level system by explicitly including the dynamics of the intermediate state. We find an analytical expression for the third-order susceptibility for a weak classical probe field. The nonlinear absorption displays the strongest resonant behavior on two-photon resonance where the detuning of the probe field equals the Rabi frequency of the control field. The nonlinear dispersion of the medium exhibits various spatial shapes depending on the interaction strength. Based on the developed model, we propose a realistic experimental scenario to observe the resonance by performing transmission measurements.