Nonlocal Nonlinear Optics in Cold Rydberg Gases

Abstract

We present an analytical theory for the nonlinear optical response of a strongly interacting Rydberg gas under conditions of electromagnetically induced transparency. Simple formulae for the third order optical susceptibility are derived and shown to be in excellent agreement with recent experiments. The obtained expressions reveal strong nonlinearities, which in addition are of highly nonlocal character. This property together with enormous strength of the Rydberg-induced nonlinearities is shown to yield a unique laboratory platform for nonlinear wave phenomena, such as collapse-arrested modulational instabilities in a self-defocussing medium.PACS numbers: 32.80. Ee, 42.50.Gy, Advances in designing materials with highly intensitydependent refraction [1][2][3] have ushered in numerous studies of nonlocal nonlinear wave phenomena [4][5][6][7][8]. Many of these settings, such as, nematic liquid crystals [1,2] or thermal media [3], require high power laser light. On the other hand, electromagnetically induced transparency (EIT) in ultracold multi-level atoms [9,10] provides an elegant mechanism to suppress photon loss and simultaneously increase light-matter interaction times to enhance nonlinear effects. Combined with sufficiently large nonlinearities, this holds great potential for fewphoton nonlinear optics [11,12] and may enable applications in communication and quantum information science.Recently, it was recognized that EIT-schemes involving highly excited atomic Rydberg levels provide promising perspectives for such applications [13][14][15][16][17][18][19][20][21][22]. In particular, the huge polarizability of Rydberg states gives rise to giant Kerr coefficients [15], but also entails strong longrange interactions, which render Rydberg-EIT media intrinsically nonlinear. Indeed, a recent theory for twophoton pulses revealed the emergence of strong effective photon-photon interactions [23], while experiments [21] and numerical calculations [24] demonstrated greatly enhanced nonlinear absorption coefficients in the opposite limit of large photon numbers.In this letter, we develop an analytical theory for the nonlinear optical response of a strongly interacting Rydberg-EIT medium to monochromatic multi-photon light sources. Based on the approach, we give a simple formula for the nonlinear absorption coefficient that provides an excellent description of recent measurements on cold Rubidium gases [21]. For large single-photon detunings, absorption is shown to be greatly suppressed -yet maintaining huge refractive nonlinearities, that exceed previous records in ultracold Kerr media [10] by several orders of magnitude. Combined with their long range this makes for an ideal nonlinear medium to study nonlocal wave phenomena, in which the strength, the range and even the sign of the nonlocal interaction kernel can be widely tuned with high accuracy. To demonstrate this¯¯¯¯8 FIG. 1: a) Three-level scheme for isolated atoms, where the atomic ground state |1 , an intermediate state |2 and a highly excited Rydberg state ...

Attractive photons in a quantum nonlinear medium

“…The repulsive Van-der-Waals interaction be- tween two Rydberg atoms V (r) = C 6 /r 6 tunes the doubly excited Rydberg state far off EIT resonance for distances |r| < r B , where r B = 6 C 6 /γ is the Rydberg blockade radius 14,29,30 , C 6 the van der Waals coefficient, γ = Ω 2 c /|4∆| is the EIT linewidth at detuning |∆| Γ, and Ω c the Rabi frequency of the control field. While for photons with large separation in the medium |r| > r B , the phase shift that would originate from the bare |g → |e probe transition is suppressed by EIT, for small photon separations |r| ≤ r B , the light acquires this phase shift (see Fig.…”

Quantum nonlinear optics — photon by photon

“…In the simplest case of resonant Rydberg EIT (both lasers resonant with their respective transitions, Fig. 4), the strong interaction between two Rydberg atoms tunes the two-photon transition out of resonance, thereby destroying the transparency and leading to absorption 22,58,59,[62][63][64] for two or more photons. The quantum nonlinearity in this case arises from the Rydberg excitation blockade 61 , which precludes the simultaneous excitation of two Rydberg atoms that are separated by less than the blockade radius r b (Fig.…”

Quantum nonlinear optics with single photons enabled by strongly interacting atoms

“…The interactions between cold Rydberg atoms have been explored in ensembles [6][7][8][9][10] and have been used to realize quantum logic gates between two Rydberg atoms 11,12,24 . Giant optical nonlinearities using Rydberg EIT 14,22,23 have been observed in a classical, multi-photon regime 13 . Very recently, the Rydberg blockade in a dense, mesoscopic atomic ensemble has been used to implement a deterministic single-photon source 30 .…”