Symmetric photon-photon coupling by atoms with Zeeman-split sublevels

Abstract

We propose a simple scheme for highly efficient nonlinear interaction between two weak optical fields. The scheme is based on the attainment of electromagnetically induced transparency simultaneously for both fields via transitions between magnetically split F = 1 atomic sublevels, in the presence of two driving fields. Thereby, equal slow group velocities and symmetric cross-coupling of the weak fields over long distances are achieved. By simply tuning the fields, this scheme can either yield giant cross-phase modulation or ultrasensitive two-photon switching. PACS number(s): 42.50.Gy, 03.67.-aThe weakness of optical nonlinearities in conventional media precludes the effective interaction of extremely feeble fields containing few photons only [1]. This weakness sets a limit on the performance of ultrasensitive photonic elements (switches and couplers), as well as on nonclassical ("squeezing") effects. It is also the main impediment towards constructing quantum logic gates, quantum teleportation and cryptography schemes operating at the few-photon level [2]. The weakness of optical nonlinearities can be compensated by photon confinement in a high-Q cavity [3]. A promising avenue has been opened by studies of enhanced nonlinear coupling via electromagnetically induced transparency (EIT) in atomic vapors in the presence of classical driving fields, which induce coherence between atomic levels [4,5]. These studies have predicted the ability to achieve an appreciable nonlinear phase shift of extremely weak optical fields [6] or a twophoton switch [7,8], using the driven N -configuration of atomic levels. The main hindrance of such schemes is the mismatch between the group velocities of the field that is subject to EIT and its nearly-free propagating partner, which severely limits their effective interaction length [9].In the present paper we propose a scheme that can remove this bottleneck, by basically modifying the nonlinear interaction of weak optical fields: in contrast to all currently known schemes, it affects both fields in a completely symmetric fashion, rendering their group velocities equal. It thereby allows their cross-coupling over very long distances and brings it to its ultimate limit of efficiency. This scheme relies solely on an intraatomic process that causes simultaneous EIT for both fields interacting with magnetically (Zeeman-) split sublevels in the presence of two driving fields. Remarkably, by simply tuning the fields, this scheme can either yield giant crossphase modulation or ultrasensitive two-photon switching in vapor [10]. It may therefore substantially advance the optical processing and communication of quantum information in conventional media, without resorting to photonic crystals [11] or resonators [12].We first outline the proposed setup. Two weak optical fields E a and E b , having σ polarization along the y axis, propagate in the atomic medium along the z axis. Two π-(x-)polarized CW driving fields E d1,2 and a static xoriented magnetic field B are applied (Fig. 1-Left Inset). In...

Nonlinear Optics with Stationary Pulses of Light

“…Specifically we demonstrate that an efficient Kerr-like interaction between two pulses can be implemented as a sequence of linear optical processes and atomic state manipulations. Coherent, controlled nonlinear processes at optical energies corresponding to a single light quanta appear feasible.Before proceeding, we note that the present work is closely related to recent studies on the resonant enhancement of nonlinear optical phenomena via EIT [8,9,10,11]. The essence of these studies is to utilize steep atomic dispersion associated with narrow EIT resonances.…”

“…Before proceeding, we note that the present work is closely related to recent studies on the resonant enhancement of nonlinear optical phenomena via EIT [8,9,10,11]. The essence of these studies is to utilize steep atomic dispersion associated with narrow EIT resonances.…”

An off-normal fibre-like texture in thin films on single-crystal substrates

“…Third, controlled conversion of propagating light into stationary light pulses opens interesting possibilities for enhanced nonlinear optical processes by combining the present technique with the resonant enhancement of nonlinear optics via EIT [24][25][26] . This combination may enable controlled interactions involving quantum few-photon fields [27][28][29][30] analogous to those feasible in cavity quantum electrodynamics 5 . Finally, extension of the present ideas to other systems might be possible using, for example, dynamic modulation of photonic bandgap materials.…”

Nonlinear quantum optical computing via measurement

“…Current proposals for detectors range from novel mesoscopic electronic devices [17], and superconducting devices [18] to novel systems that use stimulated Raman scattering [19,20] and EIT [21] The technology that might deliver a Kerr nonlinear device with the required strength is more difficult to identify. Recent progress in EIT schemes [22,23,24,25] and cavity QED processes [26,27] may offer some hope. It might be argued that if a Kerr nonlinearity with large single photon phase shifts was available conventional circuit based quantum computing could be achieved and there would be no need to use the measurement based scheme in this paper.…”