Far-off resonance conditional phase-shifter using the ac Stark shift

We suggest a conditional phase-shifter that achieves a phase shift of p radians between two weak laser beams with a total energy density on the level of 1000 photons per atomic cross-section. The two laser beams interact through the simple nonlinear technique of ac Stark shifting the common ground state of a V-type system. We find that this switch can operate in the far-off resonance regime, with low absorption and high phase accumulation. Additionally, the bandwidth of this switch can be increased independently of the energy requirement. Published by Elsevier B.V. Interacting low-power laser beams is a subject of considerable attention in nonlinear and quantumoptics [1–3]. Nonlinear interactions between weak beams can form optical switches with possible applications in all-optical information processing. Furthermore, if achieved at the single photon level, these interactions can also be used to entangle single photons, which may form the basis of a future photonic quantum computing device. In traditional nonlinear materials, the weakness of optical nonlinearities prohibit observing significant nonlinear effects between weak beams. Over the last decade, suggestions involving Electromagnetically Induced Transparency (EIT) have generated much enthusiasm in this field [4–11]. Recent experiments have demonstrated optical switching at 10 photons per atomic cross-section using EIT-based approaches [10,12]. Additionally, switching with optical instabilities has been demonstrated in an atomic vapor at less than one photon per atomic cross-section [13]. A well-known scheme for interacting laser beams is through the ac Stark shift of a common ground state [1–3]. Here, an intense laser beam can modify the refractive index experienced by a weak beam by changing its frequency detuning from a resonance. In this communication, we analyze this effect in an alkali atomic vapor where the two beams are far-off resonance from the excited electronic state. We find that a conditional phase shift on the order of radians can be obtained with an energy density around 1000 photons per atomic cross-section, k=ð2pÞ. Our results show that the scheme detailed here could operate as a simple, high-bandwidth, all optical switch with low absorption. Although the physics of what we are going to discuss is well-understood, to our knowledge, B.V. the possibility of constructing an ultra-low energy switch by using far-off resonance ac Stark shift has not been discussed before. Before describing the scheme in detail, we note the several advantages of this approach when compared with similar optical switches utilizing other approaches: (1) This scheme does not require a strong coupling laser as is required by EIT. As a result, the total energy density requirement of our switch is at the 1000-photon level per atomic cross-section. (2) The bandwidth of our switch can be large and one can work with nanosecond time scale optical pulses. The bandwidth can be increased until the rotating-wave approximation breaks down at the expense of an increased density-length product. (3) For sufficiently large detuned beams, Doppler broadening becomes unimportant and as a result, our scheme is well suited for vapor cells. Due to these advantages, our approach may be particularly useful for constructing ultra-low energy, high-bandwidth all-optical switches with possible applications in current fiber-optic networks. As shown in Fig. 1, we begin with a neutral alkali atomic medium containing a ground state j1i and two excited states, j2i and j3i. A probe beam, Ep, and a switch beam, Es, are tuned far-off resonance from the j1i–j2i and j1i–j3i transitions, respectively. Without the switch beam, the weak probe laser will experience phase accumulation and absorption as determined by the linear susceptibility of the atomic medium. These quantities depend on the probe’s frequency detuning from the atomic resonance, Dp. When both the probe and switch propagate together through the medium, the detuning of the probe effectively changes. This is because the switch beam will ac Stark shift the common ground state 1 In general, this phase-shifter scheme is not exclusive to V-systems. For example, one may tune both beams to the same lower and upper states in a two-level scheme. Then, the switch beam will ac Stark shift both the lower and upper states.