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Frontiers in Optics

Enhancement of Cross Phase Modulation Via a Resonating Cavity: Semiclassical Description

Julián Martínez-Rincón, John C. Howell

Published Jan 1, 2015• 0 citations
Publisher

Abstract

We present a semi-classical description of cavity-based cross phase modulation in a ladder atomic system. Very large single-photon detuning is required and enhancement proportional to the finesse of the resonator is found. This approach overcomes most problems present on other protocols and has a self-defined far-off-resonance effective cooperativity of unity.

DOI
10.1364/fio.2015.jw2a.38

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We present a semi-classical description of cavity-based cross phase modulation in a ladder atomic system. Very large single-photon detuning is required and enhancement proportional to the finesse of the resonator is found. This approach overcomes most problems present on other protocols and has a self-defined far-off-resonance effective cooperativity of unity.
We evaluate the advantages of performing cross-phase modulation (XPM) on a very-far-off-resonance atomic system. We consider a ladder system with a weak (few-photon level) control coherent field imparting a conditional nonlinear phase shift on a probe beam. We find that by coupling to an optical resonator, the optimal XPM is enhanced proportional to the finesse of the resonator by a factor of F/4π. We present a semiclassical description of the system and show that the phenomenon is optimal in the self-defined condition of off-resonance effective cooperativity equal to one.
Deterministic optical quantum logic requires a nonlinear quantum process that alters the phase of a quantum optical state by π through interaction with only one photon. Here, we demonstrate a large conditional cross-phase modulation between a signal field, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. This approach avoids fundamental limitations associated with multimode effects for traveling optical photons. We measure a conditional cross-phase shift of [Formula: see text] (and up to [Formula: see text] by postselection on photons that remain in the system longer than average) between the retrieved signal and control photons, and confirm deterministic entanglement between the signal and control modes by extracting a positive concurrence. By upgrading to a state-of-the-art cavity, our system can reach a coherent phase shift of π at low loss, enabling deterministic and universal photonic quantum logic.
Many effects in the interaction between atoms and a cavity that are usually de-scribed in quantum mechanical terms (cavity quantum electrodynamics, cavity QED) can be understood and quantitatively analyzed within a classical framework. We adopt such a classical picture of a radiating dipole oscillator to derive explicit ex- pressions for the coupling of single atoms and atomic ensembles to Gaussian modes in free space and in an optical resonator. The cooperativity parameter of cavity QED is shown to play a central role, and is given a geometrical interpretation. The classical analysis yields transparent, intuitive results that are useful for analyzing applications of cavity QED such as atom detection and counting, cavity cooling, cavity spin squeezing, cavity spin optomechanics, or phase transitions associated with the self-organization of the ensemble-light system.
Single-photon cross phase shifts and other single-photon nonlinearities have numerous applications in all-optical quantum information processing. Generating these nonlinearities though can be difficult. This has been done previously using sophisticated experiment setups, for instance using cold atoms optically trapped within the field mode of a high-finesse cavity. Several groups have experimentally achieved single-photon phase shifts on the order of ? using these systems. However, nonlinearities weaker than this have important applications as well. In this work we introduce and demonstrate the idea of using metastable xenon gas in a high-finesse cavity to produce weak single-photon nonlinearities. Our system is relatively simple and robust, avoids problems associated with the accumulation of alkali atoms on mirror surfaces, and is capable of approaching the strong coupling regime of cavity quantum electrodynamics. It can compete with the performance of state-of-the-art cavity systems up to a single-atom cooperativity of roughly ? ? 1. Beyond this, the effects of atomic motion begin to play a larger role and improving the system performance becomes more difficult. After a brief introduction to the use of optical cavities and the spectroscopic properties of metastable xenon, we demonstrate the feasibility of our approach by reviewing two proof-of-principle demonstrations performed in our lab. In these experiments, we measured absorption saturation and cross-phase modulation using a cavity of moderately high finesse F = 3,000. We found that nonlinear effects occurred at ultralow input power levels, proving that the presence of the cavity strongly enhanced the inherent optical nonlinearity of metastable xenon. We close by reviewing our recent progress in building an improved cavity system, which is expected to produce enhanced single photon cross phase shifts.
The radiative properties of atoms inside an optical cavity can be dramatically changed with respect to those in free space. In the strong-coupling limit, the reversible dipole interaction between an atom and the cavity field dominates the irreversible decay resulting from spontaneous emission and cavity damping. In this limit the atom and field can no longer be regarded as separate quantities but instead form a composite dynamic system. To enhance the dipole coupling constant and increase the photon storage time, our experiments are performed with a small cavity 1 mm long, with a finesse of 8 × 104. On average, 0.4 photons are sufficient to saturate the resonance transition at 852 nm for the cesium atoms used, while the cooperativity parameter for a single atom is 2. Optical bistability is studied in this system over the range 3 < N < 65 atoms inside the cavity, with the semiclassical theory predicting bistability for N > 5. We report observations of manifestly quantum effects in this regime, including photon antibunching and sub-Poissonian photon statistics, with the magnitude of these nonclassical effects observed to be largely independent of the number of intracavity atoms.
We propose a two-channel cross-phase modulation (XPM) scheme in a multi-atom cavity quantum electrodynamics system consisting of three-level atoms confined in a cavity and coupled by a free-space control laser. A signal laser field is coupled into the cavity, and its transmission through the cavity and reflection from the cavity form two output channels. We show that the free-space control laser induces quantum destructive interference in the normal mode excitation, which can be used to modulate the phase of the output signal light of the reflection channel and the transmission channel. The analytical results and numerical calculations show that large XPM in the coupled cavity–atom system can be realized at low light intensities.