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Conference on Lasers and Electro-Optics

Nonlinear optics at the two-photon level

J. D. Franson, T. B. Pittman

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given.Nonlinear optical effects are normally limited to high-intensity fields containing a large number of photons because the electric field associated with a single photon is usually very weak. Nonlinear phase shifts at the two-photon level previously have been observed using high-Q cavities and atomic beams. The authors recently predicted that nonlocal effects involving pairs of atoms in a medium could enhance the nonlinear interaction between two photons to the point that nonlinear phase shifts could be obtained in an ordinary medium without the use of resonant cavities.

DOI
10.1109/iqec.1998.680190

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Summary form only given.Nonlinear optical effects are normally limited to high-intensity fields containing a large number of photons because the electric field associated with a single photon is usually very weak. Nonlinear phase shifts at the two-photon level previously have been observed using high-Q cavities and atomic beams. The authors recently predicted that nonlocal effects involving pairs of atoms in a medium could enhance the nonlinear interaction between two photons to the point that nonlinear phase shifts could be obtained in an ordinary medium without the use of resonant cavities.
In this thesis I report the first experimental observation of an interaction between a postselected single photon and an electromagnetic field containing a few thousand photons.This is the first observation of the nonlinear interactions due to a single freely propagatingphoton. To achieve this pioneering result, we have theoretically and experimentally studied nonlinear optics at the few-photon level. To the best of our knowledge, the pulse energy levels used for our experiments are the lowest energies used for cross-phase modulation in free space.Photon-photon interaction is vanishingly weak; the strength of this interaction can be enhanced in the presence of a material medium as mediator. In our experiment, we use an atomic coherence effect, namely Electromagnetically-induced Transparency (EIT), to produce a `giant' nonlinear interaction between two optical fields. We have observed a nonlinear phase shift of 18 ± 4 µrad per freely propagating single photon. This is done by sending very weak coherent state pulses into the medium and subsequently detecting single photons, inferring the existence of a photon in the interaction region.The optical setup, electronics and software that have been developed during the completion of this thesis provide the basis for several exciting future light-matter interaction experiments. We have produced phase-stable laser beams to create EIT in our cold Rubidium sample prepared in a Magneto-optical Trap (MOT). The laser system and the improved MOT setup have been built to be stable so that we can do very long data acquisition runs. We also have develop ed to ols and software with high precision and stability such that we can measure phase shifts down to micro-radian level.
I present experimental and theoretical work on extending nonlinear optical effects to the quantum domain. First, I experimentally demonstrate an incoherent nonlinear effect linked to the amplification stage of photon detection in a single-photon counter. The detector, in the high-efficiency regime, does not follow Glauber's quantum mechanical model for photodetection and, as a result, quantum interference effects are observable in the singles rate of one detector. I then go on to theoretically describe and experimentally demonstrate two coherent nonlinear optical effects at the single-photon level. In both experiments, the usually weak nonlinear optical properties of a common nonlinear crystal are enhanced by over 10 orders of magnitude using interference. The first of these coherent processes uses interference to frequency double all photon pairs from a couple of very weak laser beams (containing, on average, less than one photon per pulse). I show how this nonlinearity might be used for �phase-sum� entanglement swapping and an experimental demonstration of Hardy's paradox. The second coherent effect is the dispersive analogue to the first; instead of frequency doubling all of the photon pairs, all photon pairs experience an additional nonlinear phase shift. It is analogous to an immensely enhanced Kerr nonlinearity. This effect is applied to the problem of Bell-state discrimination and can be used to entangle and disentangle the polarization states of a pair of photons under certain conditions. The final experiment in this thesis is a demonstration of a technique for creating coherent superpositions of zero and one photon based on the detection of a single, �trigger� photon.
Nonlinear interactions between two photons would have many potential applications, including the implementation of quantum logic gates for use in quantum computing. We are investigating a new mechanism for nonlinear optics at the two-photon level that is based on the exchange of photons by pairs of atoms in a medium, such as an atomic vapor. The effect can be understood as being due to a factor of two increase in the probability of having two excited atoms in the medium compared to the case in which the two photons propagate in two separate media. These effects are expected to be sufficiently large that cavities and traps should not be required, which may eventually allow the construction of large numbers of simple quantum logic gates. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering, being of both fundamental and technological significance. We describe and demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption and phase shift for photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Finally, we will discuss our progress towards realization of integrated quantum photonic systems, based on deterministic coupling of individual atoms and atom-like systems to photonic crystal cavities.
In the previous chapter we examined nonlinear propagation in a two-level medium, which leads to amplification or absorption of the radiation field. As we will see further on in this volume, when the medium is placed in an optical cavity one realizes a laser in the case of amplification or an optically bistable system in the absorptive configuration. On the other hand, the nonlinear response of the atomic polarization to the electric field leads to further fascinating scenarios [29, 51–60]. For example, a field with central ω 0 can generate harmonic components with central frequencies 2 ω 0 , 3 ω 0 etc., processes that are called second-harmonic generation, third-harmonic generation etc. Furthermore, the interaction of two fields with central frequencies ω 1 and ω 2 , with ω 1 > ω 2 , can generate components with central frequency ω 1 + ω 2 (sum-frequency generation) and ω 1 − ω 2 (difference-frequency generation). Such phenomena have not yet appeared in this volume because we have assumed that the electric field corresponds to a narrow frequency band around a central frequency ω 0 only, whereas to describe them it is necessary to assume that the electric field is the superposition of a number of frequency bands. In this chapter we will provide a description of the basic elements which are necessary to describe these phenomena and we will discuss a small number of them for the case of materials with a quadratic nonlinearity, referring to textbooks in nonlinear optics for the description of other phenomena. The following chapter is devoted, instead, to the case of materials with cubic nonlinearities. The starting point of nonlinear optics is the expansion of the atomic polarization in powers of the electric field, when the electric field is not too intense. In our treatment in Chapter 5 we saw that the expansion of the nonlinear susceptibility contains only even powers of the electric field (see Eq. (5.27)), and therefore the expansion of the polarization includes only odd powers.