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arXiv:quant-ph/0101020 · Physical Review Letters

Nonlinear Optics with Less Than One Photon

Kevin J. Resch, Jeff S. Lundeen, Aephraim M. Steinberg

Published Aug 30, 2001• 49 citations
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Abstract

We demonstrate suppression and enhancement of spontaneous parametric down-conversion via quantum interference with two weak fields from a local oscillator (LO). Effectively, pairs of LO photons up-convert with high efficiency for appropriate phase settings, exhibiting an effective nonlinearity enhanced by at least 10 orders of magnitude. This constitutes a two-photon switch and promises to be applicable to a wide variety of quantum nonlinear optical phenomena.

DOI
10.1103/physrevlett.87.123603

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We demonstrate suppression and enhancement of spontaneous parametric down-conversion via quantum interference with two weak fields from a local oscillator (LO). Effectively, pairs of LO photons up-convert with high efficiency for appropriate phase settings, exhibiting an effective nonlinearity enhanced by at least 10 orders of magnitude. This constitutes a two-photon switch and promises to be applicable to a wide variety of quantum nonlinear optical phenomena.
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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.
Quantum states of light, such as single photons, pairs of entangled photons, and squeezed light are a key resource for photonic quantum technologies. All these states can be obtained via the nonlinear optical effect of spontaneous parametric down-conversion (SPDC). In SPDC, a higher-energy photon of a coherent beam (pump) splits in two lower-energy daughter photons, called signal and idler. The photons of such a pair can be entangled in polarization, time/frequency, and position/momentum. Efficient generation of photon pairs requires a high second-order susceptibilityχ(2)\chi^{(2)}χ(2)of the material where it occurs, and the phase matching between the pump and the down-converted photons.
Genuine quantum interference between independent nonlinear processes of different order provides a route to coherent control that cannot be reduced to a classical field interference. Here we present an all-optical analogue of coherent carrier injection by exploiting interference between second- and third-order quantum nonlinear processes in an integrated photonic platform. Photon pairs generated via spontaneous parametric down-conversion and spontaneous four-wave mixing coherently contribute to the same final two-photon state, resulting in a phase-dependent modulation of both the generation rate and the spectral structure of the emitted biphoton state. We illustrate the features of such interference and how it can be used to shape biphoton wavefunctions and their quantum correlations. These results identify interference between nonlinear processes of different order as a distinct form of coherent quantum control within quantum nonlinear optics.
It is shown that quantum interference with classical beams may be used to suppress or enhance the rate of spontaneous photon-pair production from a nonlinear crystal. Sum-frequency generation of the classical beams is simultaneously enhanced or suppressed via interference with a classical pump. In the extreme case, a crystal which is transparent to individual photons may block all photon pairs, converting them to 2w. This constitutes a coherent nonlinear response at the single-photon level, enhanced by a factor of approximately 10 10 Experimental data and a theoretical description are presented, and an attempt is made to delineate the classical and quantum aspects of these effects.