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Nonlinear Optics

Nonlinear optics with two photons (or less)

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

Published Jan 1, 2002• 0 citations
Publisher

Abstract

Nonlinear optical effects are generally limited to the high-intensity regime due to the small value of typical nonlinear coefficients. We demonstrate novel effects where a strong spectator field mediates a large nonlinear interaction between two photons. Such effects open the door to a new field of {\it quantum} nonlinear optics, potentially useful for two-photon all-optical switches (e.g., optical quantum logic gates) as well as other nonlinear effects such as the formation of quantum solitons. I will talk about enhanced upconversion, quantum state preparation, two-photon cross-phase modulation, and potential quantum-information applications to tasks such as Bell state determination.

DOI
10.1364/nlo.2002.md4

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Nonlinear optical effects are generally limited to the high-intensity regime due to the small value of typical nonlinear coefficients. We demonstrate novel effects where a strong spectator field mediates a large nonlinear interaction between two photons. Such effects open the door to a new field of {\it quantum} nonlinear optics, potentially useful for two-photon all-optical switches (e.g., optical quantum logic gates) as well as other nonlinear effects such as the formation of quantum solitons. I will talk about enhanced upconversion, quantum state preparation, two-photon cross-phase modulation, and potential quantum-information applications to tasks such as Bell state determination.
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Large nonlinearity at the single-photon level can pave the way for the implementation of universal quantum gates. However, realizing large and noiseless nonlinearity at such low light levels has been a great challenge for scientists in the past decade. We present a proposal for using quantum memory to enhance the cross-phase modulation (XPM) of two optical fields. Our memory, which is based on the gradient echo memory (GEM) scheme, maps the optical fields into Fourier transformed polaritonic excitations in an atomic ensemble. We show that nonlinear interactions can be induced in GEM. Due to the slowing down and subsequent storage of light fields within a memory, nonlinear interaction time between the fields can be extended resulting in an enhancement of the effective nonlinearity. We present results showing noiseless cross-phase modulations and discuss plans to further increase the cross-phase modulation strength to a level useful for implementing quantum gates.
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.
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.
Nonlinear interactions between two photons are required for the construction of optical quantum logic gates, but those interactions are normally very weak due to the small magnitude of the electric field associated with a single photon. We note that exchange interactions can have a large effect even when there is no physical interaction between two particles, and we exploit this property for the construction of optical quantum logic gates. We show that the probability of there being two virtually-excited atoms in a medium can be a factor of 2 larger when two nonresonant photons propagate through the same medium as compared to the case in which they propagate through two separate media, in analogy with photon bunching. As a result, the application of one or more laser pulses will produce a nonlinear phase shift that can be used to construct an XOR quantum logic gate. This provides an example of a quantum control process in which one photon can control the state of another photon even when there is no sequence of physical interactions linking the two photons. From a classical point of view, it is not possible to identify a path for the flow of information or a specific cause for the outcome of the control process.