Nonlinear optics with less than one photon

Experimental joint weak measurement on a photon pair as a probe of Hardy's paradox

It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy's paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the paradox. Remarkably, the resulting weak probabilities verify all of these statements but, at the same time, resolve the paradox.

Optical switching mediated by quantum interference of Raman transitions

We report an experimental study of quantum interference between two-photon Raman transitions and demonstration of the phase control of light attenuation/transmission in cold Rb atoms. By varying the phase and frequency of a weak control laser, either constructive interference or destructive interference between the two-photon Raman transitions in a three-level Lambda system can be manipulated. The interference enables absorptive switching of one field by another field at low light levels.

All-optical switching at ultralow light levels

We report an experimental demonstration of all-optical switching at ultralow light levels in coherently prepared Rb atoms. A signal light pulse is switched on and off by a control light pulse at different frequencies in a four-level atomic system based on multiphoton interferences. We observed a switching efficiency of 55% with the signal and control light pulses containing approximately 20 photons each, corresponding to a control energy density of approximately 10(-5) photons per atomic cross section lambda(2)/(2pi).

Interferences in parametric interactions driven by quantized fields

We report interferences in the quantum fluctuations of the output of a parametric amplifier when the cavity is driven by a quantized field at the signal frequency. The interferences depend on the phase fluctuations of the input quantized field and result in splitting of the spectrum of the output, and thus the recent observation [H. Ma, Phys. Rev. Lett. 95, 233601 (2005)10.1103/PhysRevLett.95.233601] of interferences in the classical domain have a very interesting counterpart in the quantum domain. The interferences can be manipulated, for example, by changing the amount of squeezing in the input field.

Nonlinear interactions with an ultrahigh flux of broadband entangled photons

We experimentally demonstrate sum-frequency generation with entangled photon pairs, generating as many as 40,000 photons per second, visible even to the naked eye. The nonclassical nature of the interaction is exhibited by a linear intensity dependence of the nonlinear process. The key element in our scheme is the generation of an ultrahigh flux of entangled photons while maintaining their nonclassical properties. This is made possible by generating the down-converted photons as broadband as possible, orders of magnitude wider than the pump. This approach can be applied to other nonlinear interactions, and may become useful for various quantum-measurement tasks.

Extracting joint weak values with local, single-particle measurements

Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure directly in practice (for instance, in optics-a common testing ground for this technique-strong photon-photon interactions would be needed to implement an appropriate von Neumann interaction). Here we derive a general, experimentally feasible, method for extracting these joint weak values from correlations between single-particle observables.

Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm

For a practical quantum computer to operate, it is essential to properly manage decoherence. One important technique for doing this is the use of "decoherence-free subspaces" (DFSs), which have recently been demonstrated. Here we present the first use of DFSs to improve the performance of a quantum algorithm. An optical implementation of the Deutsch-Jozsa algorithm can be made insensitive to a particular class of phase noise by encoding information in the appropriate subspaces; we observe a reduction of the error rate from 35% to 7%, essentially its value in the absence of noise.

Violation of Bell's inequality with photons from independent sources

We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the postselection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.

Resonant second-order nonlinear optical processes in quantum cascade lasers

We demonstrate an efficient intracavity nonlinear interaction of laser modes in a specially adapted quantum cascade laser. A two-wavelength quantum cascade laser structure emitting at wavelengths of 7.1 and 9.5 micrometer included cascaded resonant optical intersubband transitions in an intracavity configuration leading to resonantly enhanced sum-frequency and second-harmonic generation at wavelengths of 4.1, 3.6, and 4.7 micrometer respectively. Laser peak optical powers of 60 and 80 mW resulted in 30 nW of sum-frequency signal and 10-15 nW of second-harmonic signal, both in good agreement with theoretical calculations.

Conditional-phase switch at the single-photon level

We present an experimental realization of a two-photon conditional phase switch, related to the " c-phis;" gate of quantum computation. This gate relies on quantum interference between photon pairs and generates entanglement between two optical modes through the process of spontaneous parametric down-conversion (SPDC). The interference effect serves to enhance the effective nonlinearity by many orders of magnitude, so it is significant at the quantum (single-photon) level. By adjusting the relative optical phase between the classical pump for SPDC and the pair of input modes, one can impress a large phase shift on one beam which depends on the presence or absence of a single photon in a control mode.

Quantum state preparation and conditional coherence

It is well known that spontaneous parametric down-conversion can be used to probabilistically prepare single-photon states. We have performed an experiment in which arbitrary superpositions of zero- and one-photon states can be prepared by appropriate postselection. The optical phase, which is meaningful only for superpositions of photon number, is related to the relative phase between the zero- and one-photon states. Whereas the light from spontaneous parametric down-conversion has an undefined phase, we show that this technique collapses one beam to a state of well-defined optical phase when a measurement succeeds on the other beam.