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 weakly in practice (for instance, in optics -- a common testing ground for this technique -- strong photon-photon interactions would be needed). Here we derive a general, experimentally feasible, method for extracting these values from correlations between single-particle observables.Comment: 6 page

Quantum Nonlocality in Two-Photon Experiments at Berkeley

We review some of our experiments performed over the past few years on two-photon interference. These include a test of Bell's inequalities, a study of the complementarity principle, an application of EPR correlations for dispersion-free time-measurements, and an experiment to demonstrate the superluminal nature of the tunneling process. The nonlocal character of the quantum world is brought out clearly by these experiments. As we explain, however, quantum nonlocality is not inconsistent with Einstein causality.Comment: 16 pages including 24 figure

Nonlinear optics with less than one photon

We demonstrate suppression and enhancement of spontaneous parametric down- conversion via quantum interference with two weak fields from a local oscillator (LO). Pairs of LO photons are observed to upconvert 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 useful for a variety of nonlinear optical effects at the quantum level.Comment: 8 pages, 5 figure

Conditional probabilities in quantum theory, and the tunneling time controversy

It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to Aharonov {\it et al.}, and hence describe the outcomes of real measurements made on subensembles. In particular, this approach is used to address the question of the history of a particle which has tunnelled across a barrier. A {\it gedankenexperiment} is presented to demonstrate the physically testable implications of the results of these calculations, along with graphs of the time-evolution of the conditional probability distribution for a tunneling particle and for one undergoing allowed transmission. Numerical results are also presented for the effects of loss in a bandgap medium on transmission and on reflection, as a function of the position of the lossy region; such loss should provide a feasible, though indirect, test of the present conclusions. It is argued that the effects of loss on the pulse {\it delay time} are related to the imaginary value of the momentum of a tunneling particle, and it is suggested that this might help explain a small discrepancy in an earlier experiment.Comment: 11 pages, latex, 4 postscript figures separate (one w/ 3 parts

Identification of Decoherence-Free Subspaces Without Quantum Process Tomography

Characterizing a quantum process is the critical first step towards applying such a process in a quantum information protocol. Full process characterization is known to be extremely resource-intensive, motivating the search for more efficient ways to extract salient information about the process. An example is the identification of "decoherence-free subspaces", in which computation or communications may be carried out, immune to the principal sources of decoherence in the system. Here we propose and demonstrate a protocol which enables one to directly identify a DFS without carrying out a full reconstruction. Our protocol offers an up-to-quadratic speedup over standard process tomography. In this paper, we experimentally identify the DFS of a two-qubit process with 32 measurements rather than the usual 256, characterize the robustness and efficiency of the protocol, and discuss its extension to higher-dimensional systems.Comment: 6 pages, 5 figure

Speakable and Unspeakable, Past and Future

In it, I discuss some questions related to what can and cannot be said about the history of a quantum mechanical system. Relying heavily on the weak- measurement formalism of Aharonov and coworkers, I argue that there is much to be learned about a system based both on its preparation and on subsequent postselection. This is illustrated with examples from a number of past, present, and future experiments from our lab, ranging from tests of quantum "paradoxes" to studies of nonlocality to non-deterministic implementations of logic operations on quantum information. The connection between weak measurements and generalized probability theory is discussed, along with some of the counterintuitive features of these "probabilities." Conclusions are for the most part left to the reader

Phase Space Tomography of Classical and Nonclassical Vibrational States of Atoms in an Optical Lattice

Atoms trapped in optical lattice have long been a system of interest in the AMO community, and in recent years much study has been devoted to both short- and long-range coherence in this system, as well as to its possible applications to quantum information processing. Here we demonstrate for the first time complete determination of the quantum phase space distributions for an ensemble of $^{85}Rb$ atoms in such a lattice, including a negative Wigner function for atoms in an inverted state.Comment: Submitted to Journal of Optics B: Quantum and Semiclassical Optics. Special issue in connection with the 9th International Conference on Squeezed States and Uncertainty Relations, to be held in Besancon, France, on 2-6 May 200