Aephraim M. Steinberg

Super-resolving phase measurements with a multiphoton entangled state

Interference phenomena are ubiquitous in physics, often forming the basis of demanding measurements. Examples include Ramsey interferometry in atomic spectroscopy, X-ray diffraction in crystallography and optical interferometry in gravitational-wave studies. It has been known for some time that the quantum property of entanglement can be exploited to perform super-sensitive measurements, for example in optical interferometry or atomic spectroscopy. The idea has been demonstrated for an entangled state of two photons, but for larger numbers of particles it is difficult to create the necessary multiparticle entangled states. Here we demonstrate experimentally a technique for producing a maximally entangled three-photon state from initially non-entangled photons. The method can in principle be applied to generate states of arbitrary photon number, giving arbitrarily large improvement in measurement resolution. The method of state construction requires non-unitary operations, which we perform using post-selected linear-optics techniques similar to those used for linear-optics quantum computing.

Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer

An experiment determined the trajectories of single photons through a two-slit interferometer. A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or “trajectory” that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.

VI: Tunneling Times and Superluminality

Publisher Summary Measurements of tunneling times by photons possess certain advantages over those by electrons or other particles, stemming from the fact that the wavelength of visible light is larger than the de Broglie wavelength of massive particles. The types of tunnel barriers for photons used in tunneling-time experiments are (1) periodic dielectric structures excited inside their band gap or stop-band, (2) frustrated total internal reflection (FTIR) in glass or dielectric prisms, and (3) waveguides beyond cutoff. The chapter discusses the problem of superluminal group velocities, which have been predicted for the propagation of wave packets tuned to transparent spectral regions of media with inverted atomic populations. The cases of superluminal wave packets tuned close to zero frequency, and those tuned close to an atomic resonance with gain in it, are discussed further in the chapter. The new kinds of superluminal propagation effects occur over much longer distances than for tunneling.

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 Hardys 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.

Experimental realization of the quantum box problem

Abstract The three-box problem is a gedankenexperiment designed to elucidate some interesting features of quantum measurement and locality. A particle is prepared in a particular superposition of three boxes, and later found in a different (but nonorthogonal) superposition. It was predicted that appropriate “weak” measurements of particle position in the interval between preparation and post-selection would find the particle in two different places, each with certainty. We verify these predictions in an optical experiment and address the issues of locality and of negative probability.

Analogies between electron and photon tunneling: A proposed experiment to measure photon tunneling times

Abstract The phenomenon of tunneling is a well-known fundamental consequence of quantum mechanics. All particles can in principle tunnel. In particular, both electrons and photons can tunnel through classically forbidden regions of space known as “barriers”. However, there have been numerous controversies over how long it takes a particle to cross a barrier. Exploiting an analogy between electrons and photons, we suggest an experiment to infer the characteristics of an electrons barrier-traversal time by measuring the time it takes a photon to traverse a similar barrier. Electron tunneling experiments are in general much more difficult to perform than analogous optical ones. With an optical technique one can construct optical barriers on the scale of microns, in contrast to theangstrom-scale barriers required for electron tunneling. Our experiment may help settle the controversies over tunneling times. By means of a newly developed quantum optical technique, we should be able to measure the tunneling times of individual photons with sub-picosecond resolution. In our experiments we are using a two-photon light source, in which a pair of tightly correlated photons is generated by the process of spontaneous parametric down-conversion. Hong, Ou and Mandel have already achieved a sub-picosecond comparison between the arrival times of two such photons at a beam splitter placed at the intersection of their paths. In our geometry, one member of the photon pair tunnels through a barrier, while the other does not. Then coincidence detection of this photon pair constitutes the detection of an individual tunneling event. The particle aspect of photon tunneling can thus be clearly observed. We propose to use the Hong-Ou-Mandel technique to measure the tunneling time. We have chosen for our tunneling barrier two glass prisms placed in close proximity, utilizing the phenomenon of frustrated total internal reflection.

Improving Quantum State Estimation with Mutually Unbiased Bases

When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases. We demonstrate improved state estimation as compared to standard measurement strategies and discuss how this can be understood from the structure of the measurements we use. We experimentally compared our method to the standard state estimation method for three different states and observe that the infidelity was up to 1.84 ± 0.06 times lower by using our technique than it was by using standard state estimation methods.

Diagnosis, prescription, and prognosis of a bell-state filter by quantum process tomography

We apply the techniques of quantum process tomography to characterize errors and decoherence in a prototypical two-photon operation, a singlet-state filter. The quantum process tomography results indicate a large asymmetry in the process and also the required operation to correct for this asymmetry. We quantify residual errors and decoherence of the filtering operation after this modification.

ABSOLUTE EFFICIENCY AND TIME-RESPONSE MEASUREMENT OF SINGLE-PHOTON DETECTORS

Using correlated photons from spontaneous parametric downconversion, we have measured both the absolute quantum efficiencies and the time responses of four single-photon detectors. Efficiencies as high as (76.4 ± 2.3)% (at 702 nm) were seen, which to our knowledge are the highest reported single-photon detection efficiencies. An auxiliary retroreflection mirror was found to increase the net detection efficiency by as much as a factor of 1.19. The narrowest time profile for coincidences between two detectors displays a peak with 300 ps FWHM. We also investigated the presence of afterpulses and the effects of saturation and varying device parameters.

Bright filter-free source of indistinguishable photon pairs

We demonstrate a high-brightness source of pairs of indistinguishable photons based on a type-II phase-matched doubly-resonant optical parametric oscillator operated far below threshold. The cavityenhanced down-conversion output of a PPKTP crystal is coupled into two single-mode fibers with a mode coupling efficiency of 58%. The high degree of indistinguishability between the photons of a pair is demonstrated by a Hong-Ou-Mandel interference visibility of higher than 90% without any filtering at an instantaneous coincidence rate of 450,000 pairs/s per mW of pump power per nm of down-conversion bandwidth. For the degenerate spectral mode with a linewidth of 7 MHz at 795 nm a rate of 70 pairs/(s mW MHz) is estimated, increasing the spectral brightness for indistinguishable photons by two orders of magnitude compared to similar previous sources.