Direct Observation of Anderson Localization of Matter Waves in a Controlled Disorder
by Juliette Billy, ....., Philippe Bouyer & Alain Aspect

In 1958, Anderson predicted the localization¹ of electronic wavefunctions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics² because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves^{3, 4, 5, 6, 7}, microwaves^{8, 9}, sound waves¹⁰ and electron gases¹¹. However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose–Einstein condensate released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle¹². We operate in a regime of pure Anderson localization, that is, with weak disorder—such that localization results from many quantum reflections of low amplitude—and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction—a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one-dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref. 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.

**Groupmeeting by Rockson Chang**

Experimental Joint Weak Measurement on a Photon Pair as a Probe of Hardy's Paradox

by Jeff Lundeen and Aephraim Steinberg

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.

**Groupmeeting by Chris Paul**

Cavity Optomechanics Using a Bose-Einstein Condensate

by Ferdinand Brennecker, Stephan Ritter, Tobias Donner, Tilman Esslinger

Cavity optomechanics studies the coupling between a mechanical oscillator and the electromagnetic field in a cavity. We report on a cavity optomechanical system in which a collective density excitation of a Bose-Einstein condensate serves as the mechanical oscillator coupled to the cavity field. A few photons inside the ultrahigh-finesse cavity trigger strongly driven back-action dynamics, in quantitative agreement with a cavity optomechanical model. We approach the strong coupling regime of cavity optomechanics, where a single excitation of the mechanical oscillator substantially influences the cavity field. The results open up new directions for investigating mechanical oscillators in the quantum regime and the border between classical and quantum physics.

**Groupmeeting by Alma Bardon**

Simplifying Quantum Logic using Higher Dimensional Hilbert Spaces

by Benjamin Lanyon,......., and Andrew White

Quantum Computation promises to solve fundamental, yet otherwise intractable, problems across a range of active fields of research. Recently, universal quantum logic gate sets - the elemntal blocks for a quantum computer - have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the large number of these gates required to uild even small quantum circuits. Here, we present and demonstrate a general technique that harnesses multi-level information carriers to significantly reduce this number, enabling the construction of key quantum circuits with existing technology. we present implementations of two key quantum circuits: the three-qubit Toffoli gate and the general two-qubit controlled-unitary gate. Although our experiment is carried out in a phtonic architecture, the technique is independent of the particular physical encoding of quantum information, and has the potential for wider application.

**Groupmeeting by Hoda Hossein-Nejad**