Ofer Firstenberg

Quantum Nonlinear Optics with Single Photons Enabled by Strongly Interacting Atoms

The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering, being of both fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Our approach paves the way for quantum-by-quantum control of light fields, including single-photon switching, all-optical deterministic quantum logic and the realization of strongly correlated many-body states of light.

Attractive photons in a quantum nonlinear medium

The fundamental properties of light derive from its constituent particles—massless quanta (photons) that do not interact with one another. However, it has long been known that the realization of coherent interactions between individual photons, akin to those associated with conventional massive particles, could enable a wide variety of novel scientific and engineering applications. Here we demonstrate a quantum nonlinear medium inside which individual photons travel as massive particles with strong mutual attraction, such that the propagation of photon pairs is dominated by a two-photon bound state. We achieve this through dispersive coupling of light to strongly interacting atoms in highly excited Rydberg states. We measure the dynamical evolution of the two-photon wavefunction using time-resolved quantum state tomography, and demonstrate a conditional phase shift exceeding one radian, resulting in polarization-entangled photon pairs. Particular applications of this technique include all-optical switching, deterministic photonic quantum logic and the generation of strongly correlated states of light.

Topological stability of stored optical vortices

We report an experiment in which an optical vortex is stored in a vapor of Rb atoms. Because of its 2pi phase twist, this mode is topologically stable and cannot unwind even under conditions of strong diffusion.

Storing images in warm atomic vapor.

Reversible and coherent storage of light in an atomic medium is a promising method with possible applications in many fields. In this work, arbitrary two-dimensional images are slowed and stored in warm atomic vapor for up to 30 micros, utilizing electromagnetically induced transparency. Both the intensity and the phase patterns of the optical field are maintained. The main limitation on the storage resolution and duration is found to be the diffusion of atoms. A technique analogous to phase-shift lithography is employed to diminish the effect of diffusion on the visibility of the reconstructed image.

Nonlinear quantum optics mediated by Rydberg interactions

By mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a nonlinear optical medium which exhibits a strong optical nonlinearity at the level of individual photons. We review the theoretical concepts and the experimental state-of-the-art of this exciting new field, and discuss first applications in the field of all-optical quantum information processing.

Colloquium: Strongly interacting photons in one-dimensional continuum

Photons, the particles of light, are in most conditions very weakly interacting. Nevertheless, it is possible to make them interact by altering environmental conditions, for instance, in the interior of certain materials or by squeezing them in confined geometries. In this Colloquium the topic of photons interacting strongly when confined to a one-dimensional geometry is discussed from experimental and theoretical perspectives.

Elimination, reversal and directional bias of optical diffraction

Electromagnetically induced transparency in an atomic gas can slow the propagation of images. It is now shown that the diffraction of such images as they propagate can be controlled and even eliminated. This is achieved by using atomic diffusion to influence the spreading of the image. Any image, imprinted on a wave field and propagating in free space, undergoes a paraxial diffraction spreading. The reduction or manipulation of diffraction is desirable for many applications, such as imaging, wave-guiding, microlithography and optical data processing. As was recently demonstrated, arbitrary images imprinted on light pulses are dramatically slowed1,2 when traversing an atomic medium of electromagnetically induced transparency3,4 and undergo diffusion due to the thermal atomic motion5,6. Here we experimentally demonstrate a new technique to eliminate the paraxial diffraction and the diffusion of slow light, regardless of its position and shape7. Unlike former suggestions for diffraction manipulation8,9,10,11,12, our scheme is linear and operates in the wavevector space, eliminating the diffraction for arbitrary images throughout their propagation. By tuning the interaction, we further demonstrate acceleration of diffraction, biased diffraction and induced deflection, and reverse diffraction, implementing a negative-diffraction lens13. Alongside recent advances in slow-light amplification14 and image entanglement15, diffraction control opens various possibilities for classical and quantum image manipulation.

Elimination of the diffraction of arbitrary images imprinted on slow light.

We present a scheme for eliminating the optical diffraction of slow light in a thermal atomic medium of electromagnetically induced transparency. Nondiffraction is achieved for an arbitrary paraxial image by manipulating the susceptibility in momentum space, in contrast to the common approach, which employs guidance of specific modes by manipulating the susceptibility in real space. For negative two-photon detuning, the moving atoms drag the transverse momentum components unequally, resulting in a Doppler trapping of light by atoms in two dimensions.

Theory of thermal motion in electromagnetically induced transparency: Effects of diffusion, Doppler broadening, and Dicke and Ramsey narrowing

We present a theoretical model for electromagnetically induced transparency (EIT) in vapor that incorporates atomic motion and velocity-changing collisions into the dynamics of the density-matrix distribution. Within a unified formalism, we demonstrate various motional effects, known for EIT in vapor: Doppler broadening of the absorption spectrum; Dicke narrowing and time-of-flight broadening of the transmission window for a finite-sized probe; diffusion of atomic coherence during storage of light and diffusion of the light-matter excitation during slow-light propagation; and Ramsey narrowing of the spectrum for a probe and pump beams of finite size.

Scattering resonances and bound states for strongly interacting Rydberg polaritons

We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments.