Sebastian Hofferberth

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.

Efficient all-optical switching using slow light within a hollow fiber

We demonstrate a fiber-optical switch that is activated at tiny energies corresponding to a few hundred optical photons per pulse. This is achieved by simultaneously confining both photons and a small laser-cooled ensemble of atoms inside the microscopic hollow core of a single-mode photonic-crystal fiber and using quantum optical techniques for generating slow light propagation and large nonlinear interaction between light beams.

Non-equilibrium coherence dynamics in one-dimensional Bose gases.

Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

Single-Photon Transistor Mediated by Interstate Rydberg Interactions

We report on the realization of an all-optical transistor by mapping gate and source photons into strongly interacting Rydberg excitations with different principal quantum numbers in an ultracold atomic ensemble. We obtain a record switch contrast of 40% for a coherent gate input with mean photon number one and demonstrate attenuation of source transmission by over ten photons with a single gate photon. We use our optical transistor to demonstrate the nondestructive detection of a single Rydberg atom with a fidelity of 0.72(4).

Probing quantum and thermal noise in an interacting many-body system

The probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. In many-body systems quantum-mechanical noise reveals non-local correlations of the underlying many-body states. Here, we provide a complete experimental analysis of the shot-to-shot variations of interference-fringe contrast for pairs of independently created one-dimensional Bose condensates. Analysing different system sizes, we observe the crossover from thermal to quantum noise, reflected in a characteristic change in the distribution functions from poissonian to Gumbel type, in excellent agreement with theoretical predictions on the basis of the Luttinger-liquid formalism. We present the first experimental observation of quasi-long-range order in one-dimensional atomic condensates, which is a hallmark of quantum fluctuations in one-dimensional systems. Furthermore, our experiments constitute the first analysis of the full distribution of quantum noise in an interacting many-body system. The analysis of the interference fringes generated by initially independent one-dimensional Bose condensates reveals contributions of both quantum noise and thermal noise, advancing our fundamental understanding of quantum states in interacting many-body systems.

Adiabatic radio-frequency potentials for the coherent manipulation of matter waves

Adiabatic dressed state potentials are created when magnetic substates of trapped atoms are coupled by a radio-frequency field. We discuss their theoretical foundations and point out fundamental advantages over potentials purely based on static fields. The enhanced flexibility enables one to implement numerous configurations, including double wells, Mach-Zehnder, and Sagnac interferometers which even allows for internal state-dependent atom manipulation. These can be realized using simple and highly integrated wire geometries on atom chips.

Radiofrequency-dressed-state potentials for neutral atoms

Potentials for atoms can be created by external fields acting on properties such as magnetic moment, charge, polarizability, or by oscillating fields that couple internal states. The most prominent realization of the latter is the optical dipole potential formed by coupling ground and electronically excited states of an atom with light. Here, we present an extensive experimental analysis of potentials derived from radiofrequency (RF) coupling of electronic ground states. The coupling is magnetic and the vector character allows the design of versatile microscopic state-dependent potential landscapes. Compared with standard magnetic trapping, we find no additional heating or (collisional) loss up to densities of 1015 atoms cm−3. We demonstrate robust evaporative cooling in RF potentials, which allows easy production of Bose–Einstein condensates in complex potentials. Altogether, this makes RF dressing a new powerful tool for manipulating ultracold atoms complementary to magnetic trapping and optical dipole potentials.

Bose–Einstein condensates: Microscopic magnetic-field imaging

Todays magnetic-field sensors are not capable of making measurements with both high spatial resolution and good field sensitivity. For example, magnetic force microscopy allows the investigation of magnetic structures with a spatial resolution in the nanometre range, but with low sensitivity, whereas SQUIDs and atomic magnetometers enable extremely sensitive magnetic-field measurements to be made, but at low resolution. Here we use one-dimensional Bose–Einstein condensates in a microscopic field-imaging technique that combines high spatial resolution (within 3 micrometres) with high field sensitivity (300 picotesla).

Coupling a single electron to a Bose-Einstein condensate

The coupling of electrons to matter lies at the heart of our understanding of material properties such as electrical conductivity. Electron–phonon coupling can lead to the formation of a Cooper pair out of two repelling electrons, which forms the basis for Bardeen–Cooper–Schrieffer superconductivity. Here we study the interaction of a single localized electron with a Bose–Einstein condensate and show that the electron can excite phonons and eventually trigger a collective oscillation of the whole condensate. We find that the coupling is surprisingly strong compared to that of ionic impurities, owing to the more favourable mass ratio. The electron is held in place by a single charged ionic core, forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size of up to eight micrometres, comparable to the dimensions of the condensate. In such a state, corresponding to a principal quantum number of n = 202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects caused by the electron exploring the outer regions of the condensate. We anticipate future experiments on electron orbital imaging, the investigation of phonon-mediated coupling of single electrons, and applications in quantum optics.

Sensing electric and magnetic fields with Bose-Einstein condensates

We experimentally demonstrate that one-dimensional Bose-Einstein condensates brought close to microfabricated wires on an atom chip are a very sensitive sensor for magnetic and electric fields reaching a sensitivity to potential variations of ∼10−14eV at 3μm spatial resolution. We measure a two-dimensional magnetic field map 10μm above a 100-μm-wide wire and show how the transverse current-density component inside the wire can be reconstructed. The relation between the field sensitivity and the spatial resolution is discussed and further improvements utilizing Feshbach-resonances are outlined.We experimentally demonstrate that one-dimensional Bose-Einstein condensates brought close to microfabricated wires on an atom chip are a very sensitive sensor for magnetic and electric fields reaching a sensitivity to potential variations of ∼10−14eV at 3μm spatial resolution. We measure a two-dimensional magnetic field map 10μm above a 100-μm-wide wire and show how the transverse current-density component inside the wire can be reconstructed. The relation between the field sensitivity and the spatial resolution is discussed and further improvements utilizing Feshbach-resonances are outlined.