Controlling the phase of a light beam with a single molecule

Deterministic Quantum Phase Estimation beyond N00N States

The modern scientific method is critically dependent on precision measurements of physical parameters. A classic example is the measurement of the optical phase enabled by optical interferometry, where the error on the measured phase is conventionally bounded by the so-called Heisenberg limit. To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex N00N states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with N00N states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a deterministic phase estimation scheme based on a source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the conventional Heisenberg limit as well as the performance of a pure N00N state protocol. Using a high-efficiency setup with a total loss of about 11%, we achieve a Fisher information of 15.8(6)  rad^{-2} per photon-a significant increase in performance compared to state of the art and beyond an ideal six photon N00N state scheme. This work represents an important achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.

Extreme Concentration and Nanoscale Interaction of Light

Concentrating light strongly calls for appropriate polarization patterns of the focused light beam and for up to a full 4π solid angle geometry. Focusing on the extreme requires efficient coupling to nanostructures of one kind or another via cylindrical vector beams having such patterns, the details of which depend on the geometry and property of the respective nanostructure. Cylindrical vector beams can not only be used to study a nanostructure, but also vice versa. Closely related is the discussion of topics such as the ultimate diffraction limit, a resonant field enhancement near nanoscopic absorbers, as well as speculations about nonresonant field enhancement, which, if it exists, might be relevant to pair production in vacuum. These cases do require further rigorous simulations and more decisive experiments. While there is a wide diversity of scenarios, there are also conceptually very different models offering helpful intuitive pictures despite this diversity.

Coherent characterisation of a single molecule in a photonic black box

Extinction spectroscopy is a powerful tool for demonstrating the coupling of a single quantum emitter to a photonic structure. However, it can be challenging in all but the simplest of geometries to deduce an accurate value of the coupling efficiency from the measured spectrum. Here we develop a theoretical framework to deduce the coupling efficiency from the measured transmission and reflection spectra without precise knowledge of the photonic environment. We then consider the case of a waveguide interrupted by a transverse cut in which an emitter is placed. We apply that theory to a silicon nitride waveguide interrupted by a gap filled with anthracene that is doped with dibenzoterrylene molecules. We describe the fabrication of these devices, and experimentally characterise the waveguide coupling of a single molecule in the gap.

The authors develop a method to measure the coupling between a single photon source and any arbitrary photonic structure having constant density of electromagnetic states over the linewidth of the emitter. They demonstrate this method by an experiment on a single molecule coupled to an interrupted nanophotonic waveguide.

Laser-Induced Frequency Tuning of Fourier-Limited Single-Molecule Emitters

The local interaction of charges and light in organic solids is the basis of distinct and fundamental effects. We here observe, at the single-molecule scale, how a focused laser beam can locally shift by hundreds of times their natural line width and, in a persistent way, the transition frequency of organic chromophores cooled at liquid helium temperature in different host matrices. Supported by quantum chemistry calculations, the results can be interpreted as effects of a photoionization cascade, leading to a stable electric field, which Stark-shifts the molecular electronic levels. The experimental observation is then applied to a common challenge in quantum photonics, i.e., the independent tuning and synchronization of close-by quantum emitters, which is desirable for multiphoton experiments. Five molecules that are spatially separated by about 50 μm and originally 20 GHz apart are brought into resonance within twice their line width. This tuning method, which does not require additional fabrication steps, is here independently applied to multiple emitters, with an emission line width that is only limited by the spontaneous decay and an inhomogeneous broadening limited to 1 nm. The system hence shows promise for photonic quantum technologies.

Collective Shift in Resonant Light Scattering by a One-Dimensional Atomic Chain

We experimentally study resonant light scattering by a one-dimensional randomly filled chain of cold two-level atoms. By a local measurement of the light scattered along the chain, we observe constructive interferences in light-induced dipole-dipole interactions between the atoms. They lead to a shift of the collective resonance despite the average interatomic distance being larger than the wavelength of the light. This result demonstrates that strong collective effects can be enhanced by structuring the geometrical arrangement of the ensemble. We also explore the high intensity regime where atoms cannot be described classically. We compare our measurement to a mean-field, nonlinear coupled-dipole model accounting for the saturation of the response of a single atom.

Nanofiber-based high-Q microresonator for cryogenic applications

We demonstrate a cryo-compatible, fully fiber-integrated, alignment-free optical microresonator. The compatibility with low temperatures expands its possible applications to the wide field of solid-state quantum optics, where a cryogenic environment is often a requirement. At a temperature of 4.6 K we obtain a quality factor of (9.9 ± 0.7) × 106. In conjunction with the small mode volume provided by the nanofiber, this cavity can be either used in the coherent dynamics or the fast cavity regime, where it can provide a Purcell factor of up to 15. Our resonator is therefore suitable for significantly enhancing the coupling between light and a large variety of different quantum emitters and due to its proven performance over a wide temperature range, also lends itself for the implementation of quantum hybrid systems.

Shifting the phase of a coherent beam with a 174 Yb + ion: influence of the scattering cross section

We discuss and measure the phase shift imposed onto a radially polarized light beam when focusing it onto an 174 Yb + ion. In the derivation of the expected phase shifts, we include the properties of the involved atomic levels. Furthermore, we emphasize the importance of the scattering cross section and its relation to the efficiency for coupling the focused light to an atom. The phase shifts found in the experiment are compatible with the expected ones when accounting for known deficiencies of the focusing optics and the motion of the trapped ion at the Doppler limit of laser cooling (Hänsch and Schawlow in Opt Commun 13:68-69, 1975).

Quadrature Demodulation of a Quantum Dot Optical Response to Faint Light Fields

The amplitude and phase of a material's nonlinear optical response provide insight into the underlying electronic dynamics that determine its optical properties. Phase-sensitive nonlinear spectroscopy techniques are widely implemented to explore these dynamics through demodulation of the complex optical signal field into its quadrature components; however, complete reconstruction of the optical response requires measuring both the amplitude and phase of each quadrature, which is often lost in standard detection methods. Here, we implement a heterodyne-detection scheme to fully reconstruct the amplitude and phase response of spectral hole-burning from InAs/GaAs charged quantum dots. We observe an ultra-narrow absorption profile and a corresponding dispersive lineshape of the phase, which reflect the nanosecond optical coherence time of the charged exciton transition. Simultaneously, the measurements are sensitive to electron spin relaxation dynamics on a millisecond timescale, as this manifests as a magnetic-field dependent delay of the amplitude and phase modulation. Appreciable amplitude modulation depth and nonlinear phase shift up to ~0.09×π radians (16°) are demonstrated, providing new possibilities for quadrature modulation at faint photon levels with several independent control parameters, including photon number, modulation frequency, detuning, and externally applied fields.

Quantum scattering theory of a single-photon Fock state in three-dimensional spaces

A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.

Large phase-by-phase modulations in atomic interfaces

Phase-resonant closed-loop optical transitions can be engineered to achieve broadly tunable light phase shifts. Such a novel phase-by-phase control mechanism does not require a cavity and is illustrated here for an atomic interface where a classical light pulse undergoes radian level phase modulations all-optically controllable over a few micron scale. It works even at low intensities and hence may be relevant to new applications of all-optical weak-light signal processing.

Coherent interaction of light and single molecules in a dielectric nanoguide

Many of the currently pursued experiments in quantum optics would greatly benefit from a strong interaction between light and matter. Here, we present a simple new scheme for the efficient coupling of single molecules and photons. A glass capillary with a diameter of 600 nm filled with an organic crystal tightly guides the excitation light and provides a maximum spontaneous emission coupling factor (β) of 18% for the dye molecules doped in the organic crystal. A combination of extinction, fluorescence excitation, and resonance fluorescence spectroscopy with microscopy provides high-resolution spatiospectral access to a very large number of single molecules in a linear geometry. We discuss strategies for exploring a range of quantum-optical phenomena, including polaritonic interactions in a mesoscopic ensemble of molecules mediated by a single mode of propagating photons.

Energy-redistribution signatures in transmission microscopy of Rayleigh and Mie particles

We describe the transmission characteristics for the interaction of an arbitrary beam with (possibly multilayered) spherical particles of arbitrary size and electric permeability. Within the generalized Lorenz-Mie theory, expressions that generalize the total cross sections to their fractional counterparts are presented, which allow for an analytic quantification of transmission signals, both on-axis and off-axis. For Gaussian (Davis) beams, the relative angular domain of collection as compared to the beam's angle of divergence determines sensitively the shape and magnitude of the interference signal. Depending on the particle's position within the beam, the transmission signatures related to a pure energy redistribution as well as to accompanying absorption are discussed for Rayleigh particles in terms of their complex-valued polarizability. Implications for positioning, temperature control, spectroscopy, and optimized extinction measurements are discussed.

Spectral interferometric microscopy reveals absorption by individual optical nanoantennas from extinction phase

Optical antennas transform light from freely propagating waves into highly localized excitations that interact strongly with matter. Unlike their radio frequency counterparts, optical antennas are nanoscopic and high frequency, making amplitude and phase measurements challenging and leaving some information hidden. Here we report a novel spectral interferometric microscopy technique to expose the amplitude and phase response of individual optical antennas across an octave of the visible to near-infrared spectrum. Although it is a far-field technique, we show that knowledge of the extinction phase allows quantitative estimation of nanoantenna absorption, which is a near-field quantity. To verify our method we characterize gold ring-disk dimers exhibiting Fano interference. Our results reveal that Fano interference only cancels a bright mode’s scattering, leaving residual extinction dominated by absorption. Spectral interference microscopy has the potential for real-time and single-shot phase and amplitude investigations of isolated quantum and classical antennas with applications across the physical and life sciences.

Absorption by an optical nanoantenna determines its interaction strength with light, yet this quantity is hidden from conventional spectroscopy. Gennaro et al. now demonstrate a spectroscopic technique that reveals a nanoantenna’s absorption by recovering its amplitude and phase response.

Antiresonance phase shift in strongly coupled cavity QED

We investigate phase shifts in the strong coupling regime of single-atom cavity quantum electrodynamics. On the light transmitted through the system, we observe a phase shift associated with an antiresonance and show that both its frequency and width depend solely on the atom, despite the strong coupling to the cavity. This shift is optically controllable and reaches 140°--the largest ever reported for a single emitter. Our result offers a new technique for the characterization of complex integrated quantum circuits.

Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase

We study the role of geometry dependent phase shifts in stimulated coherent spectroscopy, a special class of heterodyne optical spectroscopy techniques. We generalize the theoretical description of stimulated spectroscopy to include spatial phase effects, and consider the measured material response for several representative excitation and detection configurations. Using stimulated Raman scattering microscopy as an example, we show that different components of the material response are measured depending the position of the object in focus. We discuss the implications of the position dependent phase in stimulated coherent microscopy and point out a detection configuration in which its effects are minimized.

Controllable optical phase shift over one radian from a single isolated atom

Fundamental optics such as lenses and prisms work by applying phase shifts of several radians to incoming light, and rapid control of such phase shifts is crucial to telecommunications. However, large, controllable optical phase shifts have remained elusive for isolated quantum systems. We have used a single trapped atomic ion to induce and measure a large optical phase shift of 1.3±0.1 radians in light scattered by the atom. Spatial interferometry between the scattered light and unscattered illumination light enables us to isolate the phase shift in the scattered component. The phase shift achieves the maximum value allowed by atomic theory over the accessible range of laser frequencies, pointing out new opportunities in microscopy and nanophotonics. Single-atom phase shifts of this magnitude open up new quantum information protocols, in particular long-range quantum phase-shift-keying cryptography.

Light-matter interaction in free space

We review recent experimental advances in the field of efficient coupling of single atoms and light in free space. Furthermore, a comparison of efficient free space coupling and strong coupling in cavity quantum electrodynamics (QED) is given. Free space coupling does not allow for observing oscillatory exchange between the light field and the atom which is the characteristic feature of strong coupling in cavity QED. Like cavity QED, free space QED does, however, offer full switching of the light field, a 180° phase shift conditional on the presence of a single atom as well as 100% absorption probability of a single photon by a single atom. Furthermore, free space cavity QED comprises the interaction with a continuum of modes.

Maximal refraction and superluminal propagation in a gaseous nanolayer

We present an experimental measurement of the refractive index of high density Rb vapor in a gaseous atomic nanolayer. We use heterodyne interferometry to measure the relative phase shift between two copropagating laser beams as a function of the laser detuning and infer a peak index n=1.26±0.02, close to the theoretical maximum of 1.31. The large index has a concomitant large index gradient creating a region with steep anomalous dispersion where a subnanosecond optical pulse is advanced by >100 ps over a propagation distance of 390 nm, corresponding to a group index n(g)=-(1.0±0.1)×10(5), the largest negative group index measured to date.

Electric field induced fluorescence modulation of single molecules in PMMA based on electron transfer

We present a method to modulate the fluorescence of non-polar single squaraine-derived rotaxanes molecules embedded in a polar poly(methyl methacrylate) (PMMA) matrix under an external electric field. The electron transfer between single molecules and the electron acceptors in a PMMA matrix contributes to the diverse responses of fluorescence intensities to the electric field. The observed instantaneous and non-instantaneous electric field dependence of single-molecule fluorescence reflects the redistribution of electron acceptors in PMMA induced by electronic polarization and orientation polarization of polar polymer chains in an electric field.

Coupling of ultrathin tapered fibers with high-Q microsphere resonators at cryogenic temperatures and observation of phase-shift transition from undercoupling to overcoupling

We cooled ultrathin tapered fibers to cryogenic temperatures and controllably coupled them with high-Q microsphere resonators at a wavelength close to the optical transition of diamond nitrogen vacancy centers. The 310-nm-diameter tapered fibers were stably nanopositioned close to the microspheres with a positioning stability of approximately 10 nm over a temperature range of 7-28 K. A cavity-induced phase shift was observed in this temperature range, demonstrating a discrete transition from undercoupling to overcoupling.