We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the Poincaré space providing a full quantum mechanical characterization of the measured polarization state.

We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering-gallery-mode resonator made of lithium niobate. A conversion efficiency of 9% is achieved at 30 mu W in-coupled continuous wave pump power. The observed saturation pump power of 3.2 mW is almost 2 orders of magnitude lower than the state-of-the-art value. This suggests an application of our frequency doubler as a source of nonclassical light requiring only a low-power pump, which easily can be quantum noise limited. Our theoretical analysis of the three-wave mixing in a whispering-gallery-mode resonator provides the relative conversion efficiencies for frequency doubling in various modes

Optical parametric down-conversion has proven to be a valuable source of nonclassical light. The process is inherently able to produce twin-beam correlations along with individual intensity squeezing of either parametric beam, when pumped far above threshold. Here, we present for the first time the direct observation of intensity squeezing of -1.2  dB of each of the individual parametric beams in parametric down-conversion by use of a high quality whispering-gallery-mode disk resonator. In addition, we observed twin-beam quantum correlations of -2.7  dB with this cavity. Such resonators feature strong optical confinement and offer tunable coupling to an external optical field. This work exemplifies the potential of crystalline whispering-gallery-mode resonators for the generation of quantum light. The simplicity of this device makes the application of quantum light in various fields highly feasible.

It has been predicted and experimentally demonstrated that by injecting squeezed light into an optomechanical device it is possible to enhance the precision of a position measurement. Here, we present a fundamentally different approach where the squeezing is created directly inside the cavity by a nonlinear medium. Counterintuitively, the enhancement of the signal to noise ratio works by de-amplifying precisely the quadrature that is sensitive to the mechanical motion without losing quantum information. This enhancement works for systems with a weak optomechanical coupling and/or strong mechanical damping. This could allow for larger mechanical bandwidth of quantum limited detectors based on optomechanical devices. Our approach can be straightforwardly extended to Quantum Non Demolition (QND) qubit detection.Recent progress in cavity optomechanics [1,2] has been so exceptional that the precision of a position measurement has been pushed until the limit set by the principles of quantum mechanics, the so-called Standard Quantum Limit (SQL) [3][4][5]. A measurement precision close to the SQL has been demonstrated in optomechanical devices with cavities both in the optical [6][7][8] and in the microwave [9] domain. Optomechanical position detection is not only of fundamental interest but finds also application in acceleration [10,11], magnetic field [12,13], and force detectors [14? ]. Thus, an important goal for the future is to develop new techniques to enhance its precision on different optomechanical platforms. Seminal efforts have focused on gravitational wave detection in optomechanical interferometers [16][17][18][19][20]. The standard route to enhance the detection precision consists in injecting squeezed light into the interferometer [16,17,21]. This technique has recently been demonstrated in the Laser Interferometer Gravitational Wave Observatory (LIGO) [22] and in a cavity optomechanics setup [23]. Externally generated squeezed light could also find application in QND qubit state detection [24,25]. Alternatively, one can enhance a dispersive quantum measurement by generating the appropriate squeezing directly inside the cavity by means of a Kerr nonlinearity [18,20,21,[26][27][28], by the dissipative optomechanical interaction [29], or potentially, by exploiting the ponderomotive squeezing [30][31][32].In this letter, we propose a new pathway to precision enhancement in optomechanical detection. In our approach, a nonlinear cavity is operated as a phase-sensitive parametric amplifier, as shown in Fig. 1. It amplifies a seed laser beam and its intensity fluctuations. Simultaneously, it de-amplifies the phase quadrature where the mechanical vibrations are imprinted. At first sight it might appear counter-intuitive that de-amplification can improve a (quantum) measurement. Here, we suggest that it might be worth to de-amplify a signal if the noise is suppressed by a larger factor thus obtaining a net enhancement of the signal to noise ratio. Indeed, our analysis shows that for optomechanical position detect...

Quantum systems such as, for example, photons, atoms, or Bose-Einstein condensates, prepared in complex states where entanglement between distinct degrees of freedom is present, may display several intriguing features. In this Letter we introduce the concept of such complex quantum states for intense beams of light by exploiting the properties of cylindrically polarized modes. We show that already in a classical picture the spatial and polarization field variables of these modes cannot be factorized. Theoretically it is proven that by quadrature squeezing cylindrically polarized modes one generates entanglement between these two different degrees of freedom. Experimentally we demonstrate amplitude squeezing of an azimuthally polarized mode by exploiting the nonlinear Kerr effect in a specially tailored photonic crystal fiber. These results display that such novel continuous-variable entangled systems can, in principle, be realized.

Free-space optical communication links are promising channels for establishing secure quantum communication. Here we study the transmission of nonclassical light through a turbulent atmospheric link under diverse weather conditions, including rain or haze. To include these effects, the theory of light transmission through atmospheric links in the elliptic-beam approximation presented by Vasylyev et al. [D. Vasylyev et al., Phys. Rev. Lett. 117, 090501 (2016); arXiv:1604.01373] is further generalized. It is demonstrated, with good agreement between theory and experiment, that low-intensity rain merely contributes additional deterministic losses, whereas haze also introduces additional beam deformations of the transmitted light. Based on these results, we study theoretically the transmission of quadrature squeezing and Gaussian entanglement under these weather conditions.

In whispering gallery mode (WGM) resonators light is guided by continuous total internal reflection along a curved surface. Fabricating such resonators from an optically nonlinear material one takes advantage of their exceptionally high quality factors and small mode volumes to achieve extremely efficient optical frequency conversion. Our analysis of the phase matching conditions for optical parametric down conversion (PDC) in a spherical WGM resonator shows their direct relation to the sum rules for photons' angular momenta and predicts a very low parametric oscillations threshold. We realized such an optical parametric oscillator (OPO) based on naturally phase-matched PDC in Lithium Niobate. We demonstrated a single-mode, strongly non-degenerate OPO with a threshold of 6.7 µW and linewidth under 10 MHz. This work demonstrates the remarkable capabilities of WGM-based OPOs and opens the perspectives for their applications in quantum and nonlinear optics, particularly for the generation of squeezed light. WGM resonators have found applications in many areas of photonics, including quantum and nonlinear optics, spectroscopy, biophysics and optomechanics (see [1][2][3] and references therein). These areas benefit from a high quality factor (Q) and strong field confinement of WGM resonators in two different aspects. First, WGM resonators provide strong coupling of the confined field to other systems such as quantum dots [4], atoms [5], mechanical oscillators [6] or other cavities [7]. Second, WGM resonators provide strong nonlinear coupling between optical fields. Here the possibilities lie in utilizing either third order nonlinear effects in fused silica [8][9][10], or nonlinear effects in crystalline materials [11][12][13][14].In this letter we demonstrate optical parametric oscillations with extremely low thresholds and narrow linewidths in a crystalline WGM disk resonator. This is achieved by taking advantage of the strong second-order optical nonlinearity of Lithium Niobate and of the high quality factor of our WGM resonator, limited by the material absorption only. This research is motivated by the perspective to develop a miniature, stable, narrow-line tunable OPO for spectroscopy applications, to study the OPO dynamics far above the threshold, and by the wide and successful use of conventional OPOs for the generation of non-classical light.To achieve efficient parametric processes in a nonlinear material phase matching conditions have to be fulfilled. For parametrically interacting plane waves in a bulk material, these phase matching conditions correspond to conservation of energy and linear momentum of pump (p), signal (s) and idler (i) photons:In spherical geometry the orbital angular momentum of the photons is conserved, along with the energy. This gives rise to WGM selection rules for the PDC process and determines the OPO threshold in-coupled pump power for various modes [15]:where c is the speed of light, λ p is the pump wavelength n = n e (λ p ) = n o (λ s ) is the phase-matched refractive index, and ...

We present a quantum communication experiment conducted over a point-topoint free-space link of 1.6 km in urban conditions. We study atmospheric influences on the capability of the link to act as a continuous-variable (CV) quantum channel. Continuous polarization states (that contain the signal encoding as well as a local oscillator (LO) in the same spatial mode) are prepared and sent over the link in a polarization multiplexed setting. Both signal and LO undergo the same atmospheric fluctuations. These are intrinsically autocompensated which removes detrimental influences on the interferometric visibility. At the receiver, we measure the Q-function and interpret the data using the framework of effective entanglement (EE). We compare different state amplitudes and alphabets (two-state and four-state) and determine their optimal working points with respect to the distributed EE. Based on the high entanglement transmission rates achieved, our system indicates the high potential of atmospheric links in the field of CV quantum key distribution. 6 Contributed equally to this work.Quantum communication refers to the distribution of quantum states between two parties via a quantum channel. With regard to this, it is crucial that this quantum channel preserves the quantum properties of the distributed states. The most common channel implementations are optical fibers and free space. The latter offers great flexibility in terms of infrastructure establishment and links to moving objects are also feasible, see e.g. [1]. For a review of representative free-space quantum communication experiments see [2].Quantum key distribution (QKD) [3,4] is probably the most practical branch of quantum communication and concerns the establishment of a secret key jointly between two legitimate parties, Alice and Bob. As the security is based on the laws of quantum mechanics, in principle information theoretic-security can be achieved [4].Free-space QKD over a real atmospheric channel was first demonstrated in 1996 [5]. Since then, a number of prepare-and-measure as well as entanglement based schemes have been implemented in free space; the longest distance so far achieved on Earth is 144 km [6,7]. Nowadays, even quantum communication between earth and space is being conceived [8][9][10][11][12][13][14]. All of the systems so far referred to here have one major aspect in common: they are based on discrete quantum variables and use single photon threshold ('click') detectors, which involves spatial, spectral and/or temporal filtering in order to reduce background noise (see e.g. [15,16] for the first point-to-point demonstrations of free-space QKD in daylight).As already shown by Bennett [17], any two non-orthogonal quantum states suffice to ensure secure key distribution. This paved the way for continuous-variable (CV) protocols (for a review see [18,19]), based on a different approach: performing homodyne measurements on weak coherent states with the help of a bright local oscillator (LO). Generally, homodyne detectors offer immunity to st...