In whispering gallery mode (WGM) resonator 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 oscillation threshold. We realized such an optical parametric oscillator (OPO) based on naturally phase-matched PDC in lithium niobate. We demonstrated a single-mode, strongly nondegenerate OPO with a threshold of 6: 7 mu W and linewidth under 10 MHz. This work demonstrates the remarkable capabilities of WGM-based OPOs.
Noise-powered probabilistic concentration of phase information
Mario A. Usuga,
Christian R. Mueller,
Christoffer Wittmann,
Petr Marek,
Radim Filip,
Christoph Marquardt,
Gerd Leuchs,
Ulrik L. Andersen
Phase-insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state(1-5). However, this fundamental noise penalty in amplification can be circumvented by resorting to a probabilistic scheme as recently proposed and demonstrated in refs 6-8. These amplifiers are based on highly non-classical resources in a complex interferometer. Here we demonstrate a probabilistic quantum amplifier beating the fundamental quantum limit using a thermal-noise source and a photon-number-subtraction scheme(9). The experiment shows, surprisingly, that the addition of incoherent noise leads to a noiselessly amplified output state with a phase uncertainty below the uncertainty of the state before amplification. This amplifier might become a valuable quantum tool in future quantum metrological schemes and quantum communication protocols.
A generator for unique quantum random numbers based on vacuum states
Christian Gabriel,
Christoffer Wittmann,
Denis Sych,
Ruifang Dong,
Wolfgang Mauerer,
Ulrik L. Andersen,
Christoph Marquardt,
Gerd Leuchs
Random numbers are a valuable component in diverse applications that range from simulations(1) over gambling to cryptography(2,3). The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics(4-11). However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique(12-15). Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators.
Naturally Phase-Matched Second-Harmonic Generation in a
Whispering-Gallery-Mode Resonator
J. U. Fuerst,
D. V. Strekalov,
D. Elser,
M. Lassen,
U. L. Andersen,
C. Marquardt,
G. Leuchs
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.
Assessing the Polarization of a Quantum Field from Stokes Fluctuations
A. B. Klimov,
G. Bjoerk,
J. Soederholm,
L. S. Madsen,
M. Lassen,
U. L. Andersen,
J. Heersink,
R. Dong,
Ch. Marquardt, et al.
We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincare sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.
We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasiparaxial photon beams in vacuum and reproduces the known results for classical beams when applied to coherent states of the field. Both the Poynting vector, alias the linear momentum, and the angular-momentum quantum operators of a light beam are calculated including contributions from first-order transverse derivatives. This permits a correct description of the energy flow in the beam and the natural emergence of both the spin and the angular momentum of the photons. We show that for collimated beams of light, orbital angular-momentum operators do not satisfy the standard commutation rules. Finally, we discuss the application of our theory to some concrete cases.
Continuous-variable entanglement distillation of non-Gaussian mixed
states
Ruifang Dong,
Mikael Lassen,
Joel Heersink,
Christoph Marquardt,
Radim Filip,
Gerd Leuchs,
Ulrik L. Andersen
Many different quantum-information communication protocols such as teleportation, dense coding, and entanglement-based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical network. The distribution of entanglement in such a network is, however, hampered by loss and noise that is inherent in all practical quantum channels. Thus, to enable faithful transmission one must resort to the protocol of entanglement distillation. In this paper we present a detailed theoretical analysis and an experimental realization of continuous variable entanglement distillation in a channel that is inflicted by different kinds of non-Gaussian noise. The continuous variable entangled states are generated by exploiting the third order nonlinearity in optical fibers, and the states are sent through a free-space laboratory channel in which the losses are altered to simulate a free-space atmospheric channel with varying losses. We use linear optical components, homodyne measurements, and classical communication to distill the entanglement, and we find that by using this method the entanglement can be probabilistically increased for some specific non-Gaussian noise channels.
Atmospheric channel characteristics for quantum communication with
continuous polarization variables
B. Heim,
D. Elser,
T. Bartley,
M. Sabuncu,
C. Wittmann,
D. Sych,
C. Marquardt,
G. Leuchs
We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100 m length on the flat roof of our institute's building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are auto-compensated. The LO also acts as a spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.
Contact
Research Group Christoph Marquardt
Max Planck Institute for the Science of Light Staudtstr. 2 91058 Erlangen, Germany
