Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.

Observation of squeezed states generated by four-wave mixing in an optical cavity

Preface 1. Planck's radiation law and the Einstein coefficients 2. Quantum mechanics of the atom-radiation interaction 3. Classical theory of optical fluctuations and coherence 4. Quantization of the radiation field 5. Single-mode quantum optics 6. Multimode and continuous-mode quantum optics 7. Optical generation, attenuation and amplification 8. Resonance fluorescence and light scattering 9. Nonlinear quantum optics Index

The quantum theory of light.

Abstract This article reviews recent progress leading to the generation of optical vortex beams. After introducing the basics of optical vortex beams and their promising applications, we summarized different approaches for optical vortex generation by discrete components and laser cavities. We place particular emphasis on the recent development of vortex generation by the planar phase plates, which are able to engineer a spiral phasefront via dynamic or geometric phase in nanoscale, and highlight the independent operation of these two different phases which leads to a multifunctional optical vortex beam generation and independent spin-orbit interaction. We also introduced the recent progress on vortex lasing, including vortex beam generation from the output of bulk lasers by modification of conventional laser cavities with phase elements and from integrated on-chip microlasers. Similar approaches are also applied to generate fractional vortex beams carrying fractional topological charge. The advanced technology and approaches on design and nanofabrications enable multiple vortex beams generation from a single device via multiplexing, multicasting, and vortex array, open up opportunities for applications on data processing, information encoding/decoding, communication and parallel data processing, and micromanipulations.

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Recent advances on optical vortex generation

We discuss nonclassical properties of single-photon subtracted squeezed vacuum states and study its decoherence under different models, We find that the state is especially robust under phase diffusion model though its phase properties are lost.

Nonclassicality and decoherence of photon-subtracted squeezed states

Beams with fast and continuously-tunable orbital angular momentum (OAM) have potential applications in classical and quantum optical communications, sensing, and in the study of beam propagation through turbulence. An acousto-optical deflector (AOD) is a sophisticated, well-studied device that continuously and rapidly tunes the deflection angle of an output beam. The log-polar HOBBIT setup can generate beams with OAM by wrapping elliptically shaped Gaussian beams with linear phase tilt to a ring. By combining the linear tilted output from the AOD with the OAM generation capabilities of the HOBBIT system, the generated OAM modes become continuously tunable at high speeds measured on the order of 400 kHz.

Rapidly tunable orbital angular momentum (OAM) system for higher order Bessel beams integrated in time (HOBBIT)

Continuous‐Variable Entanglement and Wigner‐Function Negativity via Adding or Subtracting Photons

We investigate a new class of nondiffracting optical beams carrying fractional orbital angular momentum (FOAM Bessel beams), which can be constructed by modifying the phase step of the spiral phase plate in a setup originally for the generation of traditional Bessel beams. The FOAM Bessel beams have entirely stable vortex structures, and form an infinite number of orthogonal and complete subsets for monochromatic scalar light in free space. With the advantages of structural stability and orthogonality-completeness, the FOAM Bessel beams are expected to be useful for study and application in various fields of modern optics.

Nondiffracting light beams carrying fractional orbital angular momentum

The braiding of two non-Abelian Majorana modes is important for realizing topological quantum computation. It can be achieved through tuning the coupling between the two Majorana modes to be exchanged and two ancillary Majorana modes. However, this coupling also makes the braiding subject to environment-induced decoherence. Here, we study the effects of decoherence on the diabatic errors in the braiding process for a set of time-dependent Hamiltonians with finite smoothness. To this end, we employ the master equation to calculate the diabatic excitation population for three kinds of decoherence processes. (1) Only pure dehasing: the scaling of the excitation population changed from ${T}^{\ensuremath{-}2k\ensuremath{-}2}$ to ${T}^{\ensuremath{-}1}$ ($k$ is the number of the Hamiltonian's time derivatives vanishing at the initial and final times) as the braiding duration $T$ exceeds a certain value. (2) Only relaxation: the scaling transforms from ${T}^{\ensuremath{-}2k\ensuremath{-}2}$ to ${T}^{\ensuremath{-}2}$ for $k=0$ and to ${T}^{\ensuremath{-}a}$ ($ag3$) for $kg0$. (3) Pure dephasing and relaxation: the original scaling switches to ${T}^{\ensuremath{-}1}$ first and then evolves to ${T}^{\ensuremath{-}2}$ in the adiabatic limit. Interestingly, the third scaling-varying style holds even when the expectation of pure dephasing rate is much smaller than that of the relaxation rate, which is attributed to the vanishing relaxation at the turning points of the braiding.

Effects of decoherence on diabatic errors in Majorana braiding

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.

Zhenshan Yang

Papers

Continuous‐Variable Entanglement and Wigner‐Function Negativity via Adding or Subtracting Photons

Nondiffracting light beams carrying fractional orbital angular momentum

Effects of decoherence on diabatic errors in Majorana braiding

Multi-variable special polynomials using an operator ordering method

Squeezed Hermite polynomial state: nonclassical features and decoherence behavior