e-xiang Xu

Quantum interference between an arbitrary-photon Fock state and a coherent state

Using the phase space method, we study the quantum interference through a Mach–Zehnder interferometer with an arbitrary-photon Fock state and a coherent state as two inputs. The statistical properties, in terms of the Wigner function, average photon number, photon number distribution and parity, are derived analytically for the field of the individual output port. These results indicate that the output state is actually a statistical mixture between a bunch of Fock state and coherent states. In addition, the phase sensitivity is also examined by using the detection scheme of intensity difference measurement.

Goos-Hänchen-like shift of three-level matter wave incident on Raman beams.

When a three-level atomic wavepacket is obliquely incident on a medium slab consisting of two far-detuned laser beams, there exists lateral shift between reflection and incident points at the surface of a medium slab, analogous to optical Goos-Hänchen effect. We evaluate lateral shifts for reflected and transmitted waves via expansion of reflection and transmission coefficients, in contrast to the stationary phase method. Results show that lateral shifts can be either positive or negative dependent on the incident angle and the atomic internal state. Interestingly, a giant lateral shift of transmitted wave with high transmission probability is observed, which is helpful to observe such lateral shifts experimentally. Different from the two-level atomic wave case, we find that quantum interference between different atomic states plays crucial role on the transmission intensity and corresponding lateral shifts.

Some Evolution Formulas on the Optical Fields Propagation in Realistic Environments

Evolution formulas of the density operator, the photon number distribution, and the Wigner function are derived for the problem on the optical fields propagation in realistic environments. Using the idea “reservoir modeled by beam splitter (BS)” and the Weyl expansion of the density operator, we obtain these formulas cleverly, which are very useful for quantum optics and quantum statistics. As an application, we study the time evolution of the photon number distribution and the Wigner function for single-photon-added coherent state in thermal environment.

M Times Photon Subtraction-Addition Coherent Superposition Operated Odd-Schrődinger-cat State: Nonclassicality and Decoherence

We introduce a new non-Gaussian state (MCSO-OSCS), generated by m times coherent superposition operation acos θ + a†sin θ (MCSO) on odd-Schrődinger-cat state |α0〉 − | − α0〉(OSCS), whose normalized constant is shown to be related to Hermite polynomials. We investigate the nonclassical properties of the MCSO-OSCS through Mandel’s Q-parameter, quadrature squeezing, the photocount distribution and Wigner function (WF), which is turned out to be influenced by parameters m, θ and α0. Especially the volume of negative region of WF could increase through controlling the parameters m, θ and α0. We also investigate the decoherence of the MCSO-OSCS in terms of the fadeaway of the negativity of WF in a thermal environment.

FRACTIONAL HADAMARD TRANSFORM WITH CONTINUOUS VARIABLES IN THE CONTEXT OF QUANTUM OPTICS

We introduce the quantum fractional Hadamard transform with continuous variables. It is found that the corresponding quantum fractional Hadamard operator can be decomposed into a single-mode fractional operator and two single-mode squeezing operators. This is extended to the entangled case by using the bipartite entangled state representation. The new transformation presents more flexibility to represent signals in the fractional Hadamard domain with extra freedom provided by an angle and two-squeezing parameters.