The effect of errors and detector noise on sensitive detection of chirp and pulse asymmetry of ultrashort laser pulses from interferometric autocorrelation signals

We have studied the effect of various types of systematic and non-systematic errors on unbalanced spectrally modified interferometric autocorrelation signals for detection of pulse chirp and asymmetry of ultrashort laser pulses. The effect of systematic errors arising due to limited number of data points per fringe, scan rate etc, and non-systematic errors due to phase noise, additive noise, multiplicative noise and quantization of interferometric autocorrelation (IAC) signals is illustrated using a linearly chirped asymmetric laser pulse. It is seen that the spectrally modified IAC signals based on difference of normalized envelope functions corresponding to different frequencies are not much sensitive to various noises, permitting their use for sensitive detection of pulse chirp and asymmetry. The analysis is supported by experimentally recorded IAC signals under different conditions.     

Interaction of a two-level atom with squeezed light

We consider a degenerate parametric oscillator whose cavity contains a two-level atom. Applying the Heisenberg and quantum Langevin equations, we calculate in the bad-cavity limit the mean photon number, the quadrature variance, and the power spectrum for the cavity mode in general and for the signal light and fluorescent light in particular. We also obtain the normalized second-order correlation function for the fluorescent light. We find that the presence of the two-level atom leads to a decrease in the degree of squeezing of the signal light. It so turns out that the fluorescent light is in a squeezed state and the power spectrum consists of a single peak only.     

Quantum interference of multimode two-photon pairs with a Michelson interferometer

We perform the second-order quantum interference experiment with the multimode photon pairs produced via an optical parametric oscillator far below threshold in a Michelson interferometer, measure the second-order correlation function in different cases. We find when the interferometer is highly unbalanced, the shape of the second-order correlation function is clearly dependent on the path length difference between two interfering beams. On the contrary, when the interferometer is nearly balanced, beside its height, the shape of the second-order correlation function is independent on the small path length difference. The second-order correlation function shows a multipeaked structure in both cases. All experimental results agree very well with the theoretical predictions.     

Quantum theory of super-resolution for optical systems with circular apertures

We present the two-dimensional quantum theory of super-resolution, applicable for a large variety of optical systems with circular pupils. Our theory is formulated in terms of circular prolate spheroidal functions which form the eigen basis of two-dimensional imaging system with circular pupils. We provide, in particular, analytical and numerical results for the point-spread function characterizing reconstruction of optical objects with super-resolution from diffraction-limited images. We evaluate the super-resolution factor as a function of the signal-to-noise ratio in the input object for coherent light and multimode squeezed light.     

Scheme for direct measurement of the Wigner characteristic function of traveling fields

We present a proposal to measure field states for traveling modes. The scheme leads, in a simple and direct way, to the characteristic function of the state, yielding the determination of the Wigner function without a demanding data analysis. We employ a Mach-Zehnder interferometer including an auxiliary nonlinear medium in one arm. Analogies with other proposals to reconstruct states of stationary fields and trapped atoms are discussed.     

Scheme for Direct Measurement of the Wigner Function via Resonant Interaction

We propose a scheme for direct measurement of the Wigner function for a cavity mode. In the scheme the cavity field resonantly interacts with an atomic ensemble. Under certain conditions, the state of the cavity mode is transferred to the atomic system. After a displacement the measurement of the parity of the atomic excitation number directly yields the Wigner function of the initial state of the cavity mode.     

Wigner function of an arbitrary-photon-catalyzed optical coherent state

In this paper, we give a detailed derivation process for the Wigner function (WF) of an arbitrary photon-catalyzed optical coherent state (APCOCS), which can be generated via interference between coherent and Fock states using quantum catalysis. We find that the WF is non-Gaussian and is related to the two-variable Hermite polynomial of the relative parameters, such as the coherent field strength, the number of catalyst photons and the control ratio of the beam splitter. It showed that the APCOCS created a wide range of nonclassical properties.     

Role of spatial mode function in the presence of two-atom events in a micromaser

In this paper, we discuss the effects of spatial mode function in an one-photon micromaser in the presence of two-atom events. It is shown that two-atom events allow us a possibility to study the effects of different cavity eigenmodes in a micromaser. We find that squeezing properties of the radiation field depend upon the parity (odd or even) and order (lower or higher) of cavity eigenmodes. For example, squeezing can be obtained for odd-order cavity eigenmodes which completely vanishes for even-order modes. Our results also show that effects similar to self-induced transparency are never obtained in the presence of two-atom events. Finally, we consider the effect of pump fluctuations and cavity losses in our system.     

Generation of a Non-Classical Correlated Photon Pair via Spontaneous Four-Wave Mixing in a Cold Atomic Ensemble

Counter propagated write and read lasers can be used to generate non-classical correlated photon pairs in an atomic ensemble. We experimentally investigate how the detuning of the write laser affects the non-classical correlation function between the Stokes photon and the anti-Stokes photon, which are generated via a spontaneous four-wave mixing process using an off-axis configuration in a cold 85 Rb atomic ensemble. The change of the time-resolved second-order correlated function between the Stokes and anti-Stokes photons is presented. The experimental result suggests that a suitable choice of detuning should be considered in such an experiment.     

Ghost diffraction, lensless system and 2-f system

We investigate two imaging schemes, lensless system and 2-f system which are used to implement ghost diffraction. It is shown that the two schemes have similar intensity fluctuation correlation functions which both realize the function of the Fourier-transform imaging, and the diffraction pattern is in agreement with that in the classical wave optics. The difference of the imaging visibility in the two systems is also discussed.     

Wigner function and tomogram of the excited squeezed vacuum state

The excited squeezed light (ESL) can be the outcome of interaction between squeezed light probe and excited atom, which can explore the status and the structure of the atom. We calculate the Wigner function and tomogram of ESL that may be comparable to the experimental measurement of quadrature-amplitude distribution for the light field obtained using balanced homodyne detection. The method of calculation seems new.     

Conditional displacement operator for traveling fields

We show that the conditional displacement operator acting upon arbitrary states of traveling waves can be well approximated by the action of a Kerr-medium placed between two beam splitters whose respective second ports are fed by highly excited coherent states. The scheme is deterministic, since it does not employ any detection event. Applications for generation of nonclassical states and measurement of Wigner function of arbitrary states are also considered.     

Eigenmode expansion of the polarization for a spherical sample of two-level atoms

We derive pseudo-orthogonality relations for both the magnetic and electric eigenmodes of a system of two-level atoms in a sphere configuration. We verify numerically that an arbitrary vector field can be reconstructed to a great accuracy from these eigenmode expansions. We apply this eigenmode analysis to explore superradiance from a sphere with initially uniform polarization.     

Anomalous Effects of Driving Field Linewidth on a One-Atom Dressed-State Laser

We examine the effects of driving field linewidth on a one-atom dressed state laser. Unexpectedly, the linewidth leads to anomalous effects on the cavity field. The mean photon number of the cavity field is raised or the normalized variance is reduced to a certain degree as the linewidth increases for an appropriate range of parameters. The responsible mechanism is attributed to the fluctuation-induced modification of the electromagnetic reservoir where the atom stays.     

Theory of nonlinear optical response of gauge invariant currents to linear and nonlinear couplings

When a gauge field interacts with a quantum condensed matter system, at first order of the gauge field it couples to the current operator of the electrons. Higher orders of the gauge field couple to electrons through other operators such as the stress tensor, etc. On the other hand, when one performs a measurement on a quantum system, not only the current operator, but also stress tensor operator of the electrons, etc. are hidden in the measurement, as they contribute to the gauge invariant current. We formulate a general problem of nonlinear optical response of the gauge invariant currents in presence of nonlinear couplings. We show that the new couplings along with new responses arising from field current have a very simple structure which can be formulated as time ordered multi-particle correlation functions. We also obtain their Lehman representation and thereby show that one need not use non-equilibrium formulations to deal with them. These new correlation functions suggest that in nonlinear optical response many new processes are possible. The experimental detection of the new terms in the current operator, and application corresponding multi-photon processes needs further theoretical and experimental investigations.     

Evolution of population in an equispaced three-level ladder-type atomic system

Transient response of nearly equispaced three-level ladder-type atomic system with a broad-band squeezed vacuum (SV) is investigated. We focus our attention in the interplay between the quantum interference and the squeezed field on the population distribution. It is shown that an atomic population inversion can be attained on one of the optical transitions due to the SV. Additionally, we show, with the proper value of the relative phase, the SV can also lead to unexpected population inversion on the transition between two different levels.     

Stretched Exponential Relaxation in Disordered Complex Systems： Fractal Time Random Walk Model

We have analytically derived the relaxation function for one-dimensional disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the relaxation function has stretched exponential, i.e. the Kohlrausch-Williams-Watts character for a fractal time random walk process.