Multimode polarization degree of mixture optical states in integrated directional couplers

Mixture multimode optical field classical states propagating in N?×?N integrated directional couplers are analyzed by using the density matrix formalism in a N-dimensional optical space. These mutimode optical fields present a kind of generalized polarization and accordingly a definition of a multimode polarization degree is proposed. It is based on the distance measure between a mixture state and an unpolarized state in a N-dimensional optical space so that in the case N=2 the standard polarization degree is recovered. It is shown that directional couplers can reduce or increase remarkably the multimode polarization degree of a mixture state. Likewise a simple measurement technique, based on Y junctions, of this multimode polarization degree is proposed. Finally all the results can be formally extended to the special case of multimode single photon quantum states.     

Optical field-strength generalized polarization of non-stationary quantum states in waveguiding photonic devices

A quantum analysis of the generalized polarization properties of multimode non-stationary states based on their optical field-strength probability distributions is presented. The quantum generalized polarization is understood as a significant confinement of the probability distribution along certain regions of a multidimensional optical field-strength space. The analysis is addressed to quantum states generated in multimode linear and nonlinear waveguiding (integrated) photonic devices, such as multimode waveguiding directional couplers and waveguiding parametric amplifiers, whose modes fulfill a spatial modal orthogonality. In particular, the generalized polarization degree of coherent, squeezed and Schrödinger’s cat states is analyzed.     

Multimode Coherent States and HeNe Laser Light

Abstract

Among the quantum optical states of a tremolant optical cavity are multimode coherent states. Such states are also possible in open cavities where the cavity stabilization time is greater than the multimode beat time. In open cavity resonator lasers they reduce the power limiting effects of spectral hole burning and therefore tend to grow at the expense of single mode coherent states.     

Quantum teleportation with a complete Bell state measurement

By using the quantum teleportation protocol, Alice can send an unknown quantum state (e.g. the polarization of a single photon) to Bob without ever knowing about it. This paper discusses a quantum teleportation experiment in which nonlinear interactions are used for the Bell state measurement. Since the Bell state measurement is based on nonlinear interactions, all four Bell states can be distinguished. Therefore, teleportation of a polarization state can occur with certainty, in principle. Details of the theory and the experimental set-up are discussed.     

Vortex optical Magnus effect in multimode fibers

A theoretical and experimental analysis is made of the optical Magnus effect in multimode optical fibers excited by a laser beam whose wavefront has a pure screw dislocation and carries the topological charge ±l, where l is the azimuthal quantum number. It is found that the angular rotation of the plane of propagation of a local wave depends on the magnitude and sign of the topological charge and changes qualitatively when the circulation of the polarization is reversed. The phase mechanism is attributed to spin-orbit interaction in the photon ensemble. It is demonstrated experimentally that the optical Magnus effect in a few-mode fiber for the CP₁₁ mode at the beat length is observed as a rotation of the axis of the pure edge dislocation field through an angle proportional to the beat length. Pis’ma Zh. Tekh. Fiz. 23, 76–81 (August 26, 1997)     

Information Transfer with Two-state Two-particle Quantum Systems

Abstract

Any future quantum information machine will contain unitary operators and entangled particle states. The Hilbert space describing the action of the quantum information machine separates into a bosonic and a fermionic sector. Because the bosonic sector is of higher dimension, it is always possible to encode more information into a multiboson state than into a multifermion state, given the same complexity, that is unitary representation, of the quantum information machine. This is explicitly studied for the case of two particles defined in two modes. There the beam splitter is a generic representation of any U(2) matrix, and it has recently been shown that one can realize any N-dimensional unitary operator by successive application of such two-dimensional operators. The two-boson two-mode Hilbert space is of dimension three, and thus one can encode log₂3 = 1·57 bits of information into such an entangled state. Finally, some explicit schemes for creating and detecting the three possible, two-photon, two-mode states spanning the bosonic Bell basis are given.     

Simulations of continuum coherent states and its use in quantum cryptographic systems

Abstract

The continuum states formalism is suitable for field quantization in optical fibre; however, they are harder to use than discrete states. On the other hand, a Hermitian phase operator can be defined only in a finite dimensional space. We approximated a coherent continuum state by a finite tensor product of coherent states, each one defined in a finite dimensional space. Using this, in the correct limit, we were able to obtain some statistical properties of the photon number and phase of the continuum coherent states from the probability density functions of the individual, finite dimensional, coherent states. Then, we performed a simulation of the BB84 protocol, using the continuum coherent states, in a fibre interferometer commonly used in quantum cryptography. We observed the fluctuations of the mean photon number in the pulses that arrive at Bob, which occurs in the practical system, introduced by the statistical property of the simulation.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

Effective preparation of the N-dimension spin Greenberger–Horne–Zeilinger state with quantum dots embedded in microcavities

We propose a scheme for preparation of the N-dimension spin Greenberger–Horne–Zeilinger state by exploiting quantum dots (QDs) embedded in microcavities. Numerically analysed results show that with the spin-selective photon reflection from the cavity, we can complete the scheme assisted by one polarized photon with high fidelity and 100% successful probability in principle. Furthermore, the set-up is just composed of simple linear optical elements, delay lines and conventional photon detectors, which are feasible with existing experimental technology. Moreover, QDs have numerous admirable features in weak-coupling regime, which are practicable in realistic cavity quantum electrodynamics system shown by previous numerical simulations and experiments. Therefore, our scheme might be realized in near future.     

PHOTONIC MATERIALS AND DEVICES Progress in relating rare-earth ion 4f and 5d energy levels to host bands in optical materials for hole burning,quantum information and phosphors

Rare-earth ions play an important role in modern technology as optically active elements in solid-state luminescent materials. In many of these materials, interactions between the electronic band states of the host crystal and the rare-earth ion's localized 4f ^N and 4f ^N?1 5d states influence the material's optical properties. The importance of these interactions is discussed for material applications in photon-gated hole burning, quantum information and phosphors. Material dependent trends in the relative binding energies of the 4f ^N states and the host bands have been observed and are summarized. An empirical model for the ion dependence of the 4f electron binding energies is formulated in terms of atomic number and compared with previous models. These models are extended to describe the 4f ^N?1 5d states with one additional parameter. Improved estimates for the free-ion ionization potentials used in the model are also presented and discussed.     

Expanded quantum cryptographic entangling probe

A generalized quantum circuit and design are given for an optimal entangling probe to be used in attacking the BB84 protocol of quantum key distribution and yielding maximum information to the probe. Probe photon polarization states become optimally entangled with the BB84 signal states on their way between the legitimate transmitter and receiver. The present design generalizes an earlier one by Brandt [J. Mod. Optics 52 2177 (2005)] to include a complete range of error rates that can be induced by the probe.     

Temperature dependence of the quantum efficiency of 4H-SiC-based Schottky photodiodes

Using metal-semiconductor structures based on a pure epitaxial layer of n-4H-SiC (N _d? N _a=4×10¹⁵ cm^?3), UV photodetectors were created with a maximum photosensitivity at 4.9 eV and a quantum efficiency up to 0.3 el/ph. The photosensitivity spectrum of the base structure is close to the spectrum of bactericidal action of the UV radiation. For photon energies in the 3.4–4.7 eV range, the quantum efficiency of the photoelectric conversion exhibits rapid growth with the temperature above 300 K, which is explained by the participation of photons in indirect interband transitions. This growth is not manifested when the photon energy is close to the threshold energy of direct optical transitions in the nondirect-bandgap semiconductor, which allows the threshold energy to be evaluated (～4.9 eV).     

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics I. Theory

Abstract

The quasi mode theory of macroscopic quantization in quantum optics and cavity QED developed by Dalton, Barnett and Knight is generalized. This generalization allows for cases in which two or more quasi permittivities, along with their associated mode functions, are needed to describe the classical optics device. It brings problems such as reflection and refraction at a dielectric boundary, the linear coupler, and the coupling of two optical cavities within the scope of the theory. For the most part, the results that are obtained here are simple generalizations of those obtained in previous work. However the coupling constants, which are of great importance in applications of the theory, are shown to contain significant additional terms which cannot be ‘guessed’ from the simpler forms. The expressions for the coupling constants suggest that the critical factor in determining the strength of coupling between a pair of quasi modes is their degree of spatial overlap. In an accompanying paper a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary is given as an illustration of the generalized theory. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes.     

Higher-generation Schrödinger cat states in cavity QED

Abstract

Higher-generation Schrödinger cat states of the quantized electromagnetic field can be produced in a high-Q cavity, starting from a coherent state, through the passage of prepared Rydberg atoms interacting dispersively across it. These states are natural generalizations of the even and odd coherent states, the N ^th-generations corresponding to specific superpositions of 2 ^N states on a circle in phase space with well defined parity, and present very peculiar properties. Their photon statistics interchange between super- and sub-Poissonian behaviours and the nature of the photon bunching oscillates as the field intensity in the cavity is varied. For higher-generation even states, the minimum value of the Mandel factor almost reaches ?1.0 and the state represents the Fock state |2 ^N ). Squeezing properties and the Wigner function of these higher-generation Schrödinger cat states are also considered.     

Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering

Abstract

A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.     

Nonlinear quantum optical computing via measurement

Abstract

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel (2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM (2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.     

Two mode theory of Bose–Einstein condensates: interferometry and the Josephson model

This topical review provides an overview of the key theoretical features of Bose–Einstein condensates (BECs) in cold atomic gases at near zero temperature in the situation where all the bosons occupy at most two single particle states or modes. This situation applies to single-component BECs in double well trap potentials and to two-component BEC in single well trap potentials, such as occur when BEC are used in interferometry experiments. The Hamiltonian is introduced in terms of field operators and mode expansions are restricted to a total of two modes. Spin operators and their eigenstates are introduced as the fundamental basis states for describing the two-mode N boson quantum system. The spin states have a macroscopic angular momentum quantum number of N/2 and the magnetic quantum number k specifies the relative number of bosons in the two modes. The treatment presented involves an extensive use of angular momentum theory, including unitary rotation operators. Important states of the two-mode system such as binomial or coherent states, relative phase eigenstates are discussed. Boson position measurements are specified via quantum correlation functions, and the use of these functions in describing coherence properties, interference patterns and fragmentation effects in BECs is presented. The Bloch vector is defined and related to the quantum correlation functions, with quantum fluctuations of the Bloch vector being treated in terms of the covariance matrix. Applications to important two-mode states are made. Spin squeezing is discussed. Based on applying variational principles, the general dynamical behaviour of the two-mode BEC is determined via generalised Gross–Pitaevskii equations for the modes and matrix mechanics equations for the probability amplitudes of the relative number basis states, the mode and amplitude equations being coupled and self-consistent. The single mode equations are also presented. The Hamiltonian is written in terms of the spin operators and the Josephson Hamiltonian obtained as a simplification in which the dynamical behaviour of the mode functions is ignored – for the one-component case the mode functions are also required to be localised and separate. Coefficients in the Josephson Hamiltonian describe tunneling/intercomponent coupling, asymmetry and collisions and these are defined via integrals involving the mode functions. The Josephson model involves using the Josephson Hamiltonian to give simple predictions of the energy states and dynamical behaviour of the two-mode system, dynamical effects on the mode functions being ignored. The three regimes – Rabi, Josephson and Fock are described, and the energy states obtained for the Fock and Rabi regimes. Dynamical behaviour treatments based on the Josephson model are outlined. In the situation where all bosons are in the same single particle state, semi-classical Bloch equations are derived and their solutions given in terms of elliptic functions. The quantum regime is treated using matrix mechanics equations for the probability amplitudes. Two representative applications of the Josephson model dynamics are treated, with graphs showing the results of numerical work being displayed. The first is in describing Heisenberg limited BEC interferometry for a single-component BEC in a double well, the treatment showing collapses and revivals in the probability distribution for the relative phase. The second treats Ramsey interferometry for a two-component BEC in a single well, the study revealing that oscillations of the Bloch vector collapse and revive, with the Bloch vector's departure from the Bloch sphere during the collapse period revealing that the BEC has fragmented. In both cases collisions cause the dephasing effects that result in the collapse, revival phenomena. The review ends with a brief outline of phase space and other approaches that extend the treatment beyond the two-mode theory, enabling decoherence effects associated with bosons in non-condensate modes to be studied. A summary of the review contents is included. Detailed mathematical derivations are included in several appendices, available as online supplementary material.     

Detailed Measurements of Nuclear Spin Polarizations in a Single InAlAs Quantum Dot Through Overhauser Shift of Photoluminescence

We investigated optical pumping of nuclear spin polarizations in a single self-assembled In_0.75Al_0.25As/Al_0.3Ga_0.7As quantum dot. The nuclear spin polarization exhibits the abrupt jump and hysteresis in the excitation power dependence at a particular excitation polarization. Measurement of circular polarization rate of the photoluminescence reveals that the abrupt change of the nuclear spin polarization is created mainly by the spin flip-flop process between nuclei and an electron of a positive charged exciton in this single quantum dot. Model calculation explains well the experimentally observed bistable behavior in InAlAs quantum dot. By using this abrupt change, the sign and magnitude of electron and hole g-factors in z-direction are verified.      

Non-classical Properties of Even and Odd Coherent States

Abstract

We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a ². We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.