P. A. Volkov

Anisotropically and high entanglement of biphoton states generated in spontaneous parametric down-conversion

We show both theoretically and experimentally that biphoton wave packets generated via spontaneous parametric down-conversion can be strongly anisotropic and highly entangled. The conditions under which these effects exist are found and discussed.

Gaussian modelling and Schmidt modes of SPDC biphoton states

A double-Gaussian model and the Schmidt modes are found for the biphoton wavefunction characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses: short, long and intermediately long.

Entanglement of biphoton states: qutrits and ququarts

We investigate, in a general form, entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of, correspondingly, degenerate and non-degenerate spontaneous parametric down-conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and polarization entanglement are fully taken into account. In the case of qutrits, the most general three-parametric families of maximally entangled and non- entangled states are found, and anticorrelation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality d = 4, which differentiates them significantly from the often used two-qubit model (d = 2). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.

Qutrits and ququarts in spontaneous parametric down-conversion, correlations and entanglement

We investigate features of biphoton qutrits and ququarts with the symmetry of biphoton wavefunctions fully taken into account. Entanglement quantifiers of such states are found as functions of qutrit and ququart parameters. For biphoton qutrits, a general relation between degrees of entanglement and polarization is established. In the case of biphoton ququarts, photon frequencies are considered as variables independent of polarization variables, with both polarization and frequency degrees of freedom equally contributing to the total ququart entanglement. Averaging over one of these two degrees of freedom is shown to reduce pure ququart states to mixed two-qubit states. The degree of polarization and degrees of correlations in mixed polarization states are investigated.

Peak doubling in spontaneous parametric down-conversion coincidence spectra with a short-pulse pump*

In this paper, we describe the double-peak structure of the coincidence spectrum of biphoton states in the process of spontaneous parametric down-conversion with a pump having the form of short pulses. The effect is shown to arise from the obligatory symmetry of biphoton wave functions that describe the states of two bosons obeying the Bose–Einstein statistics. Parameters of the peaks are found and the conditions under which the effect can be experimentally observed are determined

Anisotropically high entanglement of biphotons

Biphoton states arising in the process of spontaneous parametric down-conversion (SPDC) are entangled with respect to continuous variables, momentum or coordinates. We discuss some novel and unexpected features of biphoton wave packets.