arXiv subjects
Publications and source records attributed to M. V. Fedorov.
We suggest and describe the protocol of measurements providing completely probabilistic representation of all parameters of biphoton polarization qutrits, i.e providing explicit expressions for all parameters of qutrits via the probabilities of getting those or other results in measurements.
As known, the degree of entanglement of biphoton states with respect to the transverse components of photon wave vectors (momenta) or coordinates can be characterized either by the parameter K associated with the Schmidt decompositions, or by the parameter R, defined as the ratio of the widths of the unconditional and conditional single-particle distributions of biphoton states. As entanglement is a fundamental characteristics of a state, it must be independent of a choice of its different representations, i.e. its entanglement parameters must be identical in the coordinate and momentum representations. Likewise, entanglement itself and its characterization parameters must remain constant along the photon propagation length. It's known, however, that only the parameter K obeys these requirements, whereas the parameter R in the coordinate representation deviates from K beyond the near zone and, thus, becomes inapplicable as a measure of the degree of entablement. But, as shown below, there is a way of saving the parameter R by means of modifying its definition in such a way that the modified parameter R turns out to be as good as the parameter K both in the momentum and coordinate representations, as well as in the near and far zones and everywhere between them. We will discuss also possible ways of measuring this newly defined parameter R experimentally.
The concept of the Lorentz-invariant mass of a group of particles is shown to be applicable to biphoton states formed in the process of spontaneous parametric down conversion. The conditions are found when the Lorentz-invariant mass is related directly with (proportional to) the Schmidt parameter $K\gg 1$ determining a high degree of entanglement of a biphoton state with respect to transverse wave vectors of emitted photons.
Density matrices of pure multiphoton Fock polarization states and of arising from them reduced density matrices of mixed states are expressed in similar ways in terms of matrices of correlators defined as averaged products of equal numbers of creation and annihilation operators. Degree of entanglement of considered states is evaluated for various combinations of parameters of states and character of their reduction.
By using the formalism of photon creation operators, we present the simplest description of the effect of quantum teleportation and describe its closest classical analog.
We consider regimes of Spontaneous Parametric Down-Conversion both noncollinear and nondegenerate in frequencies. Parameters characterizing degrees of noncollinearity and of nondgeneracy are defined, and they are shown to be not independent of each other. At a given degree of nondegeneracy the emitted photons are shown to propagate along two different cones opening angles of which are determined by the degree of nondegeneracy. Based on this, the degree of nondegeneracy can be controlled by means of the angular selection of photons, e.g., with the help of appropriately installed slits. For such selected photons their wave functions are found depending on two frequency or on two temporal variables. Interference effects arising in such states are tested by analyzes of the Hong-Ou-Mandel type scheme with the varying delay time in one of two channels and with photons from two channels sent to the beamsplitter. The temporal pictures arising after the beamsplitter are found to demonstrate extremely strong interference exhibiting itself in formation of finite-size temporal combs filled with quantum beats. Parameters of combs depend on the degree of nondegeneracy, and the physical reasons of this dependence are clarified.
The well-known Hong-Ou-Mandel effect is revisited. Two physical reasons are discussed for the effect to be less pronounced or even to disappear: differing polarizations of photons coming to the beamsplitter and delay time of photons in one of two channels. For the latter we use the concepts of biphoton frequency and temporal wave functions depending, correspondingly, on two frequency continuous variables of photons and on two time variables $t_1$ and $t_2$ interpreted as the arrival times of photons to the beamsplitter. Explicit expressions are found for the probability densities and total probabilities for photon pairs to be split between two channels after the beamsplitter and to be unsplit, when two photons appear together in one of two channels.
Single-particle and coincidence distributions of photons are analyzed for the noncollinear frequency-degenerate type-I regime of Spontaneous Parametric Down-Conversion. Noncollinearity itself is shown to provide a new mechanism of strong broadening of the single-particle distributions in Cartesian components of the photon's transverse wave vectors. Related to this, the degree of entanglement appears to be very high and, in fact, this is the same enormous resource of azimuthal entanglement which was found to occur in the formalism of spherical angles used for characterization of photon wave vectors (Phys. Rev. A, {\bf 93}, 033830, 2016). In Cartesian variables this phenomenon manifests itself as a strong broadening and a very unusual and peculiar shape of the arising single-particle distribution curves. In theory, the key reason for these effects is the reduction of the total wave function of two photons over one of two orthogonal degrees of freedom. In the suggested and discussed experimental scheme this means that all photons of the emission cone have to be taken into account rather than only photons propagating in one given plane which is a common practice in many experiments.
We analyze the origins of the luminescence in germania-silica fibers with high germanium concentration (about 30 mol. % GeO2) in the region 1-2 μm with a laser pump at the wavelength 532 nm. We show that such fibers demonstrate the high level of luminescence which unlikely allows the observation of photon triplets, generated in a third-order spontaneous parametric down-conversion process in such fibers. The only efficient approach to the luminescence reduction is the hydrogen saturation of fiber samples, however, even in this case the level of residual luminescence is still too high for three-photon registration.
The total mass of noncollinear photons forming diverging light pulses is defined and found explicitly. Both classical and quantum derivations are presented. The quantum derivation is based on the use of multimode coherent states, and links between parameters of these states and those of the classical field strength are established.
Purely azimuthal entanglement is analyzed for noncollinear frequency-degenerate biphoton states. The degree of azimuthal entanglement is found to be very high, with the Schmidt parameter $K$ on the order of the ratio of the pump waist to its wavelength. A scheme is suggested for partial realization of this high entanglement resource in the form of a multichannel Schmidt-type decomposition.
We investigate the third order spontaneous parametric down-conversion process in a nonlinear media with inversion centers. Specifically, we analyze in details the three-photon differential count rate in unit frequency and angular regions, total count rate and measurement time for rutile and calcite crystals which have comparatively large cubic susceptibilities. Special attention is given to consideration of limited frequency and angular detection ranges in order to calculate experimentally available detection rate values.
We consider polarization states of three photons, each in the same given spectral-angular mode. A general form of such states is a superposition of four basic three-photon polarization modes, to be referred to as three-photon polarization ququarts. All such states can be considered as consisting of one- and two-photon parts, which can be entangled with each other. The degrees of entanglement and polarization as well as the Schmidt decomposition and Stokes vectors of three-photon polarization ququarts are found and discussed.
We analyze features of mixed biphoton polarization states which arise from pure states of polarization-frequency biphoton ququarts after averaging over frequencies of photons. For mixed states we find their concurrence C, Schmidt parameter K and degree of polarization P, as well as the von Neumann mutual information I. In some simple cases we find also the relative entropy S_{rel} and the degree of classical correlations C_{cl}. We show that in mixed states the Schmidt parameter does not characterize anymore the degree of entanglement, as it does in pure states. Nevertheless, the Schmidt parameter remains useful even in the case of mixed states because it remains directly related to the degree of polarization. We compare results occurring in the cases of full pure polarization-frequency states of ququarts, mixed states (averaged over frequencies) and states with separated high- and low-frequency parts. Differences between these results can be seen in experiments with and without a dichroic beam-splitter, as well as with and without frequency filters in front of detector.
A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long.
We verified operational approach based on direct measurement of entanglement degree for bipartite systems. In particular spectral distributions of single counts and coincidence for pure biphoton states generated by train of short pump pulses have been measured and entanglement quantifier calculated. The approach gives upper bound of entanglement stored in total biphoton states, which can reach extremely high value up to $10^{4}-10^{5}$.
Spectral and temporal coincidence and single-particle photon wave packets are described and their widths and durations are found. The degree of entanglement is characterized by the experimentally measurable parameter R defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration. This function is shown to have a minimum and even in the minimum, at rather natural conditions, the parameter R is found to be very high (R=73>>1). The Schmidt number K is found for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of R and K are found to be identical and numerical difference between them is shown to be not exceeding 20%. Two-time temporal wave function of a biphoton state is investigated in details, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter R is defined as the ratio of durations of the single-particle and coincidence signals, and the defined in such a way parameter R is shown to be very close to the Schmidt number K.
We show that the wave packet of a biphoton generated via spontaneous parametric down conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison of measurements performed in two different schemes: when the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected new results as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degree of entanglement. The results are predicted theoretically and confirmed experimentally.