Grassmann phase space methods for fermions. II. Field theory

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential

Improving the quantity, quality and transparency of data used to derive radionuclide transfer parameters for animal products. 2. Cow milk

Under the International Atomic Energy Agency (IAEA) MODARIA (Modelling and Data for Radiological Impact Assessments) Programme, there has been an initiative to improve the derivation, provenance and transparency of transfer parameter values for radionuclides from feed to animal products that are for human consumption. A description of the revised MODARIA 2016 cow milk dataset is described in this paper. As previously reported for the MODARIA goat milk dataset, quality control has led to the discounting of some references used in IAEA's Technical Report Series (TRS) report 472 (IAEA, 2010). The number of Concentration Ratio (CR) values has been considerably increased by (i) the inclusion of more literature from agricultural studies which particularly enhanced the stable isotope data of both CR and Fm and (ii) by estimating dry matter intake from assumed liveweight. In TRS 472, the data for cow milk were 714 transfer coefficient (Fm) values and 254 CR values describing 31 elements and 26 elements respectively. In the MODARIA 2016 cow milk dataset, Fm and CR values are now reported for 43 elements based upon 825 data values for Fm and 824 for CR. The MODARIA 2016 cow milk dataset Fm values are within an order of magnitude of those reported in TRS 472. Slightly bigger changes are seen in the CR values, but the increase in size of the dataset creates greater confidence in them. Data gaps that still remain are identified for elements with isotopes relevant to radiation protection

Synchronized pulse control of decoherence

We present a new strategy for multipulse control over decoherence. When a two-level system interacts with a reservoir characterized by a specific frequency, we find that the decoherence is effectively suppressed by synchronizing the pulse-train application with the dynamical motion of the reservoir.Comment: 14 pages, 8 figure

Improving the quantity, quality and transparency of data used to derive radionuclide transfer parameters for animal products. 1. Goat milk

Under the MODARIA (Modelling and Data for Radiological Impact Assessments Programme of the International Atomic Energy Agency), there has been an initiative to improve the derivation, provenance and transparency of transfer parameter values for radionuclides. The approach taken for animal products is outlined here and the first revised table for goat milk is provided. Data from some references used in TRS 472 were removed and reasons given for removal. Particular efforts were made to improve the number of CR (concentration ratio) values which have some advantages over transfer coefficients. There is little difference in most of the new CR and Fm (transfer coefficient) values for goat milk compared with those in TRS 472. In TRS 472, 21 CR values were reported for goat milk. In the 2015 dataset for goat milk CR values for a further 14 elements are now included. The CR and Fm values for only one element (Co) were removed

Grassmann Variables and the Jaynes-Cummings Model

This paper shows that phase space methods using a positive P type distribution function involving both c-number variables (for the cavity mode) and Grassmann variables (for the two level atom) can be used to treat the Jaynes-Cummings model. Although it is a Grassmann function, the distribution function is equivalent to six c-number functions of the two bosonic variables. Experimental quantities are given as bosonic phase space integrals involving the six functions. A Fokker-Planck equation involving both left and right Grassmann differentiation can be obtained for the distribution function, and is equivalent to six coupled equations for the six c-number functions. The approach used involves choosing the canonical form of the (non-unique) positive P distribution function, where the correspondence rules for bosonic operators are non-standard and hence the Fokker-Planck equation is also unusual. Initial conditions, such as for initially uncorrelated states, are used to determine the initial distribution function. Transformations to new bosonic variables rotating at the cavity frequency enables the six coupled equations for the new c-number functions (also equivalent to the canonical Grassmann distribution function) to be solved analytically, based on an ansatz from a 1980 paper by Stenholm. It is then shown that the distribution function is the same as that determined from the well-known solution based on coupled equations for state vector amplitudes of atomic and n-photon product states. The treatment of the simple two fermion mode Jaynes-Cummings model is a useful test case for the future development of phase space Grassmann distribution functional methods for multi-mode fermionic applications in quantum-atom optics.Comment: 57 pages, 0 figures. Version

Non-Markovian Decay of a Three Level Cascade Atom in a Structured Reservoir

We present a formalism that enables the study of the non-Markovian dynamics of a three-level ladder system in a single structured reservoir. The three-level system is strongly coupled to a bath of reservoir modes and two quantum excitations of the reservoir are expected. We show that the dynamics only depends on reservoir structure functions, which are products of the mode density with the coupling constant squared. This result may enable pseudomode theory to treat multiple excitations of a structured reservoir. The treatment uses Laplace transforms and an elimination of variables to obtain a formal solution. This can be evaluated numerically (with the help of a numerical inverse Laplace transform) and an example is given. We also compare this result with the case where the two transitions are coupled to two separate structured reservoirs (where the example case is also analytically solvable)

Bounds and optimisation of orbital angular momentum bandwidths within parametric down-conversion systems

The measurement of high-dimensional entangled states of orbital angular momentum prepared by spontaneous parametric down-conversion can be considered in two separate stages: a generation stage and a detection stage. Given a certain number of generated modes, the number of measured modes is determined by the measurement apparatus. We derive a simple relationship between the generation and detection parameters and the number of measured entangled modes.Comment: 6 pages, 4 figure