Effects of Length and Diameter of Open-Ended Coaxial Sensor on its Reflection Coefficient

This paper presents a calibration technique for a coaxial sensor using a transmission signal approach. The sensor was fabricated from commercially available RG402/U and RG405/U semi-rigid coaxial cable. The length of the coaxial sensor was correlated with the attenuation and standing wave inside the coaxial line. The functions of multiple reflection amplitude and tolerance length with respect to the actual length of coaxial line were empirically formulated using regression analysis. The tolerances and the undesired standing wave which occurs along the coaxial line were analyzed in detai

A binary mixture of spinor atomic Bose-Einstein condensates

We study the ground state and classify its phase diagram for a mixture of two spin-1 condensates in the absence of external magnetic (B-) field according to atomic parameters for intra- and inter-species spin exchange coupling and singlet pairing interaction. Ignoring the inter-species singlet pairing interaction, the ground state phases are found analytically. Numerical approach of simulated annealing is adopted when the singlet pairing interaction is present. Our results on the phase diagram and the boundaries between phases allow for easy identifications of quantum phase transitions, that can be induced through the tuning of optical traps and atom numbers. They provide the first insight and guidance for several ongoing experiments on mixtures of spinor condensates.Comment: 5 pages, 4 figure

Quantum entangled ground states of two spinor Bose-Einstein condensates

We revisit in detail the non-mean-field ground-state phase diagram for a binary mixture of spin-1 Bose-Einstein condensates including quantum fluctuations. The non-commuting terms in the spin-dependent Hamiltonian under single spatial mode approximation make it difficult to obtain exact eigenstates. Utilizing the spin z-component conservation and the total spin angular momentum conservation, we numerically derive the information of the building blocks and evaluate von Neumann entropy to quantify the ground states. The mean-field phase boundaries are found to remain largely intact, yet the ground states show fragmented and entangled behaviors within large parameter spaces of interspecies spin-exchange and singlet-pairing interactions.Comment: 7 pages, 5 figure

Quantum spin mixing in a binary mixture of spin-1 atomic condensates

We study quantum spin mixing in a binary mixture of spin-1 condensates including coherent interspecies mixing process, using the familiar spinor condensates of $^{87}$Rb and $^{23}$Na atoms in the ground lower hyperfine F=1 manifolds as prototype examples. Within the single spatial mode approximation for each of the two spinor condensates, the mixing dynamics reduce to that of three coupled nonlinear pendulums with clear physical interpretations. Using suitably prepared initial states, it is possible to determine the interspecies singlet-pairing as well as spin-exchange interactions from the subsequent mixing dynamics.Comment: 6 pages, 3 figure

Quantum states of a binary mixture of spinor Bose-Einstein condensates

We study the structure of quantum states for a binary mixture of spin-1 atomic Bose-Einstein condensates. In contrast to collision between identical bosons, the s-wave scattering channel between inter-species does not conform to a fixed symmetry. The spin-dependent Hamiltonian thus contains non-commuting terms, making the exact eigenstates more challenging to obtain because they now depend more generally on both the intra- and inter-species interactions. We discuss two limiting cases, where the spin-dependent Hamiltonian reduces respectively to sums of commuting operators. All eigenstates can then be directly constructed, and they are independent of the detailed interaction parameters.Comment: 5 pages, no figure