We describe a novel approach to directly measure the energy of the narrow, low-lying isomeric state in 229Th. Since nuclear transitions are far less sensitive to environmental conditions than atomic transitions, we argue that the 229Th optical nuclear transition may be driven inside a host crystal with a high transition Q. This technique might also allow for the construction of a solid-state optical frequency reference that surpasses the short-term stability of current optical clocks, as well as improved limits on the variability of fundamental constants. Based on analysis of the crystal lattice environment, we argue that a precision (short-term stability) of 3×10(-17)<Δf/f<1×10(-15) after 1 s of photon collection may be achieved with a systematic-limited accuracy (long-term stability) of Δf/f∼2×10(-16). Improvement by 10(2)-10(3) of the constraints on the variability of several important fundamental constants also appears possible.

We describe a new error reconciliation protocol Winnow based on the exchange of parity and Hamming's "syndrome" for N −bit subunits of a large data set. Winnow was developed in the context of quantum key distribution and offers significant advantages and net higher efficiency compared to other widely used protocols within the quantum cryptography community. A detailed mathematical analysis of Winnow is presented in the context of practical implementations of quantum key distribution; in particular, the information overhead required for secure implementation is one of the most important criteria in the evaluation of a particular error reconciliation protocol. The increase in efficiency for Winnow is due largely to the reduction in authenticated public communication required for its implementation.

Over a period of eight months, we have monitored transition frequencies between nearly degenerate, opposite-parity levels in two isotopes of atomic dysprosium (Dy). These transition frequencies are highly sensitive to temporal variation of the fine-structure constant (α) due to relativistic corrections of large and opposite sign for the opposite-parity levels. In this unique system, in contrast to atomic-clock comparisons, the difference of the electronic energies of the opposite-parity levels can be monitored directly utilizing a radio-frequency (rf) electric-dipole transition between them. Our measurements show that the frequency variation of the 3.1-MHz transition in 163 Dy and the 235-MHz transition in 162 Dy are 9.0±6.7 Hz/yr and -0.6±6.5 Hz/yr, respectively. These results provide a value for the rate of fractional variation of α of (−2.7 ± 2.6) × 10 −15 yr −1 (1 σ) without any assumptions on the constancy of other fundamental constants, indicating absence of significant variation at the present level of sensitivity.

We report on the spectroscopy of radio-frequency transitions between nearly degenerate, opposite-parity excited states in atomic dysprosium (Dy). Theoretical calculations predict that these states are very sensitive to variation of the fine-structure constant α owing to large relativistic corrections of opposite sign for the opposite-parity levels. The near degeneracy reduces the relative precision necessary to place constraints on variation of α, competitive with results obtained from the best atomic clocks in the world. Additionally, the existence of several abundant isotopes of Dy allows isotopic comparisons that suppress common-mode systematic errors. The frequencies of the 754-MHz transition in 164Dy and 235-MHz transition in 162Dy are measured over the span of two years. The linear variation of α is α·/α=(-5.8±6.9([1σ]))×10(-17)  yr(-1), consistent with zero. The same data are used to constrain the dimensionless parameter kα characterizing a possible coupling of α to a changing gravitational potential. We find that kα=(-5.5±5.2([1σ]))×10(-7), essentially consistent with zero and the best constraint to date.

The frequency spectrum of the finite temperature correction to the Casimir force can be determined by use of the Lifshitz formalism for metallic plates of finite conductivity. We show that the correction for the TE electromagnetic modes is dominated by frequencies so low that the plates cannot be modeled as ideal dielectrics. We also address issues relating to the behavior of electromagnetic fields at the surfaces and within metallic conductors, and calculate the surface modes using appropriate low-frequency metallic boundary conditions. Our result brings the thermal correction into agreement with experimental results that were previously obtained. We suggest a series of measurements that will test the veracity of our analysis.