"Doubly-magic" conditions in magic-wavelength trapping of ultracold alkalis

In experiments with trapped atoms, atomic energy levels are shifted by the trapping optical and magnetic fields. Regardless of this strong perturbation, precision spectroscopy may be still carried out using specially crafted, "magic" trapping fields. Finding these conditions for particularly valuable microwave clock transitions in alkalis has so far remained an open challenge. Here I demonstrate that the microwave clock transitions for alkalis may be indeed made impervious to both trapping laser intensity and fluctuations of magnetic fields. I consider driving multiphoton transitions between the clock levels and show that these "doubly-magic" conditions are realized at special values of trapping laser wavelengths and fixed values of relatively weak magnetic fields. This finding has implications for precision measurements and quantum information processing with qubits stored in hyperfine manifolds.Comment: 4 pages, 3 figs, 1 tabl

Detecting dark matter waves with precision measurement tools

Virialized Ultra-Light Fields (VULFs) are viable cold dark matter candidates and include scalar and pseudo-scalar bosonic fields, such as axions and dilatons. Direct searches for VULFs rely on low-energy precision measurement tools. While the previous proposals have focused on detecting coherent oscillations of the VULF signals at the VULF Compton frequencies at individual devices, here I consider a network of such devices. VULFs are essentially dark matter {\em waves} and as such they carry both temporal and spatial phase information. Thereby, the discovery reach can be improved by using networks of precision measurement tools. To formalize this idea, I derive a spatio-temporal two-point correlation function for the ultralight dark matter fields in the framework of the standard halo model. Due to VULFs being Gaussian random fields, the derived two-point correlation function fully determines $N$-point correlation functions. For a network of $N_{d}$ devices within the coherence length of the field, the sensitivity compared to a single device can be improved by a factor of $\sqrt{N_{d}}$. Further, I derive a VULF dark matter signal profile for an individual device. The resulting line shape is strongly asymmetric due to the parabolic dispersion relation for massive non-relativistic bosons. I discuss the aliasing effect that extends the discovery reach to VULF frequencies higher than the experimental sampling rate. I present sensitivity estimates and develop a stochastic field SNR statistic. Finally, I consider an application of the developed formalism to atomic clocks and their networks.Comment: 16 pages, 5 figs. Revised and expanded versio

Rydberg blockade with multivalent atoms: effect of Rydberg series perturbation on van der Waals interactions

We investigate the effect of series perturbation on the second order dipole-dipole interactions between strontium atoms in $5sns({^1}S_0)$ and $5snp({^1}P_1)$ Rydberg states as a means of engineering long-range interactions between atoms in a way that gives an exceptional level of control over the strength and the sign of the interaction by changing $n$. We utilize experimentally available data to estimate the importance of perturber states at low $n$, and find that van der Waals interaction between two strontium atoms in the $5snp({^1}P_1)$ states shows strong peaks outside the usual hydrogenic $n^{11}$ scaling. We identify this to be the result of the perturbation of $5snd({^1}D_2)$ intermediate states by the $4d^2({^1}D_2)$ and $4dn's({^1}D_2)$ states in the $n<20$ range. This demonstrates that divalent atoms in general present a unique advantage for creating substantially stronger or weaker interaction strengths than those can be achieved using alkali metal atoms due to their highly perturbed spectra that can persist up to high-$n$

Theory of "magic" optical traps for Zeeman-insensitive clock transitions in alkalis

Precision measurements and quantum information processing with cold atoms may benefit from trapping atoms with specially engineered, "magic" optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of a recently observed magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying "magic" bias B-field along circularly polarized trapping laser field. We map out these B-fields as a function of trapping laser wavelength for all commonly-used alkalis.Comment: 4 pages, 2 fig, 1 table (v3: added discussion of the correct way of computing polarizabilities

Fourth-order perturbative extension of the singles-doubles coupled-cluster method

Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wavefunction. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulae are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e. contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed.Comment: 12 pages, 6 figure