Towards a compact, optically interrogated, cold-atom microwave clock

A compact platform for cold atoms opens a range of exciting possibilities for portable, robust and accessible quantum sensors. In this work, we report on the development of a cold-atom microwave clock in a small package. Our work utilises the grating magneto-optical trap and high-contrast coherent population trapping in the lin$\perp $lin polarisation scheme. We optically probe the atomic ground-state splitting of cold 87Rb atoms using a Ramsey-like sequence whilst the atoms are in free-fall. We have measured a short-term fractional frequency stability of $5{\times}{10}^{-11}/\sqrt{\tau }$ with a projected quantum projection noise limit at the ${10}^{-13}/\sqrt{\tau }$ level.

The Economic Impact of State Splitting in Brazil

The Brazilian state of Tocantins was splinted from the state of Goiás in 1988. This was the most recent first-tier subnational border reform in Brazil and involved an area that corresponds to 7.6% of the whole national territory. Using the synthetic control method, this paper estimates that the split increased the per capita GDP of the affected region by an average of 8.26%, and the positive effect persisted over the years. Additionally, we show that the Tocantins benefited more from the border reform than Goiás, and the increase of fiscal capacity of affected subnational governments may partially explain the positive effects of splitting.

On the Entanglement Cost of One-Shot Compression

We revisit the task of visible compression of an ensemble of quantum states with entanglement assistance in the one-shot setting. The protocols achieving the best compression use many more qubits of shared entanglement than the number of qubits in the states in the ensemble. Other compression protocols, with potentially larger communication cost, have entanglement cost bounded by the number of qubits in the given states. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is needed. Motivated by questions in communication complexity, we lift certain restrictions that are placed on compression protocols in tasks such as state-splitting and channel simulation. We show that an ensemble of the form designed by Jain, Radhakrishnan, and Sen (ICALP'03) saturates the known bounds on the sum of communication and entanglement costs, even with the relaxed compression protocols we study. The ensemble and the associated one-way communication protocol have several remarkable properties. The ensemble is incompressible by more than a constant number of qubits without shared entanglement, even when constant error is allowed. Moreover, in the presence of shared entanglement, the communication cost of compression can be arbitrarily smaller than the entanglement cost. The quantum information cost of the protocol can thus be arbitrarily smaller than the cost of compression without shared entanglement. The ensemble can also be used to show the impossibility of reducing, via compression, the shared entanglement used in two-party protocols for computing Boolean functions.

Влияние решеточного и спин-фононного вкладов на температурное поведение расщепления основного состояния Gd-=SUP=-3+-=/SUP=- в SrMoO-=SUB=-4-=/SUB=-

The temperature behavior of the EPR spectra of the Gd^3+ impurity center in single crystals of SrMoO_4 in the temperature range T = 99–375 K is studied. The analysis of the temperature dependences of the spin Hamiltonian b _2 ^0 ( T ) = b _2( F ) + b _2( L ) and P _2 ^0 ( T ) = P _2( F ) + P _2( L ) (for Gd^157) describing the EPR spectrum and contributing to the Gd^3+ ground state splitting Δ E is carried out. In terms of the Newman model, the values of b _2( L ) and P _2( L ) depending on the thermal expansion of the static lattice are estimated; the b _2( F ) and P _2( F ) spin-phonon contributions determined by the lattice ion oscillations are separated. The analysis of b _2 ^0 ( T ) and P _2 ^0 ( T ) is evidence of the positive contribution of the spin-phonon interaction; the model of the local oscillations of the impurity cluster with close frequencies ω describes well the temperature behavior of b _2( F ) and P _2( F ).